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LichengJiao Lipo Wang Guangming Shi ShuangWang Xinbo Gao Jing Liu (Eds.) Advances in Natural Computation and Data Mining
The 2nd International Conference on Natural Computation and The 3rd International Conference on Fuzzy Systems and Knowledge Discovery ICNC-FSKD 2006 Xi'an,China,September 2006 Proceedings
^ XIDIAN UNIVERSITY PRESS ~ http:/ywww.xduph.com Licheng Jiao Lipo Wang Guangming Shi Shuang Wang Xinbo Gao Jing Liu (Eds.)
Advances in Natural Computation and Data Mining
The 2nd International Conference on Natural Computation and The 3rd International Conference on Fuzzy Systems and Knowledge Discovery ICNC-FSKD 2006 Xi'an, China, September 2006 Proceedings
XIDIAN UNIVERSITY PRESS 2006 Advances in Natural Computation and Data Mining The 2nd International Conference on Natural Computation and The 3rd International Conference on Fuzzy Systems and Knowledge Discovery ICNC-FSKD 2006 September, 2006, Xi’an, China
IN i t Jf 1 -j isR=Advances in Natural Computation and Data Mining/ 2006.8 ISBN 7-5606-1735-2 I. g... n. &... III. (DfcWJW— £* — 3 S £ IV. TP3-53 + S J i£ M T O C I P &&&¥■ (2006) % 089923
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts is permitted only under Xidian University Press. © Xidian University Press 2006
Ife iS (029)88242885 88201467 AP 31 710071 http://www.xduph.com E-mail: [email protected] & m mmws fig & 2006 ^ 9 ^ ¥ ,1 fiS 2006 ^ 9 H i & W J 787 % * - 1092 S * 1/16 EPifc 29.875 ISBN 7 - 5606 - 1735 - 2 / TP • 0431 XDUP 202700 * * * $n£EP3SHHnTiS& * * * Preface
This book is the proceeding of the 2nd International Conference on Natural Computation (ICNC 2006), jointly held with the 3rd International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2006) from 24 to 28 September 2006 in Xi’an, Shaanxi, China. In its budding run, the joint ICNC-FSKD 2006 received 3189 submissions from 35 countries/regions. The ICNC-FSKD 2006 featured the most up-to-date research results in com putational algorithms inspired from nature, including biological, ecological, and physical systems. It is an exciting and emerging interdisciplinary area in which a wide range of techniques and methods are being studied for dealing with large, complex, and dynamic problems. The joint conferences also promoted cross fertilization over these exciting and yet closely-related areas, which had a sig nificant impact on the advancement of these important technologies. Specific areas included neural computation, quantum computation, evolutionary com putation, DNA computation, chemical computation, information processing in cells and tissues, molecular computation, computation with words, fuzzy com putation, granular computation, artificial life, swarm intelligence, ants colonies, artificial immune systems, etc., with innovative applications to knowledge dis covery, finance, operations research, and more. In addition to the large number of submitted papers, we were blessed with the presence of six renowned keynote speakers. On behalf of the Organizing Committee, we thank Xidian University for sponsorship, and the National Natural Science Foundation of China, the Inter national Neural Network Society, the Asia-Pacific Neural Network Assembly, the IEEE Circuits and Systems Society, the IEEE Computational Intelligence Soci ety, the IEEE Computational Intelligence Singapore Chapter, and the Chinese Association for Artificial Intelligence for technical co-sponsorship. We thank the members of the Organizing Committee, the Advisory Board, and the Program Committee for their hard work in the past 12 months. We wish to express our heartfelt appreciation to the keynote speakers, session chairs, reviewers, and stu dent helpers. Our special thanks go to the publish, Xidian University Press, for publishing the Advance in Natural Computation and Data Mining proceeding. Finally, we thank all the authors and participants for their great contributions that made this conference possible and all the hard work worthwhile.
September 2006 Licheng Jiao Lipo Wang Organization
ICNC-FSKD 2006 was organized by Xidian University and technically co-sponsored by the National Natural Science Foundation of China, the International Neural Network Society, the Asia-Pacific Neural Network Assembly, the IEEE Circuits and Systems Society, the IEEE Computational Intelligence Society, the IEEE Computational Intelligence Singapore Chapter, and the Chinese Association for Artificial Intelligence.
O rganizing Com m ittee
Honorary Conference Chairs: Shun-ichi Amari (RIKEN BSI, Japan) Xin Yao (University of Birmingham, UK) General Co-Chairs: Lipo Wang (Nanyang Technological University, Singapore) Licheng Jiao (Xidian University, China) Program Committee Chairs: ICNC 2006: Xinbo Gao (Xidian University, China) Feng Wu (Microsoft Research Asia, China) FSKD 2006: Guangming Shi (Xidian University, China) Xue Li (The University of Queensland, Australia) Local Arrangement Chairs: Yuanyuan Zuo (Xidian University, China) Xiaowei Shi (Xidian University, China) Proceedings Chair: Jing Liu (Xidian University, China) Publicity Chair: Yuping Wang (Xidian University, China) Sponsorship Chair: Yongchang Jiao (Xidian University, China) Secretaries: Bin Lu (Xidian University, China) Tiantian Su (Xidian University, China) Webmasters: Yinfeng Li (Xidian University, China) Maoguo Gong (Xidian University, China)
A dvisory Board
Zheng Bao Xidian University, China Zixing Cai Central South University, China Guoliang Chen University of Science and Technology of China, China Huowang Chen National University of Defense Technology, China David Corne The University of Exeter, UK Dipankar Dasgupta University of Memphis, USA Kalyanmoy Deb Indian Institute of Technology Kanpur, India Baoyan Duan Xidian University, China Kunihiko Fukushima Tokyo University of Technology, Japan Tom Gedeon The Australian National University, Australia Aike Guo Chinese Academy of Science, China Yao Hao Xidian University, China Zhenya He Southeastern University, China Fan Jin Southwest Jiaotong University, China Yaochu Jin Honda Research Institute Europe, Germany Janusz Kacprzyk Polish Academy of Sciences, Poland Lishan Kang China University Of Geosciences, China Nikola Kasabov Auckland University of Technology, New Zealand John A. Keane The University of Manchester, UK Soo-Young Lee KAIST, Korea Yanda Li Tsinghua University, China Zhiyong Liu National Natural Science Foundation of China China Erkki Oja Helsinki University of Technology, Finland Nikhil R. Pal Indian Statistical Institute, India Yunhe Pan Zhe Jiang University, China Jose Principe University of Florida, USA Witold Pedrycz University of Alberta, Canada Marc Schoenauer University of Paris Sud, France Zhongzhi Shi Chinese Academy of Science, China Harold Szu Office of Naval Research, USA Shiro Usui RIKEN BSI, Japan Shoujue Wang Chinese Academy of Science, China Xindong Wu University of Vermont, USA Lei Xu Chinese University of Hong Kong, China Bo Zhang Tsinghua University, China Nanning Zheng Xi’an Jiaotong University, China Yixin Zhong University of Posts & Telecommunications, China Syozo Yasui Kyushu Institute of Technology, Japan Jacek M. Zurada University of Louisville, USA
