Advances in Natural and Applied Sciences, 8(9) August 2014, Pages: 118-127 AENSI Journals Advances in Natural and Applied Sciences
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Ranking of the cities in Khoozestan province based on development indexes using Shannon Entropy model and VIKOR technique
Mehdi Momeni and Zeinab Mousavi
Faculty of Literature and Humanities, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran
ARTICLE INFO ABSTRACT Article history: One of the effects of underdevelopment and barriers of development is regional Received 25 June 2014 disparity or inequality in economic and social fields. Nowadays, disparity reduction in Received in revised form using resources and facilities is considered as one of the most important criteria of 1 July 2014 sustainable development in all of the country’s regions. The present study aimed at Accepted 31 August 2014 determining the priority of the cities in Khoozestan province, Iran, according to the Available online 15 September development indexes based on the statistics in 2011. In order to obtain the rate of 2014 regional disparities in the cities of the province, a combined approach of multi-criteria decision-making models was used. In this way, the weight of indexes was calculated Keywords: using the Shannon entropy technique and after prioritizing the criteria by the weight of Development indexes, Shannon major criteria, each of the cities was prioritized by VIKOR technique. The statistical entropy model, VIKOR model, population of this study includes 23 cities in Khoozestan province. They have been Khoozestan province investigated based on 6 main indexes and 26 sub-indexes. To achieve this, the indexes were examined based on quantitative methods. The findings of this study show the weighting of indexes and prioritization of the cities in the province in terms of the amount of suitability, and regret of the prioritization of each city in the province explained in the levels of development.
© 2014 AENSI Publisher All rights reserved. To Cite This Article: Mehdi Momeni and Zeinab Mousavi., Ranking of the cities in Khoozestan province based on development indexes using Shannon Entropy model and VIKOR technique. Adv. in Nat. Appl. Sci., 8(9): 118-127, 2014
INTRODUCTION
Development is defined as movement from the present situation to another situation which provides more chances and facilities for effective use of resources (Momeni, 2008). Although reducing regional disparities and inequalities has been one of the policies of the country’s civil programs and is seen as headlines in journals and magazines as the main aim, the failure to do this is because fighting against each problem would be impossible without recognizing the problem fully and this reveals its importance and necessity (Gharabaghian, 1996). In fact, development must be considered as a multi-dimensional process which involves fundamental changes in social structure, the public attitudes, national organizations, accelerating and increasing economic growth, decreasing inequality and disparity, and eradicating absolute poverty. Development must show that the social system set has changed from the previous adverse form of life and is compatible with the fundamental various needs, requests, and desires of individuals and social groups in the system and is propelling to a life situation or state which is “better” financially and spiritually. In general, development is movement from the “unstable” present situation to a “stable” favorable situation that leads to an increase in the social, economic, politic, cultural, and environmental welfare indexes and directs human societies to growth and high efficiency (Mirzaee, 2005). It is worth noting that notions of growth and progress are often brought up when defining development and are sometimes used interchangeably. Growth means quantitative increase and is often used in economic issues and discussions of the increase in consumption of materials, while development means qualitative increase and actualizing a potential power (Frazier, 1997). Nowadays, theorists bring up the necessities of regional planning in order to achieve balanced development and believe that balanced development is one which provides the best conditions and facilities for comprehensive progress and minimizes the differences between interregional (within regional) and intraregional (between regional) life quality to the least and finally eradicates them (Bhati, 2004). Paul Stertin believes that the ultimate goal of development is providing continuous improvement in individuals’ state and situation and grants its benefits to everyone (Masoomi Ashkoori, 1997). In this regard, the development of the cities in a province many not be an appropriate process sometimes due to heterogeneous spatial distribution of resources as
Corresponding Author: Mehdi Momeni, Faculty of Literature and Humanities, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran. E-mail: [email protected] 119 Mehdi Momeni and Zeinab Mousavi, 2014 Advances in Natural and Applied Sciences, 8(9) August 2014, Pages: 118-127 well as economic, and social factors (Molaee, 1996). Therefore, in the planning process for achieving development and being put on its track, recognizing and understanding conditions and requirements of human communities and societies and their needs from different dimensions is among the essential measures which must be taken in this regard (Ziari, 1997). In spite of its considerable natural wealth and resources, Khoozestan province suffers from a wide regional developed and undeveloped dichotomy. The regional development should provide better conditions and facilities for all people, and reduce the differences of life quality between regions. Thus, the characteristic of regional development is being comprehensive and not being limited to mere economic aspects and giving priority to equal distribution in all regions and reducing the intensity of differences between the living standards (Magobonj, 1989).The purpose of this study was to evaluate the development of the cities in Khoozestan province in 2011 using the two VIKOR and Shannon entropy techniques.
