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Neutrosophic Sets and Systems Neutrosophic Sets and Systems Volume 2 Article 1 1-1-2014 Full Issue Neutrosophic Sets and Systems Follow this and additional works at: https://digitalrepository.unm.edu/nss_journal Recommended Citation Systems, Neutrosophic Sets and. "Full Issue." Neutrosophic Sets and Systems 2, 1 (2014). https://digitalrepository.unm.edu/nss_journal/vol2/iss1/1 This Full Issue is brought to you for free and open access by UNM Digital Repository. It has been accepted for inclusion in Neutrosophic Sets and Systems by an authorized editor of UNM Digital Repository. For more information, please contact [email protected], [email protected], [email protected]. Neutrosophic Sets and Systems, Vol. 1, 2013 1 Vol. 2, 2014 Neutrosophic Sets and Systems An International Journal in Information Science and Engineering ISSN 2331-6055 (print) ISSN 2331-608X (online) ISSN 2331-6055 (print) ISSN 2331-608X (online) Neutrosophic Sets and Systems An International Journal in Information Science and Engineering Editor-in-Chief: Associate Editors: Dmitri Rabounski and Larissa Borissova, independent researchers. Prof. Florentin Smarandache W. B. Vasantha Kandasamy, IIT, Chennai, Tamil Nadu, India. Department of Mathematics and Science Said Broumi, Univ. of Hassan II Mohammedia, Casablanca, Morocco. University of New Mexico A. A. Salama, Faculty of Science, Port Said University, Egypt. 705 Gurley Avenue Yanhui Guo, School of Science, St. Thomas University, Miami, USA. Gallup, NM 87301, USA Francisco Gallego Lupiañez, Universidad Complutense, Madrid, Spain. E-mail: [email protected] Peide Liu, Shandong Universituy of Finance and Economics, China. Home page: http://fs.gallup.unm.edu/NSS Pabitra Kumar Maji, Math Department, K. N. University, WB, India. S. A. Albolwi, King Abdulaziz Univ., Jeddah, Saudi Arabia. Jun Ye, Shaoxing University, China. Ştefan Vlăduţescu, University of Craiova, Romania. Volume 2 2014 Contents Shawkat Alkhazaleh and Emad Marei. Mappings on W. B. Vasantha Kandasamy, Florentin Smarandache. Measure and 42 Neutrosophic Soft Classes............................................... 3 Neutrosophic Lattices..............................................8 Neutro....... 3 Said Broumi and Florentin Smarandache. On Jun Ye, Qiansheng Zhang. Single Valued Neutrosophic Neutrosophic Implications............................................... 9 Similarity Measures for Multiple Attribute Decision- Making............................................................................. 48 Rıdvan Şahin. Neutrosophic Hierarchical Clustering Algoritms......................................................................... 18 Mumtaz Ali, Florentin Smarandache, Muhammad A. A. Salama, Florentin Smarandache, Valeri Shabir, Munazza Naz. Soft Neutrosophic Bigroup and 55 Kroumov. Neutrosophic Crisp Sets & Neutrosophic Soft Neutrosophic N-Group ............................................ Crisp Topological Spaces............................................... 25 Surapati Pramanik and Tapan Kumar Roy. Karina Pérez-Teruel and Maikel Leyva-Vázquez. Neutrosophic Game Theoretic Approach to Indo-Pak Neutrosophic Logic for Mental Model Elicitation and Analysis........................................................................... Conflict over Jammu-Kashmir......................................... 31 82 A.A.A. Agboola, B. Davvaz. On Neutrosophic Pranab Biswas, Surapati Pramanik, and Bibhash C. Giri. Entropy Based Grey Relational Analysis Method Canonical Hypergroups and Neutrosophic Hyperrings.. 34 for Multi-Attribute Decision Making under Single 10 Valued Neutrosophic Assessments................................... 2 Pingping Chi, and Peide Liu. An Extended TOPSIS Method for the Multiple Attribute Decision Making Problems Based on Interval Neutrosophic Set ………... 63 Copyright © Neutrosophic Sets and Systems Neutrosophic Sets and Systems, Vol. 2, 2014 pss -Header will be provided by the publisher 1 2 3 Neutrosophic Sets and Systems 4 An International Journal in Information Science and Engineering 5 6 7 Copyright Notice 8 9 10 Copyright @ Neutrosophics Sets and Systems academic or individual use can be made by any user 11 without permission or charge. The authors of the articles 12 All rights reserved. The authors of the articles do hereby published in Neutrosophic Sets and Systems retain their 13 grant Neutrosophic Sets and Systems non-exclusive, rights to use this journal as a whole or any part of it in any 14 worldwide, royalty-free license to publish and distribute other publications and in any way they see fit. Any part of 15 the articles in accordance with the Budapest Open Neutrosophic Sets and Systems howsoever used in other 16 Initiative: this means that electronic copying, distribution 17 publications must include an appropriate citation of this and printing of both full-size version of the journal and the 18 journal. 