Program Com m ittee
IC N C 2006
Shigeo Abe Kobe University, Japan Davide Anguita University of Trento, Italy Abdesselam Bouzerdoum University of Wollongong, Australia
2 Laiwan Chan The Chinese University of Hong Kong, China Li Chen Northwest University, China Guanrong Chen City University of Hong Kong, China Shu-Heng Chen National Chengchi University, Taiwan, China Tianping Chen Fudan University, China YanQiu Chen Fudan University, China Vladimir Cherkassky University of Minnesota, USA Sung-Bae Cho Yonsei University, Korea Sungzoon Cho Seoul National University, Korea Tommy W. S. Chow City University of Hong Kong, China Vic Ciesielski RMIT, Australia Keshav Dahai University of Bradford, UK L.N. de Castro Catholic University of Santos, Brazil Emilio Del-Moral-Hernandez University of Sao Paulo, Brazil Andries Engelbrecht University of Pretoria, South Africa Tomoki Fukai Tamagawa University, Japan Lance Fung Murdoch University, Australia Takeshi Furuhashi Nagoya University, Japan Hiroshi Furutani University of Miyazaki, Japan John Q. Gan The University of Essex, UK Wen Gao The Chinese Academy of Science, China Peter Geczy AIST, Japan Zengguang Hou University of Saskatchewan, Canada Jiwu Huang Sun Yat-Sen University, China Masumi Ishikawa Kyushu Institute of Technology, Japan Yongchang Jiao Xidian University, China Robert John De Montfort University, UK Mohamed Kamel University of Waterloo, Canada Yoshiki Kashimori University of Electro-Communications, Japan Samuel Kaski Helsinki University of Technology, Finland Andy Keane University of Southampton, UK Graham Kendall The University of Nottingham, UK Jong-Hwan Kim KAIST, Korea JungWon Kim University College London, UK Natalio Krasnogor University of Nottingham, UK Vincent C.S. Lee Monash University, Australia Stan Z. Li Chinese Academy of Science, China Yangmin Li University of Macau, Macau Xiaofeng Liao Chongqing University, China Derong Liu University of Illinois at Chicago, USA Ding Liu Xi’an University of Technology, China Jing Liu Xidian University, China Ke Liu National Natural Science Foundation of China, China
3 Baoliang Lu Shanghai Jiao Tong University, China Frederic Maire Queensland University of Technology, Australia Jacek Mandziuk Warsaw University of Technology, Poland Satoshi Matsuda Nihon University, Japan Masakazu Matsugu Canon Research Center, Japan Bob McKay University of New South Wales, Australia Ali A. Minai University of Cincinnati, USA Hiromi Miyajima Kagoshima University, Japan Hongwei Mo Harbin Engineering University, China Mark Neal University of Wales,Aberystwyth, UK Pedja Neskovic Brown University, USA Richard Neville The University of Manchester, UK Tohru Nitta National Institute of Advanced Industrial Science and Technology, Japan Yusuke Nojima Osaka Prefecture University, Japan Takashi Omori Hokkaido University, Japan Yew Soon Ong Nanyang Technological University, Singapore M. Palaniswami The University of Melbourne, Australia Andrew P. Paplinski Monash University, Australia Asim Roy University of Arizona, USA Bernhard Sendhoff Honda Research Centre Europe, Germany Leslie Smith University of Stirling, UK Andy Song RMIT, Australia Lambert Spaanenburg Lund University, Sweden Changyin Sun Southeast University, China Mingui Sun University of Pittsburgh, USA Johan Suykens KULeuven, Belgium Kay Chen Tan National University of Singapore, Singapore Jonathan Timmis University of York, UK Seow Kiam Tian Nanyang Technological University, Singapore Peter Tino The University of Birmingham, UK Kar-Ann Toh Institute of Infocomm Research, Singapore Yasuhiro Tsujimura Nippon Institute of Technology, Japan Ganesh Kumar University of Missouri-Rolla, USA Venayagamoorthy Ray Walshe Dublin City University, Ireland Lei Wang Xi’an University of Technology, China Xiaofan Wang Shanghai Jiaotong University, China Xufa Wang University of Science and Technology of China, China Yuping Wang Xidian University, China Sumio Watanabe Tokyo Institute of Technology, Japan Gang Wei South China University of Technology, China Stefan Wermter University of Sunderland, UK
4 Kok Wai Wong Murdoch University, Australia Feng Wu Microsoft Research Asia, China Xihong Wu Peking University, China Zongben Xu Xi’an Jiaotong University, China Ron Yang University of Exeter, UK Li Yao Beijing Normal University, China Daniel Yeung The Hong Kong Polytechnic University, China Ali M. S. Zalzala Heriot-Watt University, UK Hongbin Zha Peking University, China Liming Zhang Fudan University, China Qingfu Zhang The University of Essex, UK Wenxiu Zhang Xi’an Jiaotong University, China Yanning Zhang Northwestern Polytechnical University, China Yi Zhang University of Electronic Science and Technology of China, China Zhaotian Zhang National Natural Science Foundation of China, China Liang Zhao University of Sao Paulo, Brazil Mingsheng Zhao Tsinghua Univerasity, China Qiangfu Zhao University of Aizu, Japan
F SK D 2006
Janos Abonyi University of Veszprem, Hungary Jorge Casillas University of Granada, Spain Pen-Chann Chang Yuanze University, Taiwan Chaochang Chiu Yuanze Universizy, Taiwan Honghua Dai Deakin University, Australia Suash Deb National Institute of Science & Technology, India Hepu Deng RMIT University, Australia Jun Gao Hefei University of Technology, China Saman Halgamuge The University of Melbourne, Australia Chongzhao Han Xi’an Jiaotong University, China Kaoru Hirota Tokyo Institute of Technology, Japan Frank Hoffmann University of Dortmund, Germany Dewen Hu National University of Defense Technology, China Jinglu Hu Waseda University, Japan Eyke Hiillermeier University of Marburg, Germany Hisao Ishibuchi Osaka Perfecture University, Japan Frank Klawoon University of Applied Sciences, Germany Naoyuki Kubota Tokyo Metropolitan University, Japan