Research Background: Spatial inequality refers to a situation in which multiple different spatial or geographical units are at different levels regarding some variables (Kanbur et al, 2005).There are several reasons for the spatial disparities between countries such as history, natural resources, human resources, political and local economy, and culture which overlap with each other and are synergistic (Chalabi, 1996). At the same time, development includes all the changes of the social system, changes that bring a society from the current adverse situation to a human situation (Hosseinzadeh, 2001). Development is a multi-dimensional process that brings about reorganization and different orientation of the entire economic and social system. There are two general frameworks of development theories: basic and modern frameworks of development. The evolutionary school of development, modernization theories, Marxist perspectives of development, and dependency theories are within the basic framework (Azkia, 2002). In all these schools, due to the dominance of the top-down approach and the sovereign role of government in development planning (Sarraafi, 1998), using quantitative methods and mathematical models by planners is inevitable for the ease of understanding the complexity of the problems in different areas (Afraakhte, 1998). In contrast, the modern framework emphasizes on bottom-up approaches of development by adopting attitudes such as local communities, the role of non-governmental organizations (NGO), gender issues, justice and democracy, citizen participation, and most importantly, the environment and sustainable development (Hodder, 2000). In this regard, the development of cities in a province may not be an appropriate procedure due to the heterogeneous spatial distribution of resources and resources as well as a variety of economic and natural factors (Molaee, 2008). Therefore, as the overall goal of development is excellence in all aspects of human societies(Asayesh, 1996), recognizing and understanding the requirements and circumstances of human societies and their needs in various aspects are necessary measures in the planning process to achieve development and being put on its path (Ziari, 2008). A lot of researches have been carried out on the assessment of regional disparities and inequalities globally and nationally, one of them is the World Development Report 2009. This report mentioned the centralization of economic activities in countries, especially in cities and spatial disparities and inequalities in developing countries are considered. Based on the findings of this research, economic growth has always been unequal and imbalanced and the policies to strike spatial balance will only lead to poverty reduction UNU-WEDER, Nel, and Regerson projects (Dadashpoor, 2011). Several studies have been conducted related to the levels of development of regions and provinces, disparities and inequalities, and regional imbalances in Iran. In a research about the degree of development of the cities in Mazandaran province, Boroozian stated that in the period of 1976 to 1986 the intensity of development reduced in the cities of the province and the improvement of the development indexes has increased in deprived cities (Boroozian, 1995). Zarabi et al. (2009) have carried out a research about developing healthcare services in Isfahan province concerning the point that healthcare services are among the basics of development and the development in this research reflects gross dramatic differences between the cities of the province regarding the state of health services development. Ziyari and Jalalian (2008) compared the cities in Fars province in a research based on 40 selected development indexes from 1976 to 1996. First, they were reduced to 12 factors or indexes based on factor analysis model so that the contribution of each factor in human development was specified and ultimately by the combined index of human development, the cities in Fars province were ranked by the consolidated index. In an investigation by Ahangari and Alvand (2005), the level of development of the cities in Lorestan province in the period of 1995 to 2003 in a general state was determined and the cities of the province were ranked in terms of the degree of development. Among the studies on foreign countries, the study by Noorbakhsh (2002) can be pointed out. It is concerned about human development and regional disparities in India which investigates inequalities between India's states.