19 individual papers published therein for non-commercial, 20 21 22 23 Information for Authors and Subscribers 24 25 Neutrosophic Sets and Systems has been created for Neutrosophic Probability is a generalization of the classical 26 publications on advanced studies in neutrosophy, neutrosophic probability and imprecise probability. 27 set, neutrosophic logic, neutrosophic probability, neutrosophic Neutrosophic Statistics is a generalization of the classical 28 statistics that started in 1995 and their applications in any field, statistics. 29 such as the neutrosophic structures developed in algebra, What distinguishes the neutrosophics from other fields is the 30 geometry, topology, etc. <neutA>, which means neither <A> nor <antiA>. 31 The submitted papers should be professional, in good <neutA>, which of course depends on <A>, can be 32 English, containing a brief review of a problem and obtained indeterminacy, neutrality, tie game, unknown, contradiction, 33 results. ignorance, imprecision, etc. 34 Neutrosophy is a new branch of philosophy that studies the 35 origin, nature, and scope of neutralities, as well as their All submissions should be designed in MS Word format using 36 interactions with different ideational spectra. our template file: 37 This theory considers every notion or idea <A> together with http://fs.gallup.unm.edu/NSS/NSS-paper-template.doc. 38 its opposite or negation <antiA> and with their spectrum of 39 neutralities <neutA> in between them (i.e. notions or ideas A variety of scientific books in many languages can be 40 supporting neither <A> nor <antiA>). The <neutA> and <antiA> downloaded freely from the Digital Library of Science: 41 ideas together are referred to as <nonA>. http://fs.gallup.unm.edu/eBooks-otherformats.htm. 42 Neutrosophy is a generalization of Hegel's dialectics (the last one 43 is based on <A> and <antiA> only). To submit a paper, mail the file to the Editor-in-Chief. To order 44 According to this theory every idea <A> tends to be neutralized printed issues, contact the Editor-in-Chief. This journal is non- 45 and balanced by <antiA> and <nonA> ideas - as a state of commercial, academic edition. It is printed from private 46 equilibrium. donations. 47 In a classical way <A>, <neutA>, <antiA> are disjoint two 48 by two. But, since in many cases the borders between notions are Information about the neutrosophics you get from the UNM 49 vague, imprecise, Sorites, it is possible that <A>, <neutA>, website: 50 <antiA> (and <nonA> of course) have common parts two by http://fs.gallup.unm.edu/neutrosophy.htm. 51 two, or even all three of them as well. 52 Neutrosophic Set and Neutrosophic Logic are generalizations 53 of the fuzzy set and respectively fuzzy logic (especially of 54 intuitionistic fuzzy set and respectively intuitionistic fuzzy logic). 55 In neutrosophic logic a proposition has a degree of truth (T), a 56 degree of indeterminacy (I), and a degree of falsity (F), where T, 57 I, F are standard or non-standard subsets of ]-0, 1+[. CopyrightCopyright © Neutrosophicline will be provided Sets and by theSystems publisher Neutrosophic Sets and Systems, Vol. 2, 2014 3 Mappings on Neutrosophic Soft Classes Shawkat Alkhazaleh1 and Emad Marei2 1 Department of Mathematics, Faculty of Science and Art, Shaqra University, Saudi Arabia. E-mail: [email protected] 2 Department of Mathematics, Faculty of Science and Art, Shaqra University, Saudi Arabia. E-mail: [email protected] Abstract. In 1995 Smarandache introduced the concept of classes where the neutrosophic soft classes are collections of neutrosophic set which is a mathematical tool for handling neutrosophic soft set. We also define and study the properties of problems involving imprecise, indeterminacy and inconsistent neutrosophic soft images and neutrosophic soft inverse images of data. In 2013 Maji introduced the concept of neutrosophic soft neutrosophic soft sets. set theory as a general mathematical tool for dealing with uncertainty. In this paper we define the notion of a mapping on Keywords: soft set, fuzzy soft set, neutrosophic soft set, neutrosophic soft classes, mapping on neutrosophic soft classes, neutrosophic soft images, neutrosophic soft inverse images. 1 Introduction properties and operations. They presented the applications of this concept to decision making problems. In 2012 Most of the problems in engineering, medical science, Salleh et al. [1] introduced the notion of economics, environments etc. have various uncertainties. multiparameterized soft set and studied its properties. In in 1995, Smarandache talked for the first time about 2010 Kharal and Ahmad [14] introduced the notion of neutrosophy and in 1999 and 2005 [15, 16] he initiated the mapping
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