5 Sam Kwong City University of Hong Kong, China Zongmin Ma Northeastern University, China Michael Margaliot Tel Aviv University, Israel Ralf Mikut IAI, Germany Pabitra Mitra Indian Institute of Technology, India Masoud Mohammadian University of Canberra, Australia Detlef Nauck BT, UK Hajime Nobuhara Tokyo Institute of Technology, Japan Andreas Nürnberger University of Magdeburg, Germany Quan Pan Northwestern Polytechnical University, China Da Ruan SCK-CEN, Belgium Thomas Runkler Siemens AG, Germany Yonghong Tan Guilin University of Electronic Technology, China Takao Terano Tokyo Institute of Technology, Japan Brijesh Verma Central Queensland University, Australia Guoyin Wang Chongqing University of Posts and Telecommunications, China Yugeng Xi Shanghai Jiaotong University, China Weixin Xie Shenzhen University, China Yiyu Yao University of Regina, Canada Gary Yen Oklahoma State University, USA Xinghuo Yu RMIT, Australia Shichao Zhang University of Technology Sydney, Australia Yanqing Zhang Georgia State University, USA Zhihua Zhou Nanjing University, China
6 R e v i e w e r s
IC N C 2006
A. A ttila ISLIER Changzhen HU Abdesselam BOUZERDOUM Chao DENG Adel AZAR Chaojian SHI Ah-Kat TAN Chaowan YIN Aifeng REN Chen YONG Aifeng REN Cheng WANG Ailun LIU Chengxian XU Aimin HOU Cheng-Yuan CHANG Aizhen LIU Cheol-Hong MOON Ales KEPRT Chi XIE Ali Bekir YILDIZ Ching-Hung LEE Alparslan TURANBOY Chong FU Anan FANG Chonghui GUO Andreas HERZOG Chong-Zhao HAN Andrew TEOH Chor Min TAN Andrew P PAPLINSKI Chu WU Andries ENGELBRECHT Chuang GUO Andy SONG Chuanhan LIU Anni CAI Chun JIN Ariel GOMEZ Chun CHEN Arumugam S Chung-Li TSENG Ay-Hwa A. LIOU Chunshien LI Bang-Hua YANG Cong-Kha PHAM Baolong GUO Cuiqin HOU Bei-Ping HOU Cunchen GAO Bekir CAKIR Daehyeon CHO Ben-Shun YI Dat TRAN Bharat BHASKER Davide ANGUITA Bin XU De XU Bin JIAO Deqin YAN Bin LI Dewu WANG Bing HAN Dexi ZHANG Binghai ZHOU Deyun CHEN Bo FU Diangang WANG Bob MCKAY Dong LIU Bohdan MACUKOW Dong Hwa KIM Bo-Qin FENG Dongbo ZHANG Brijesh VERMA Dongfeng HAN Caihong MU Donghu NIE CeFAN Dong-Min WOO Changyin SUN Du-Yun BI
7 Emilio DEL-MORAL-HERNANDEZ Gwi-Tae PARK En-Min FENG Hai TAO Ergun ERASLAN Hai-Bin DUAN Euntai KIM Haifeng DU Fajun ZHANG Haiqi ZHENG Fang LIU Haixian WANG Fangshi WANG Haixiang GUO Fan-Hua YU Haiyan JIN Fei HAO Hajime NOBUHARA Fei GAO Hanjun JIN Feng SHI Hao WANG Feng XUE Haoran ZHANG Feng DING Haoyong CHEN Feng CHEN He JIANG Feng JIAO Hengqing TONG Feng GAO Hiroshi FURUTANI Fenlin LIU Hong JIN Fu-Ming LI Hong ZHANG Gabriel CIOBANU Hong LIU Gang WANG Hong Jie YU Gang CHEN Hongan WANG Gaofeng WANG Hongbin DONG Gaoping WANG Hongbing JI Gary YEN Hongcai ZHANG Gexiang ZHANG Honghua SHI Golayoglu Fatullayev AFET Hongsheng SU Graham KENDALL Hongwei MO Guang REN Hongwei LI Guang TIAN Hongwei SI Guang LI Hongwei HUO Guangming SHI Hongxin ZHANG Guangqiang LI Hongyu LI Guang-Qiu HUANG Hongzhang JIN Guangrui WEN Hua-An ZHAO Guang-Zhao CUI Huaxiang LU Guanjun WANG Hua-Xiang WANG Guanlong CHEN Huayong LIU Guanzheng TAN Hui YIN Gui-Cheng WANG Hui LI Guixi LIU Hui WANG Guojun ZHANG Huizhong YANG Guowei YANG Hyun YOE Guoyin WANG Hyun Chan CHO Guo-Zheng LI Hyun-Cheol JEONG Gurvinder BAICHER Ihn-Han BAE
8 Ilhong SUH Jinhui ZHANG In-Chan CHOI Jinling ZHANG I-Shyan HWANG Jinping LI Ivan Nunes Da SILVA Jintang YANG Jae Hung YOO Jin-Young KIM Jae Yong SEO Jiqing QIU Jae-Jeong HWANG Jiquan SHEN Jae-Wan LEE Ji-Song KOU Jea Soo KIM Jiu-Chao FENG Jia LIU Jiulong ZHANG Jiafan ZHANG Jiuying DENG Jian YU Jiyang DONG Jian SHI Jiyi WANG Jian CHENG Johan SUYKENS Jian XIAO John Q GAN Jianbin SONG Jong-Min KIM Jiang CUI Joong-Hwan BAEK Jiangang LU Jorge CASILLAS Jianguo JIANG Jose SEIXAS Jianhua PENG Jr-Syu YANG Jianjun WANG Ju Cheng YANG Jianling WANG Ju Han KIM Jian-Sheng QIAN Juan LIU Jianwei YIN Jumin ZHAO Jianwu DANG Jun GAO Jianyuan JIA Jun YANG Jiating LUO Jun CAO Jidong SUO Jun JING Jie LI Jun MENG Jie HU Jun-An LU Jie WANG Jung-Hyun YUN Jie LI Jungsik LEE Jih-Chang HSIEH Junguo SUN Jih-Fu TU Junping ZHANG Jih-Gau JUANG Jun-Seok LIM Jili TAO Jun-Wei LU Jil-Lin LIU Junyi SHEN Jin YANG Junying ZHANG Jinchao LI Kay Chen TAN Jinfeng YANG Kay-Soon LOW Jing LIU Ke LU Jing-Min WANG Kefeng FAN Jingwei LIU Kenneth REVETT Jingxin DONG Keun-Sang PARK Jin-Ho KIM Khamron SUNAT
9 Kok Wai WONG Mehmet Zeki BILGIN Kwan Houng LEE Mei TIAN Kwang-Baek KIM Meihong SHI Kyung-Woo KANG Meiyi LI Laicheng CAO Mengxin LI Laiwan CHAN Michael MARGALIOT Lambert SPAANENBURG Min LIU Lan GAO Min FANG Lance FUNG Ming BAO Lean YU Ming LI Lei LIN Ming LI Lei WANG Ming CHEN Leichun WANG Mingbao LI Li MEIJUAN Mingguang WU Li WU Minghui LI Li DAYONG Mingquan ZHOU Li SUN Moh Lim SIM Li ZHANG Mudar SAREM Liang GAO Nagabhushan P Liang XIAO Naigang CUI Liang MING Nak Yong KO Lian-Wei ZHAO Naoko TAKAYAMA Lianxi WU Naoyuki KUBOTA Liefeng BO Ning CHEN Lili ZHOU Otvio Noura TEIXEIRA Liming CHEN Pei-Chann CHANG Li-Ming WANG Peide LIU Lin CONG Peixin YE Lincheng SHEN Peizhi WEN Ling WANG Peng TIAN Ling CHEN Peter TINO Lingl WANG Phill Kyu RHEE Liqing ZHANG Ping JI Liquan SHEN Pu WANG Lixin ZHENG Qi WANG Luo ZHONG Qi LUO Lusheng ZHONG Qiang LV Luyang GUAN Qiang SUN Manjaiah D H Qijuan CHEN Maoguo GONG Qing GUO Maoguo GONG Qing LI Maoyuan ZHANG Qinghe MING Masahiko TOYONAGA Qingming YI Masakazu MATSUGU Qingqi PEI Masumi ISHIKAWA Qiongshui WU
10 Qiyong GONG Sunjun LIU Quan ZHANG Sunkook YOO Renbiao WU Tae Ho CHO Renpu LI Tae-Chon AHN Renren LIU Tai Hoon CHO Richard EPSTEIN Takao TERANO Richard NEVILLE Takeshi FURUHASHI Robo ZHANG Tan LIU Roman NERUDA Tao SHEN Rong LUO Tao WANG Rongfang BIE Taoshen LI Ronghua SHANG Thi Ngoc Yen PHAM Ronghua SHANG Tianding CHEN Rubin WANG Tiantian SU Rui XU Tianyun CHEN Ruijun ZHU Tie-Jun ZHOU Ruiming FANG Ting WU Ruixuan LI Tong-Zhu FANG Ruochen LIU Vianey Guadalupe CRUZ SANCHEZ S.G LEE Vic CIESIELSKI Sanyang LIU Wang LEI Satoshi MATSUDA Wanli MA Seok-Lyong LEE Wei ZOU Seong Whan KIM Wei WU Serdar KUCUK Wei LI Seunggwan LEE Wei FANG Sezai TOKAT Weida ZHOU Shan TAN Wei-Hua LI Shangmin LUAN Weiqin YIN Shao-Ming FEI Weiyou CAI Shao-Xiong WU Wei-Yu YU Shigeo ABE Wen ZHU Shiqiang ZHENG Wenbing XIAO Shuguang ZHAO Wenbo XU Shuiping GOU Wenchuan YANG Shui-Sen CHEN Wenhui LI Shui-Sheng ZHOU Wenping MA Shunman WANG Wenping MA Shunsheng GUO Wenqing ZHAO Shutao LI Wen-Shyong TZOU Shuyuan YANG Wentao HUANG Soo-Hong PARK Wentao HUANG Soon Cheol PARK Wenxing ZHU Sung-Bae CHO Wenxue HONG Sungshin KIM Wenyu LIU