120 Mehdi Momeni and Zeinab Mousavi, 2014 Advances in Natural and Applied Sciences, 8(9) August 2014, Pages: 118-127
The Realm of the Research: Khoozestan province with an area of about 6/636333 km, between 29 degrees and 57 minutes to 33 degrees and zero minutes of north latitude from the equator and 47 degrees 40 minutes to 50 degrees 33 minutes of eastern longitude is located in the Southwest of Iran. It is bordered by Lorestan province from the north, by Chahar Mahal Bakhtiari and Boyer Ahmad provinces from the northeast and by Booshehr province from the southeast and by Persian Gulf from the south and by Iraq from the west (Statistical Yearbook of Khoozestan, 2011).
Fig. 1: The Realm of the Research.
Methodology: This research is an applied one with regard to its purpose and descriptive- analytic in nature. The population includes the cities in Khoozestan province. In order to prioritize the levels of benefits that the areas in the province enjoyed and considering the issue of having access to the data, 26 variables were determined in educational, cultural, demographic, health, social services and infrastructure fields. Statistics and information were gathered from the yearbook of 1390 and the administrative center of the province. Finally, statistical Shannon's entropy method and VIKOR technique were used for analyzing the data and the development of the cities was identified.
Introducing Development Indexes: Development indexes were identified and categorized based on six main criteria of educational (C1), culture (C2), population and employment (C3), health (C4), social services (C5) and infrastructure (C6). These indexes are presented in Table 1. For the sake of simplicity, a symbol is considered for each index. Later, the symbols are used in the study.
121 Mehdi Momeni and Zeinab Mousavi, 2014 Advances in Natural and Applied Sciences, 8(9) August 2014, Pages: 118-127
Table 1: Development Indexes. Overall index Main indexes Main variables Symbol Development Educational (C1) Number of literate men over six years old S11 Index Number of literate women over six years old S12 Number of elementary school teachers S13 Number of guidance school teachers S14 Number of high school teachers S15 Cultural (C2) Number of libraries S21 Number of intellectual development centers S22 Number of mosques S23 Number of publication offices S24 Number of exhibitions S25 Population and Economically active population S31 Employment (C3) Unemployed population S32 Number of mortalities S33 Employed population S34 Health (C4) Number of hospitals S41 Number of drugstores S42 Number of laboratories S43 Number of physicians S44 Number of emergency centers S45 Social services (C5) Number of banks S51 Area of parks S52 Infrastructure (C6) Number of passenger terminals S61 Number of post offices (express post) S62 Number of issued structural proteins S63 Number of villages having electricity S64 The number of public accommodation S65
Calculating the Weight of Indexes Using Shannon Entropy Technique: In this study, to identify criteria influencing development, first a set of different items were collected based on the literature and interviews with experts. In most of multi-criteria decision makings issues, especially multi- indexes decision making issues, having and knowing the relative weights of the present indexes are essential steps in the process of problem solving and are required. In this study, the Shannon entropy method, as one of the most popular methods for calculating the weights of indexes is utilized. Details of this method are as follows. Like other methods of multi-criteria decision making, decision making matrix is formed in the first stage. If the decision matrix is represented by M and every element of it by mij, the decision matrix should be normal. Normal matrix is presented by N and each of its elements by nij. In entropy technique, the normalization is done by a linear method.