11 X. B. CAO Xun WANG Xian-Chuan YU Xuyan TU Xianghui LIU Yan ZHANG Xiangrong ZHANG Yan LIANG Xiangwei LAI Yan ZHANG Xiaobing LIU Yang YAN Xiaodong KONG Yangmi LIM Xiaofeng SONG Yangmin LI Xiaoguang ZHANG Yangyang LI Xiaoguang L IU ' Yangyang WU Xiaohe LI Yanling WU Xiaohua YANG Yanning ZHANG Xiaohua WANG Yanning ZHANG Xiaohua ZHANG Yanpeng LIU Xiaohui YUAN Yanping LV Xiaohui YANG Yanxia ZHANG Xiaojian SHAO Yanxin ZHANG Xiao-Jie ZHAO Yan-Xin ZHANG Xiaojun WU Yaoguo DANG Xiaoli LI Yaping DAI Xiaosi ZHAN Yaw-Jen CHANG Xiaosuo LU Yeon-Pun CHANG Xiaoyi FENG Yezheng LIU Xiaoying PAN Yidan SU Xiaoyuan WANG Yifeng NIU Xin XU Yimin YU Xin YUAN Ying GUO Xinbo GAO Ying GAO Xinchao ZHAO Ying TIAN Xingming SUN Yingfang FAN Xinsheng YAO Yingfeng QIU Xinyu WANG Yinghong PENG Xiu JIN Yingying LIU Xiu-Fen YU Yong ZHAO Xiufeng WANG Yong YANG Xiuhua GAO Yong FAN Xiuli MA Yong-Chang JIAO Xiyang LIU Yonggui KAO Xiyue HUANG Yonghui JIANG Xu YANG Yong-Kab KIM Xu CHEN Yongqiang ZHANG Xuejun XU Yongsheng DING Xueliang BI Yongsheng ZHAO Xuerong CHEN Yongzhong ZHAO Xuezhou XU Yoshikii KASHIMORI
12 You-Feng LI Zhanli LI Youguo PI Zhao ZHAO You-Ren WANG Zhaoyang ZHANG Yu GUO Zhe-Ming LU Yu GAO Zhen YANG Yuan KANG Zhenbing ZENG Yuehui CHEN Zhengxing CHENG Yuehui CHEN Zhengyou XIA Yufeng LIAO Zhi LIU Yuheng SHA Zhidong ZHAO Yukun BAO Zhifeng HAO Yulong LEI Zhigang XU Yumin LIU Zhigeng FANG Yumin TIAN Zhihui LI Yun-Chia LIANG Zhiqing MENG Yunjie ZHANG Zhixiong LIU Yuping WANG Zhiyong ZHANG Yurong ZENG Zhiyu ZHANG Yusuke NOJIMA Zhonghua LI Yutao QI Zhurong WANG Yutian LIU Zi-Ang LV Yuyao HE Zixing CAI Yu-Yen OU Zong Woo GEEM Yuzhong CHEN Zongmin LI Zafer BINGUL Zongying OU Zeng-Guang HOU Zoran BOJKOVIC Zhang YANG
F SK D 2006
Aifeng REN Byung-Joo KIM Andrew TEOH Changjian FENG Andries ENGELBRECHT Changyin SUN Baolin LIU Chao DENG Baolong GUO Chaojian SHI Bekir CAKIR Chen YONG Ben-Shun YI Chengxian XU Bernardete RIBEIRO Cheng-Yuan CHANG Bin XU Cheol-Hong MOON Bing HAN Chi XIE Binghai ZHOU Chijian ZHANG Bo LIU Ching-Hung LEE Bobby GERARDO Chor Min TAN Bo-Qin FENG Chuanhan LIU Brijesh VERMA Chun JIN
13 Chunning YANG Hong JIN Chunshien LI Hong GE Da-Kuan WEI Hongan WANG Daniel NEAGU Hongcai ZHANG Davide ANGUITA Hongwei 'LI Defu CHENG Hongwei SI Deok-Hwan KIM Hong-Yong YANG Deqin YAN Huai-Liang LIU Detlef NAUCK Huaizhi SU Dongbo ZHANG Huang NING Donghu NIE Hua-Xiang WANG Dug Hun HONG Hui-Yu WANG Du-Yun BI Hyun Chan CHO Ergun ERASLAN Hyun-Cheol JEONG Eun-Jun YOON I-Shyan HWANG Fajun ZHANG Ivan Nunes Da SILVA Fangshi WANG Jae Yong SEO Fei HAO Jaeho CHOI Feng CHEN Jae-Jeong HWANG Feng GAO Jae-Wan LEE Frank KLAWOON Jeong Seop SIM Fuyan LIU Jia LIU Fu-Zan CHEN Jia REN Gang LI Jian YU Gang CHEN Jian XIAO Gaoshou ZHAI Jian YIN Gexiang ZHANG Jianbin SONG Golayoglu Fatullayev AFET Jiancang XIE Guang TIAN Jiang CUI Guang-Qiu HUANG Jianguo NING Guangrui WEN Jianhua PENG Guanjun WANG Jianjun XU Guanlong CHEN Jianjun WANG Gui-Cheng WANG Jianming ZHANG Guixi LIU Jianqiang YI Guo-Chang LI Jian-Rong HOU Guojian CHENG Jianwei YIN Guoyin WANG Jian-Yun NIE Gwi-Tae PARK Jiating LUO H. B. QIU Jie HU Hasan CIMEN Jili TAO He JIANG Jimin LIANG Hengqing TONG Jin YANG Hexiao HUANG ’ Jingwei LIU Hisao ISHIBUCHI Jinhui ZHANG
14 J inping LI Lianxi WU Jinwu GAO Licheng JIAO Jiqing QIU Liguo ZHANG Jiquan SHEN Lin WANG Jiulun FAN Lin GAO Jiuying DENG Lirong JIAN Jiyi WANG Longbo ZHANG John Q GAN Long-Shu LI Jong Seo PARK Manjaiah D H Jong-Bok KIM Maoguo GONG Joong-Hwan BAEK Maoyuan ZHANG Jorge CASILLAS Maurizio MARCHESE Jorge ROPERO Meihong SHI Jr-Syu YANG Michael MARGALIOT Juan LIU Ming LI Juanying XIE Ming LIU Jun JING Mingquan ZHOU Jun MENG Ming-Wen SHAO Jun WU Mudar SAREM Jun ZHAO Myo-Taeg LIM Junping ZHANG Nagabhushan P J unping WANG Naigang CUI Junying ZHANG Nak Yong KO Kaoru HIROTA Nakaji HONDA Kar-Ann TOH Ning XU Ke LU Ning CHEN Kefeng FAN Pei-Chann CHANG Kejun TAN Peide LIU Keon Myung LEE Phill Kyu RHEE Kongfa HU Ping GUO Kwan Houng LEE Ping ZHOU Kyung Ha SEOK Ping JI Lambert SPAANENBURG Ping YAN Lance FUNG Pu WANG Lean YU Qiang ZHANG Lei WANG Qianjin GUO Leichun WANG Qinghe MING Leslie SMITH Qing-Ling ZHANG Li WU Qingqi PEI Li DAYONG Quan ZHANG Li SUN Robo ZHANG Li ZHANG Rongfang BIE Liang GAO Ruijun ZHU Liang XIAO Ruiming FANG Liang MING Seok-Lyong LEE
15 Shangmin LUAN Wenxue HONG Shanmukhappa ANGADI Xian-Chuan YU Shaosheng FAN Xianggang YIN Shi ZHENG Xiangrong ZHANG Shigeo ABE Xianjin ZHA Shihai ZHANG Xiaobing LIU Shi-Hua LUO Xiaodong LIU Shi-Jay CHEN Xiaoguang YANG Shitong WANG Xiaoguang LIU Shuiping GOU Xiaohui YUAN Shunman WANG Xiaohui YANG Shutao LI Xiaoqing LU Shuyuan YANG Xiaosuo LU Soo-Hong PARK Xin LI Sung Kyung HONG Xinbo GAO Sungshin KIM Xinbo ZHANG Tae-Chon AHN Xinghua FAN Takao TERANO Xingming SUN Tan LIU Xinming TANG Tan RAN Xinyu YANG Tao SHEN Xinyuan LU Thi Ngoc Yen PHAM Xiongfei LI Tianli LI Xiqin HE Ting SUN Xiu JIN Tinghua XU Xiuli MA Tinghuai MA Xiyue HUANG Toly CHEN Xue-Feng ZHANG Toshio EISAKA Xuejun XU Wanchun DOU Xueliang BI Wang LEI Xueling MA Wei ZOU Xuemei XIE Wei XIE Xueqin FENG Wei LI Xufa WANG Wei FANG Yaguang KONG Weida ZHOU Ya-Jun DU Wei-Dong KOU Yan LI Weimin MA Yan LIANG Wei-Ping WANG Yang TAO Weixing ZHU Yangyang WU Wenbing XIAO Yanmei CHEN Wenchuan YANG Yanning ZHANG Wenpeng LIN Yanning ZHANG Wenqing ZHAO Yanping LV Wen-Shyong TZOU Yanxia ZHANG Wen-Xiu ZHANG Yan-Xin ZHANG
16 Ye DU Yuechao MA Ye BIN Yuehui CHEN Yecai GUO Yufeng LIAO Yeon-Pun CHANG Yukun BAO Yezheng LIU Yulong LEI Yidan SU Ynmin TIAN Yigong PENG Yunjie ZHANG Yijun YU Yurong ZENG Yingfang FAN Yutian LIU Yinggang XIE Zhang YANG Yinghong PENG Zhanhuai LI Yong FANG Zhe-Ming LU Yong ZHAO Zhenbing ZENG Yong YANG Zhengxing CHENG Yong FAN Zhigang XU Yonggui KAO Zhigeng FANG Yongqiang ZHANG Zhi-Hong DENG Yongqiang ZHAO Zhihui LI Yongsheng DING Zhiqiang ZUO Yon-Sik LEE Zhiyun ZOU Young Chel KWUN Zhonghua LI Young Hoon JOO Zixing CAI Young-Koo LEE Zongben XU Yu GUO Zong-Yuan MAO Yuan KANG Zoran BOJKOVIC
17 Table of Contents
Artificial Neural Network
Terrain Classification Using 3D Co-Occurrence Features and Artificial Neural Network Dong-Min Woo, Dong-Chul Park, Quoc-Dat Nguyen ...... 1
Multiresolution-based BiLinear Recurrent Neural Network for Time Series Pre diction Nhon Huu Tran, Dong-Chul Park ...... 8
An Implementation and Performance Evaluation of Fuzzy and Neural Network- Based the KSSL Recognizer Jung-Hyun Kim,Kwang-Seok Hong ...... 17
Thouless-Anderson-Palmer Equation and Self-Consistent Signal-to-Noise Analy sis for Hopfield Model with Multibody Interaction Akihisa Ichiki, Masatoshi Shiino ...... 28
An Information Filtering System Using Cognitive Mapping Jinhwa Kim, Seunghun Lee, Hyunsoo Byun ...... 40
Evolutionary Computation: Theory and Algorithms
Genetic Algorithms with Social Interaction Phase as Phenotype Characterization Otdvio Noura Teixeira, Felipe Houat de Brito, Artur Noura Teixeira, Roberto Celio Liniao de Oliveira ...... 48
VLSI Floorplanning with Boundary Constraints Using Genetic Algorithms Hua-An ZHAO, Zhenyu YANG, Ruigang WANG, Tetsuji MIHARA, Weigang WANG, Li SHEN, Chen LIU ...... 59
Evolutionary Optimization of Boolean Queries in Fuzzy Information Retrieval Systems Suhail Owais, Pavel Kromer, Vaclav Snasel, Dusan Husek, Roman Neruda...... 69 Other Types in Natural Computation
A Web-based System for Finding Subtrees on Phylogenetic Trees Sun-Yuan Hsieh, Chao-Wen Huang ...... gj
A Visualized Product Recommendation System Using Fisheye Views and Data Adjacency Hyunsoo Byun, Jinhwa Kim, Seunghoon Lee ...... 9 2
Induction of Multiple Decision Trees Using Multiobjective Particle Swarm Opti mization Roselyn D. Santos, Prospero C. Naval, Jr...... ¡ 0 2
A Performance Improvement of Solvirfg the Traveling Salesman Problem through Uniting Changing Crossover Operators to Ant Colony Optimization Ryouei Takahashi...... 114
Demand Prediction with Multi-Stage Neural Processing Maciej Grzenda, Bohdan Macukow ...... 1 3 j
Development of a New Incremental Search Particle Swarm Optimization (ISPSO) Algorithm for Clustering Problems Karthi. R, Arumugam. S ...... 242
Natural Computation Techniques Other than Neural Networks
Image Watermarking Algorithm Using DWT on Human Visual System Jin Soo NOH, Kang Hyeon RHEE...... ¡ 5 4
Person Tracking with Mobile-Robot Using Particle Filtering Ho Sang Kwon, Young Joong Kim, Jeong Woo, Myo Taeg Lim ...... 164
Improved Digital Signal Processing Approach for Gene Prediction Dah-Jing Jwo, Wen-Shyong Tzou, Jia-Rong Chen ...... j 73
The Early Stage of a Consciousness Model for Robotic Artifact Dulee Maria Haljpap, Gilberto Corrta de Souzal, Jodo Bosco da Mota Alves...... 185
Remote Sensed Image Efficient Compression Algorithm Using Wavelet Packet Transform and Selective Variable Block Vector Quantization Jung-Youp Suk, Sung-Kun Jang, Bo-Yeoun Yeou, Dong-Ju Lee ...... 193
Sparse Bayesian Simplified Models for ECG Compression B Ribeiro, M Brito, J Henriques, M Antunes...... 202
2 Computational Learning Approach to Adaptive Signal Processing of Noisy Image Chunshien Li, Chan-Hung Yeh ...... 211
XML Document Categorization Using Support Vector Machines Srinivasa K G, Venugopal KR, Lalit M Patnaik ...... 222
Implementation of an Endoscope Embedded Control System Using Image Proc essing Cheol-Hong Moon, Sung-Oh Kim ...... 234
Hardware
Application of Middleware Technique in Web of Flood Forecasting System with Multiple Models Ma Yu-Xin, Xiao Gang, Song Yang, Xie Jian-Cang...... 246
On Seamless Service Delivery Junaid Ahsenali Chaudhry, Seungkyu Park ...... 253
Fuzzy Theory and Algorithms
Design and Evaluation of a Rough Set-Based Anomaly Detection Scheme for Mobile Networks Ihn-Han Bae ...... 262
A New Method for Ranking Fuzzy Numbers Based on the Shapes and the Devia tions of Fuzzy Numbers Li-Wei Lee, Shyi-Ming Chen...... 269
A New Method for Ranking Fuzzy Numbers Based on the Alpha-Cuts, the Belief Features and the Signal/Noise Ratios Chih-Huang Wang, Shyi-Ming Chen ...... 281
A Common Fixed Point Theorem in the Intuitionistic Fuzzy Metric Spaces Jin Han Park, Jong Seo Park, Young Chel Kwun ...... 293
Mathematical Modeling of Nonlinear TCP Network via T-S Fuzzy Approach Kuo-Hui Tsai, Hong-Wu Lin, Wen-Jer Chang, Yu-Teh Meng...... 301
Stability Margin for Linear Systems with Fuzzy Parametric Uncertainty P e tr H u se k ...... 313
A New Method for Handling the Similarity Measure Problems of Interval-Valued Fuzzy Numbers Shi-Jay Chen ...... 325
3 Compromise Fuzzy LP with Fuzzy Objective Function Coefficients and Fuzzy Constraints \J Sani Susanto, Arijit Bhattacharya, Pandian Vasant, Fransiscus Rian Pratikto...... 335
Knowledge Discovery Theory and Algorithms
Absorber Filter-A New Efficient and Cost Reduced Search Filter Jau-Ji Shen, Chin-Chen Chang, Yung-Chen Chou ...... 3 4 6
Optimal Design of Long Distance Pumping Water Supply System ManLin Zhu, YanHe Zhang, Tao Wang...... 35g
Application of Decision Trees for Mass Classification in Mammography Kuldeep Kumar, Ping Zhang, Brijesh Verma...... 3 6 6
Implementation of GIS Spatial Data Mining Based on Cloud Theory Xiao Gang, Ma Yu-Xin, Wang Xiao-Hui, Xie Jian-Cang...... 37 7
Influence of the Background Color of the Computer Display on the Task Keun-Sang Park, Milda Park, Chang-Han Kim, Seoung-Soo Lee ...... 385
A Comparison of Pursuit Eye Movement and Perception in Moving Direction of Observed Object Keun-Sang Park, Milda Park, Chang-Han Kim, Seoung-Soo Lee...... 393
For Partner Robots: A Hand Instruction Learning System Using Transient-SOM Takashi Kuremoto, Tomoe Hano, Kunikazu Kobayashi, Masanao Obayashi...... 403
Diagram Matching based on the Dual Ant Colony Optimization Algorithm Kar Seng Loke, Choon Ling Tan ...... 4 1 5
Ship Wakes Detection in SAR Image Based on Mapping Stationary Wavelet Biao Hou, Peiyun Di, Shuang Wang, and Licheng Jiao ...... 428
Spatial Data Mining and Visualisation: Beppu 2000 Census Case Study Subana Shanmuganathan, Yan Li, Monte Cassim ...... 4 3 8
Author Index...... 450
4 Compromise Fuzzy LP with Fuzzy Objective Function Coefficients and Fuzzy Constraints
Sani Susanto1, Arijit Bhattacharya2, Pandian Vasant3, Fransiscus Rian Pratikto4
'Senior Lecturer, ^Lecturer, '■ departm ent of Industrial Engineering, Parahyangan Catholic University, Jl. Ciumbuleuit 94, Bandung - 40141, Indonesia. 2Examiner of Patents & Designs, The Patent Office, Bouddhik Sampada Bhawan, CP - 2, Sector - V, Salt Lake, Kolkata - 700 091, West Bengal, India. 3Research Lecturer, Electrical and Electronic Engineering Program, Block 23, Room 29, Universiti Teknologi Petronas, 31750 Tronoh, BSI, Perak DR, Malaysia. ' Sjrhfgibdg.centrin.net.id, [email protected], [email protected], 4frianp@home. unpar. ac. id
Abstract. For large-scale production planning problems, it is observed that there has been lack of precise information on the various parameters that need industry’s utmost attention. These imprecise information often hinder decision makers to make a fruitful decision in regard to optimal product-mix to be manufactured. To make it ease for the decision makers while making a robust decision for product-mix optimization problems, a fuzzy linear programming (FLP) model is presented in this paper. The present methodology is a fuzzy linear programming model having fuzzification of both the objective function coefficients and fuzzy resources. An example of a chocolate manufacturing firm has been delineated to validate the practicability of the proposed FLP approach. The degree of optimality and the level-of-satisfaction of the solution have been discussed at the end of this paper.