The final weight will be calculated using the following algorithm. 1 k ; a= number of choices Ln(a) E k n LN(n ) j ij ij D 1 E j j
D W j j D j According to the obtained weights of indexes in this stage, the indexes with more weights are more important than other indexes and have greater influence in selecting the optimal choice. Therefore, the decision matrix is formed in the first step. The scores obtained from the decision matrix are presented in Table 2. After forming decision matrix, the next step is normalization of the obtained numbers. For this purpose, a simple linear normalization method was used. Normal matrix is a matrix in which the sum of the elements of each column is equal to one. The following formula is used for the normalization of decision matrix in which nij is any element of the normal matrix. Normalization results are presented in Table 3:
122 Mehdi Momeni and Zeinab Mousavi, 2014 Advances in Natural and Applied Sciences, 8(9) August 2014, Pages: 118-127
Table 2: Scores Obtained from the Decision Matrix. City S11 S12 S13 S14 S15 S21 S22 S23 S24 S25 S31 S32 S33 Abadan 120202 121377 828 596 583 6 6 127 12 7 77195 20862 1736 Omidie 40149 39846 464 301 373 2 3 45 5 6 26214 6325 382 Andika 22470 21856 168 119 92 2 1 1 1 1 13817 4185 172 Andimeshk 77787 73517 637 470 525 6 3 80 12 9 52806 18064 692 Ahwaz 619763 614819 3632 2471 3714 15 9 319 75 23 393299 104385 7412 Ize 88551 90394 837 668 534 6 1 111 3 6 57185 14406 796 Baghmalak 46359 46951 624 388 231 8 1 160 3 7 28923 3941 384 Bavi 38840 37586 390 232 199 3 1 1 1 3 21598 8153 1 BandareMahshahr 122414 120961 851 516 557 6 2 63 16 8 81746 16971 994 Behbahan 81721 80604 776 595 623 10 4 214 15 8 54992 9702 996 Khoramshahr 70013 72448 498 383 318 5 4 46 4 7 44642 13483 773 Dezfool 197636 184780 1445 929 991 15 4 238 27 10 130113 265030 1683 DashteAzadegan 43269 43226 383 212 198 10 3 99 4 9 23614 8492 431 Ramhormoz 46988 46333 438 303 363 4 1 125 7 7 30061 6025 550 Shadgan 65930 66124 586 347 369 3 1 54 3 5 37708 13523 684 Shoosh 89476 88745 938 584 518 10 1 167 6 9 54396 12383 1066 Shooshtar 86659 83334 745 448 518 6 2 219 17 8 53591 14513 919 MasjedSoleiman 50641 50643 484 282 229 5 1 54 8 7 33659 14612 712 Lali 16570 16003 135 102 94 2 1 38 2 3 10330 1276 155 Hendijan 16481 16607 174 55 90 3 1 29 2 3 11184 1910 176 Ramshir 21511 21134 269 177 145 2 1 54 2 4 13928 3396 193 Gatoond 29348 27885 298 195 190 5 1 67 2 3 18058 4145 194 Hoveize 15007 14510 182 95 75 1 1 1 1 2 8766 1375 190 Abadan 56323 4 30 14 115 6 59 105 4 13 812 77 246 Omidie 19889 2 8 6 32 3 16 1848 1 25 124 62 65 Andika 9632 1 1 1 15 4 2 100 1 1 75 169 1 Andimeshk 34742 1 14 11 58 6 31 220 3 15 719 142 227 Ahwaz 288914 20 245 82 927 30 329 28726 5 115 3185 408 1175 Ize 42779 1 12 7 82 5 22 922 1 55 602 326 107 Baghmalak 24981 1 8 7 45 5 11 397 2 7 564 145 61 Bavi 13445 1 1 1 1 1 2 1 1 1 295 1 1 BandareMahshahr 64775 3 35 16 84 4 63 876 2 21 548 40 228 Behbahan 45290 4 25 16 120 7 47 