1 Introduction
Managers, decision makers, analysts and experts dealing with optimization problems often have lack of precise information on the values of some parameters used in real- life problems [2], To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve these problems [2], These imprecision are “soft constraints”. Fuzzy sets have proven to be a suitable representation for modelling some sort of soft constraints [6] and vagueness of data [15], Prior research works in the field of fuzzy linear programming are enormous. Literature contains several works from Fang et al. [3], Liu and Liu [7], Tsai et al. [13], Nakamura et al. [8], Gasimov and Yenilmez [4], Giines [5], Wang [16], Ren and Sheridan [9], Cadenas and Verdegay [2], Kaymak and Sousa [6], and many others. Different variations of fuzzy linear programming (FLP) model have been proposed by researchers. A fuzzy inference method was suggested by Liu and Liu [7] for addressing conflicts. Tsai et al. [13] reported how a fuzzy linear programming approach be used to model and solve manufacturing cell formation (CF) problems. In their FLP model only objective function and constraints were fuzzified. Nakamura et al. [8] modified the FLP model in which each constraint had different grade of satisfaction. Gasimov and Yenilmez [4] reported two kinds of fuzzy LP problems. The first kind of fuzzy LP problem was developed with only fuzzy technological coefficients. The second kind of fuzzy LP problem was modelled with fuzzy numbers in both the right-hand side and the technological coefficients. Ren and Sheridan [9] proposed a methodology by combining quantitative and qualitative reasoning to deal with objective crisp and subjective fuzzy information simultaneously. The subjective fuzzy information was tackled and calibrated by a fuzzy knowledge base (FKB), and the objective crisp information was handled by FLP. Kaymak and Sousa [6] reported that weighted satisfaction of problem constraints and goals could be demonstrated by using a FLP approach. Vasant et al. [14] and Susanto et al. [10] modelled a “compromise linear programming having fuzzy objective function coefficients” (CLPFOFC) with fuzzy sensitivity. Their CLPFOFC model was used to solve a chocolate manufacturing firm’s product-mix decision. Susanto et al. [11] reported fuzzy optimization of product-mix problem with a compromise linear programming having fuzzy resources (CLPFR) only. The present methodology is a fuzzy linear programming model having fuzzification of both the objective function coefficients and fuzzy resources.
2 Algorithm of the Compromise Fuzzy LP model
According to Bellman and Zadeh [1] and Fang et al. [3], the “decision” in a fuzzy environment can be viewed as the intersection of fuzzy constraints and fuzzy objective functions. The relationship between constraints and objective functions in a fuzzy environment is fully symmetric. In the light of above, we try to model the compromise fuzzy LP having fuzzy objective function coefficients and fuzzy constraints. In a large-scale linear programming problem the value of an objective function coefficient never takes a single value, but lies in an interval. To maintain a balance some right hand side of constraints need some tolerances. Let us assume that (i) the constraints (except for the non-negativity constraints) are of the form ‘ < ’, (ii) the constraints to be fuzzified are the first ‘k’ constraints among ‘m’ original constraints. Assuming the above basics, a generalized compromise fuzzy LP model is built based upon the following few steps. Step 1: The generalized LP model is in the form of
maximize(or minimize) z = ^c-x- (1) j=i subject to: (A* \< b t (2) x> 0 (3) where i = 1, 2, ..., m; Cj = objective function coefficients; A and x are vector quantities.
336 Step 2\ The model of Step 1 is converted into a LP model having fuzzy objective function coefficients (readers are referred to Vasant et al. [14] and Susanto et al. [10] for further details): max a (4) subject to iZi(x)>a or (c-c)x+a(z1max-z1mm)
Objective function-1: max a (16) Objective function-2: m ax9 (17) subject to ¡ i2i (x) > a or (c* - c )x + a ( z r - z ”111) < z ”“ (18) m 2(x )> a or c * x -a(z 2max- z 2mm) > z r (19) (x) > a or (c+ -c*)x-a(z3max -z3mm)>z™n (20) c x -9 (z ' -z°)>z° (21) (Ax)t
337 and, tl,t2,...,tk relate to the tolerances of the first ‘k’ constraints Step 5: In order to solve the model formulated in Step 4, the following sub-steps are followed: Step 5.1: The following relation is defined: y= min {a, 6} (27) constraints (18)-( 26) Step 5.2: The problem in Step 4 is transformed into the following equivalent form: max j (28) subject to constraints (18) to (26) and a > y (29) 9 > y (30) 9 e [0,1] (31) Step 5.3: Finally the problem formulated in Step 5.2 is solved.
3 Problem Formulation
The example problem of Chocoman, Inc., which is illustrated here, has been adopted from Tabucanon [12], The firm Chocoman, Inc. produces 8 different kinds of chocolate products. A total of 8 raw materials are to be mixed in different proportions and 9 different processes to be utilized. The product demand and objective coefficients are illustrated in Tables 1 and 2 respectively. Table 3 depicts required materials for manufacturing each of the products.
Table 1. Demand for products
Product codes Product Fuzzy Interval (x 103) units MC 250 Milk chocolate, 250 g [500,625) MC 100 Milk chocolate, 100 g [800,1000) CC 250 Crunchy chocolate, 250 g [400,500) CC 100 Crunchy chocolate, 100 g [600,750) CN 250 Chocolate with nuts, 250g [300,375) CN 100 Chocolate with nuts, 100 g [500,625) CANDY Chocolate candy [200,250) WAFER Wafer [400,500)
338 Table 2. Objective function coefficients
Product Fuzzy Interval Profit (US $/100 unit) Milk chocolate, 250 g [135,225) Milk chocolate, lOOg [62,104) Crunchy chocolate, 250g [115,191) Crunchy chocolate, lOOg [54,90) Chocolate with nuts, 250g [97,162) Chocolate with nuts, lOOg [52,87) Chocolate candy [156,261) Chocolate wafer [62,104)
Table 3. Material requirement (Non-Fuzzy)
Product Types Materials MC MC CC CC CN CN required/100 CANDYWAFER 250 100 250 100 250 100 0 units Cocoa (kg) 87.5 35 75 30 50 20 60 12 Milk (kg) 62.5 25 50 20 50 20 30 12 Nuts (kg) 0 0 37.5 15 75 30 0 0 Cons, sugar 100 40 87.5 35 75 30 210 24 (kg) Flour (kg) 0 0 0 0 0 0 0 72 Alum. foil 500 0 500 0 0 0 0 250 (ft2) Paper (ft2) 450 0 450 0 450 0 0 0 Plastic (ft2) 60 120 60 120 60 120 1600 250
The following decision variables have been used in regard to the optimal product- mix solution of Chocoman, Inc. = milk chocolate of 250 g to be produced ( in ’000 ) = MC 250, x2 = milk chocolate of lOOg to be produced ( in ’000 ) = MC 100, x3 = crunchy chocolate of 250g to be produced ( in ’000 ) = CC 250, x4 = crunchy chocolate of lOOg to be produced ( in ’000 ) = CC 100, x5 = chocolate with nuts of 250g to be produced ( in ’000) = CN 250, x6 = chocolate with nuts of lOOg to be produced ( in ’000) = CN 100, x7 = chocolate candy to be produced ( in ’000 packs ) = Candy, and x8 = chocolate wafer to be produced ( in ’000 packs ) = Wafer. Two types of fuzziness have been introduced into the product-mix problem, viz.: (i) the fuzziness of the value of an objective function coefficient [10, 14], and (ii) the fuzziness of the value of some right hand side of constraints [11]. For the product-mix problem of Chocoman, Inc., the LP model is formulated as follows: max y
339 subject to:
(45xj + 21x2 + ^ x3 + l^x4 + 33xj + 18xg + 52xy + 21xg) + 67215.600a < 67215.600
(180xj + 83x2 + 153xj + 72x^ +130xj + 70xg + 208xy + 83xg)- 266184.900a > 0
(45xj + 21x2 + 38xj + 18x^ + 32xj + 17xg + 53xy + 21xg) - 66495.230a> 0
180xj + 83x2 + 153xj + 72x^ +130xj + 70xg + 208xy + 83xg - 57661.60 >266184.9000
87.5xj + 35x2 + 75x^ + 30x^ + 50xj + 20xg + 60xy + 12xg + 2 5 0 0 0 8 < 125000
6 2 .5 x-y + 25x2 + 50xg + 20x^ + 50xj + 20x^ + 30xy + 12xg + 300000 < 150000
3 7 .5 * 3 + l 5 x 4 + 75jc5 + 30jc6 + 150000 ^ 75000
lOOxj + 40x2 + 87.5.Xg + 35.X4 + 75x^ + 30x^ + 210xy + 24x8 + 500000 < 2 5 0 0 0 0
72x8 + 50000 < 25000
5 0 0 ^ + 5 0 0 jc3 + 250xg +1250000 < 625000
450xj + 450.*3 + 450x5 + 1250000 < 625000
6 0 x j + 1 2 0 x 2 + 6 OX3 +120x^ +60x^ +120xg +1600xy + 250xg +1250000 < 625000
0 . 5 x j + 0 .2 x 2 + 0.425x2 + 0.17x^ + 0.35xj + 0.14xg + 0.60xy + 0.096xg + 2500 < 1250
0.15x2 + O.O6 X4 + 0.25xj + O.lOxg + 500 < 250
0.75xj + 0.3x 2 + 0.75xg + O.3OX4 + 0.75xj + 0.30xg + 0.90xy + 0.36xg + 3750 < 1875
0 .2 5 x 3 +0.10x4 +500 < 250
0.30xg +250 < 125
0.50xj + 0 . 1 0 x 2 + O.lOxg + O.lOx^ + O.lOxg + O.lOxg + 0.20 Xy +1000 < 500
0.25xj + 0.25xg + 0.25xj + O.lOxg + 1000 < 500
0.05xj + 0.30x2 + 0.05x2 + O.3 OX4 + 0.05xj + 0.30xg + 2.50Xy + 0.15x8 + 3000 < 1500
0.30xj + 0.30x2 + 0.30x2 + O.3 OX4 + 0.30xj + 0.30xg + 2.50Xy + 0.25xg + 2500 < 1250
Xj < 0 .6 x 2 , x 3 < 0 .6 x 4 ; x 5 < 0 . 6 x 6 >
400x? +150xg < 56.25xj +22.5x2 + 60xg +24x^ +63x^ +26.25xg
X j < 5 0 0 , x 2 < 8 0 0 , x 3 < 4 0 0 , x 4 < 6 0 0 , x 5 < 300 , x6 < 500 , x7 < 200 , x8 < 400, a e [0,1], a > y , 0 > y . 6 e [0,1], and non-negativity constraints: xl,...,x8 > 0 •
340 4 Results
Table 4 indicates the product-mix solution for the Chocoman, Inc.’s chocolate manufacturing problem. Results are obtained using WinQSB® software.
Table 4. Optimal product-mix solution to chocolate manufacturing problem
Decision variable Solution value Xi 407.541 X2 679.234 X3 360.000 X4 600.000 X5 0.000 X6 0.000 x 7 185.517 X8 0.000 0 0.0072 a 0.0072
Y 0.0072
These optimal decision variable values correspond to the following values of membership functions (MFs):
O ) = (407.541 679.234 360 600 0 0 185.517 0) = 0.0072
^ (x) = (407.541 679.234 360 600 0 0 185.517 0) =1
O ) = (407.541 679.234 360 600 0 0 185.517 0) =1
n .O ) = Ho( 407.541 679.234 360 600 0 0 185.517 0 ) = 0.0072
n .O ) = H ( 407.541 679.234 360 600 0 0 185.517 0 ) = 0.3774
H2(x) = Ha( 407.541 679.234 360 600 0 0 185.517 0) =1
n 30 ) = H3( 407.541 679.234 360 600 0 0 185.517 0) =1
^ 4(x) = H4( 407.541 679.234 360 600 0 0 185.517 0) =1
n 30 ) = H3( 407.541 679.234 360 600 0 0 185.517 0) =1
H«(x) = H(( 407.541 679.234 360 600 0 0 185.517 0) =1
n ,(x ) = H7( 407.541 679.234 360 600 0 0 185.517 0) =1
i‘, W = ( 407.541 679.234 360 600 0 0 185.517 0) =1
341 (X) = (407.541 679.234 360 600 0 0 185.517 = 1 1 s ‘ 9 0 )
o( 407.541 679.234 360 600 0 0 185.517 = 1 ,(*) =: 0 )
(X) = (407.541 679.234 360 600 0 0 185.517 0 ) = 1
a( 407.541 679.234 360 600 0 0 185.517 = 1 ,(*) =: 0 )
,(*) = i ( 407.541 679.234 360 600 0 0 185.517 0 ) = 1
4( 407.541 679.234 360 600 0 0 185.517 = 0.9520 ,(*) =: 0 )
3( 407.541 679.234 360 600 0 0 185.517 = 1 ,(*) =: 0 )
(X) = ( ( 407.541 679.234 360 600 0 0 185.517 = 1 : 0 )
(407.541 679.234 360 600 0 0 185.517 = 1 , « =: 0 ) From Table 4 it is observed that the value of the objective function (max.) is 0.0072. Alternate solution exists for the same product-mix problem. But due to rapid convergence of the solution, results of Table 4 is considered as the optimal one. Table 4 is translated with the physical interpretation of the notations used which results in Table 5. Table 5 illustrates the optimal combination of the products to be manufactured.
Table 5. The optimal combination of products
Product Quantity to produce (in 1000 units)
MC 250 407.541
MC 100 679.234 CC 250 360.000 CC 100 600.000 CN 250 0.000 CN 100 0.000 CANDY 185.517 WAFER 0.000
5 Discussions and Conclusions
The value of ‘a ’, used in Step 4 of the algorithm, corresponds to the MF /j (x). From this MF the interpretation of the value of ‘a’ can be obtained through the following steps:
342 (i) firstly, from the definitions of z x, z2 and z3, as given in references [10, 14], corresponding to the optimal solution in Table 4, one gets the following values: zl =45(407.541)+21(679.234)+38(360)+180(600)+33(0)+18(0)+52(185.517)+21(0) = 66730.1535; z2=180(407.541)+83(679.234)+153(360)+72(600)+130(0)+70(0)+208(185.517)+83(0)= 266601.3796; z3 = 45(407.541)+21(679.234)+38(360)+18(600)+32(0)+17(0)+53(185.517)+21(0)= 66915.6708. (iii) secondly, from the definition of u_ (x), one gets: 67 215.600-(45x. +21x~ + 38x, + 28x. +33x. +18x, + 52x_ +21x„) (X) = ------i------i ------*------4------5------6------/------8_ Y 67215.600-0 _ 67215.600-66730.1535 _ Q 00?2 ” 67215.600 ” ' The value of fi (x ) represents the level-of-satisfaction achieved by the optimal solution in Table 4 and Table 5. The highest and the lowest level-of-satisfaction are achieved when the differences between the values cx and cx, i.e., (c-c")x, are 0 and 67215.600, respectively. By linear interpolation, it can be easily shown that the value (c-c ) x = zi= 66730.1535 corresponds to the level-of-satisfaction /J (x)= 0.0072. It is noticed that the alternative optimal solutions (which has not been tabulated in this paper) has the same level of satisfaction, i.e., a = 0.0072. The readers may follow the same computational procedures to verify the fact. The value of the optimal objective function for the case with no-tolerance in all constraint is z° = 266184.9000. From the definition, the value of z° = 266184.9000 corresponds to ju0 = 0. Again, the value of the optimal solution for the case using maximum-tolerance in each of the first 17 constraints is z1 = 323 846.5000. From the definition, the value of z1 = 323846.5000 corresponds to ju0 = 1. Therefore, the optimal value of the objective function is:
180(407.541)+83(679.234)+l 53(360)+72(600)+130(0)+70(0)+208(l 85.517)+83(0)= 266601.3796. It is observed using linear interpolation that this optimal value of the objective function corresponds to a degree of optimality ¡u0 = 0.0072. Let us discuss on the value of //,. Case I: If the usage of cocoa resource is less than or equal to the current capacity, i.e., 100000 kg., no tolerance for this resource is required. This situation corresponds to the value of //, = 1 indicating that there is no violation of the original constraint for the availability of cocoa resource. Case II: If the usage of cocoa resource is greater than or equal to the capacity having maximum tolerance, i.e., 125000 kg., the situation corresponds to the value =0. This situation indicates that there is maximum violation of the original constraint for the availability of cocoa resource. It is calculated that the optimal solution the usage level of cocoa resource is:
87.5(407.541) + 35(679.234) + 75(360) + 30(600) + 50(0) + 20(0) + 60(185.517) + 12(0) = 115564.0533.
343 Using linear interpolation it is obtained that this value corresponds to the level-of- satisfaction of the 1st constraint (constraint for the availability of cocoa) as //, = 0.3774. In the same fashion the physical interpretations for the other MFs, viz., |i2 to (in, can be obtained. In the example problem having fuzzy constraints, the aim is to achieve the following two goals simultaneously: (i) to achieve the maximum profit by exploiting the use of all the constraints tolerance available, and (ii) to maintain to the level of resource usage such that no single constraint is violated. Such an aim is often not achievable, so a compromise is required for trading-off suitably between these two goals. This compromise is achieved through the application of “max-min” principle to: (a) the degree of optimality of the solution, represented by the value of the membership function ju0 , and (b) the level-of-satisfaction of constraints (1) to (17), respectively, represented by the MFs ju^, /u2 , ...,/i17. The problem formulated is to maximize the value of 8 = min {//„,//, . From the discussion of the values of ju0 , //,. U2 ...... jilu , it is clear why we get 8 = 0.0072 in the optimal solution. The value of 8 means that the values of the degree of optimality of the solution, and the level-of-satisfaction of constraints (1) to (17) will not be less than 0.0072. Now let us discuss on the value of y. Equation (27) defines y as follows: 7 = m in {(X, 6} . It is to be noted that: (i) the a value relates to the degree of optimality of the objective functions (c - c" )x , cx and (c+ - c)x , and (ii) the 8 value relates to the level-of-satisfaction of the fuzzified constraints (1) to (17), then the optimal value of the decision variables tabulated in Table 4 guarantee that those degree is at least 0.0072. However, in fact the optimal solution of the proposed fuzzified LP model for the chocolate manufacturing firm’s problem results in maximum level-of-satisfaction (i.e., 1) in most of the objective functions and constraints (refer to Results section for the membership functions values ju0,jul,ju2,...,jul7).
References
1. Bellman, R.E., Zadeh, L.A.: Decision-Making in A Fuzzy Environment. Management Science 17(1970) 141-164. 2. Cadenas, J.M., Verdegay, J.L.: Using fuzzy numbers in linear programming. IEEE Trans. Sys., Man, and Cyber. — Part B: Cybernetics, 27(6) (1997), 1016 - 1022.
344 3. Fang, S.C., Hu, C.F., Wang, H.F., Wu, S.Y.: Linear Programs with Fuzzy Coefficient in Constraints. Comp. & Maths, with Applications 37(10) (1999) 63-76. 4. Gasimov, R.N., Yenilmez, K.: Solving Fuzzy Linear Programming Problems with Linear Membership Functions. Turkish J. Maths. 26 (2002) 375-396. 5. Günes, M.: Fuzzy Approaches to The Production Problems: The Case of Refinery Industry. Proc. Third IEEE Int. Conf. Information Fusion. Vol. 1 (2000) TUD4/3 - TUD4/7. 6. Kaymak, U., Sousa, J.M.: Weighting of constraints in fuzzy optimization. Proc. IEEE Int. Fuzzy Sys. Conf., (2001) 1131 - 1134. 7. Liu, S.-Y., Liu, S.-C.: A fuzzy linear programming approach for group decision making. IEEE Int. Conf. Sys., Man and Cybernetics, Vol. 1 (1996) 286-291. 8. Nakamura, S., Kosaka, K.-i., Kawaguchi, M.F., Nonaka, H., Da-te, T.: Fuzzy linear programming with grade of satisfaction in each constraint. Proc. IEEE Int. Conf. Fuzzy Sys., Vol.2 (1995) 781 -786. 9. Ren, J., Sheridan, T.B.: Optimization with fuzzy linear programming and fuzzy knowledge base. Proc. Third IEEE Conf. Fuzzy Sys., Vol. 2 (1994) 1389 - 1393. 10. Susanto, S., Vasant, P., Bhattacharya, A., Kahraman, C.: Chocolate manufacturing firm’s product-mix decision-making with compromise linear programming having fuzzy objective function coefficients (CLPFOFC). Paper submitted to 7th International FLINS Conference on Applied Artificial Intelligence, August 29-31, 2006, Accepted Paper. 11. Susanto, S., Bhattacharya, A., Vasant, P., Suryadi, D.: Optimising product-mix with compromise linear programming having fuzzy resources (CLPFR), 36th Int. Conf. Comp. & Indl. Engg. (ICCIE2006), June 20-23, 2006, Accepted Paper. 12. Tabucanon, M.T.: Multi objective programming for industrial engineers. Mathematical programming for industrial engineers, Marcel Dekker, Inc., New York (1996) 487-542. 13. Tsai, C.-C., Chu, C.-H., Barta, T.A.: Fuzzy Linear Programming Approach to Manufacturing Cell Formation. Proc. Third IEEE Conf. Fuzzy Sys., Vol. 2 (1994) 1406 - 1411. 14. Vasant, P., Bhattacharya, A., Susanto, S.: Compromise linear programming having fuzzy objective function coefficients (CLPFOFC) with fuzzy sensitivity - methodology and application. Journal of the Operational Research Society, 2006, Paper under review. 15. Vasant, P.M.: Fuzzy production planning and its application to decision making. J. Intelligent Manfg. 17(1) (2006) 5-12. 16. Wang, L.-X.: A Course in Fuzzy Systems and Control. Prentice-Hall Int., London (1997).
345 Author Index
Akihisa Ichiki 28 Ho Sang Kwon 164 Arijit Bhattacharya 335 Hua-An Zhao 59 Artur Noura Teixeira 48 Hyunsoo Byun 40, 92 Arumugam. S 142 Ihn-Han Bae 262 Biao Hou 428 Jau-Ji Shen 346 Bohdan Macukow 131 Jeong Woo 164 Bo-Yeoun Yeou 193 J Henriques 202 B Ribeiro 202 Jia-Rong Chen 173 Brijesh Verma 366 Jin Han Park 293 Chan-Hung Yeh 211 Jinhwa Kim 40, 92 Chang-Han Kim 385, 393 Jin Soo Noh 154 Chao-Wen Huang 81 Joao Bosco da Mota Alves 185 Chen Liu 59 Jong Seo Park 293 Cheol-Hong Moon 234 Junaid Ahsenali Chaudhry 253 Chih-Huang Wang 281 Jung-HyunKim 17 Chin-Chen Chang 346 Jung-Youp Suk 193 Choon Ling Tan 415 Kang Hyeon Rhee 154 ChunshienLi 211 Karthi. R 142 Dah-Jing Jwo 173 Kar Seng Loke 415 Dong-Chul Park 1,8 Keun-Sang Park 385, 393 Dong-Ju Lee 193 Kuldeep Kumar 366 Dong-Min Woo 1 Kunikazu Kobayashi 403 Dulce Maria Halfpap 185 Kuo-HuiTsai 301 Dusan Hüsek 69 Kwang-Seok Hong 17
Felipe Houat de Brito 48 Lalit M Patnaik 222 Fransiscus Rian Pratikto 335 Licheng Jiao 428 Limao de Oliveira 48 Gilberto CorrSa de Souza 1 185 Li Shen 59 Hong-Wu Lin 301 Li-Wei Lee 269 Maciej Grzenda 131 Srinivasa K G 222 ManLin Zhu 358 Subana Shanmuganathan 438 M Antunes 202 Suhail Owais 69 Masanao Obayashi 403 Sung-Oh Kim 234 Masatoshi Shiino 28 Sung-Kun Jang 193 Ma Yu-Xin 246, 377 Sun-Yuan Hsieh 81 M Brito 202 Takashi Kuremoto 403 Milda Park 385, 393 Tao Wang 358 Monte Cassim 438 Tetsuji M ih a ra 59 M yoTaegLim 164 Tomoe Hano 403 Nhon Huu Tran 8 Vaclav Snasel 69 Otävio Noura Teixeira 48 Venugopal KR 222
Pandian Vasant 335 Wang Xiao-Hui 377 Pavel Kromer 69 Weigang Wang 59 Peiyun Di 428 Wen-Jer Chang 301 PetrHuSek 313 Wen-Shyong Tzou 173
Ping Zhang 366 Xiao Gang 246, 377 Prospero C. Naval, Jr. 102 Xie Jian-Cang 246, 377 Quoc-DatNguyen 1 YanHe Zhang 358 Roberto Ce o 48 Yan Li 438 RomanNeruda 69 Young Chel Kwun 293 Roselyn D. Santos 102 Young Joong Kim 164 Ruigang Wang 59 Yung-Chen Chou 346 Ryouei Takahashi 114 Yu-Teh Meng 301 Sani Susanto 335 Zhenyu Yang 59 Seoung-Soo Lee 385, 393 Seunghun Lee 40, 92 Seungkyu Park 253 Shi-Jay Chen 325 Shuang Wang 428 Shyi-Ming Chen 269, 281 Song Yang 246
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LichengJiao Lipo Wang Guangming Shi SfauangWang XinboGao JingLiu (Eds.) Advances ini Natural Computation and Data Mining
The 2nd International Conference on Natural Computation and The 3rd Infernational Conference on Fuzzy Systems and Knowledge Disco very ICNC-KSKD 2006 Xi'an.China, September 2006. Proceedings
ISBN 7-5606-1735-2
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