1346 1 35 987 199 181 Khoramshahr 31159 1 12 8 47 5 33 128 1 9 660 32 80 Dezfool 103583 4 48 22 178 1 68 1129 4 32 1637 156 298 DashteAzadegan 15122 1 10 7 54 4 19 4027 1 5 362 82 68 Ramhormoz 24026 1 9 6 49 8 9 1577 2 13 559 172 108 Shadgan 24185 1 7 6 50 2 21 67 2 4 81 377 72 Shoosh 42013 1 18 9 71 9 27 8400 2 27 224 178 196 Shooshtar 39078 3 19 7 71 4 30 2458 1 19 239 124 198 MasjedSoleiman 19047 3 13 7 48 4 24 4227 1 18 133 381 116 Lali 9054 1 2 2 23 2 5 450 3 1 399 171 1 Hendijan 9274 1 3 2 10 3 9 60 1 1 110 44 1 Ramshir 10532 1 6 3 30 1 9 60 1 1 303 141 1 Gatoond 13913 1 6 2 22 3 9 1 1 1 464 40 1 Hoveize 7391 1 2 1 9 3 8 1 1 1 168 36 1
Table 3: Normalized Decision Matrix. City S11 S12 S13 S14 S15 S21 S22 S23 S24 S25 S31 S32 S33 Abadan 0.060 0.061 0.052 0.057 0.051 0.044 0.113 0.055 0.053 0.045 0.060 0.037 0.082 Omidie 0.020 0.020 0.029 0.029 0.032 0.015 0.057 0.019 0.022 0.039 0.021 0.011 0.018 Andika 0.011 0.011 0.011 0.011 0.008 0.015 0.019 0.000 0.004 0.006 0.011 0.007 0.008 Andimeshk 0.039 0.037 0.040 0.045 0.046 0.044 0.057 0.035 0.053 0.058 0.041 0.032 0.033 Ahwaz 0.309 0.311 0.230 0.236 0.322 0.111 0.170 0.138 0.329 0.148 0.308 0.184 0.348 Ize 0.044 0.046 0.053 0.064 0.046 0.044 0.019 0.048 0.013 0.039 0.045 0.025 0.037 Baghmalak 0.023 0.024 0.040 0.037 0.020 0.059 0.019 0.069 0.013 0.045 0.023 0.007 0.018 Bavi 0.019 0.019 0.025 0.022 0.017 0.022 0.019 0.000 0.004 0.019 0.017 0.014 0.000 BandareMahshahr 0.061 0.061 0.054 0.049 0.048 0.044 0.038 0.027 0.070 0.052 0.064 0.030 0.047 Behbahan 0.041 0.041 0.049 0.057 0.054 0.074 0.075 0.093 0.066 0.052 0.043 0.017 0.047 Khoramshahr 0.035 0.037 0.032 0.037 0.028 0.037 0.075 0.020 0.018 0.045 0.035 0.024 0.036 Dezfool 0.098 0.093 0.092 0.089 0.086 0.111 0.075 0.103 0.118 0.065 0.102 0.467 0.079 DashteAzadegan 0.022 0.022 0.024 0.020 0.017 0.074 0.057 0.043 0.018 0.058 0.018 0.015 0.020 Ramhormoz 0.023 0.023 0.028 0.029 0.031 0.030 0.019 0.054 0.031 0.045 0.024 0.011 0.026 Shadgan 0.033 0.033 0.037 0.033 0.032 0.022 0.019 0.023 0.013 0.032 0.030 0.024 0.032 Shoosh 0.045 0.045 0.059 0.056 0.045 0.074 0.019 0.072 0.026 0.058 0.043 0.022 0.050 Shooshtar 0.043 0.042 0.047 0.043 0.045 0.044 0.038 0.095 0.075 0.052 0.042 0.026 0.043 MasjedSoleiman 0.025 0.026 0.031 0.027 0.020 0.037 0.019 0.023 0.035 0.045 0.026 0.026 0.033 Lali 0.008 0.008 0.009 0.010 0.008 0.015 0.019 0.016 0.009 0.019 0.008 0.002 0.007 Hendijan 0.008 0.008 0.011 0.005 0.008 0.022 0.019 0.013 0.009 0.019 0.009 0.003 0.008 Ramshir 0.011 0.011 0.017 0.017 0.013 0.015 0.019 0.023 0.009 0.026 0.011 0.006 0.009 Gatoond 0.015 0.014 0.019 0.019 0.016 0.037 0.019 0.029 0.009 0.019 0.014 0.007 0.009 Hoveize 0.007 0.007 0.012 0.009 0.007 0.007 0.019 0.000 0.004 0.013 0.007 0.002 0.009 Abadan 0.059 0.069 0.056 0.058 0.054 0.050 0.069 0.002 0.095 0.031 0.061 0.022 0.072 Omidie 0.021 0.034 0.015 0.025 0.015 0.025 0.019 0.032 0.024 0.060 0.009 0.018 0.019 Andika 0.010 0.017 0.002 0.004 0.007 0.033 0.002 0.002 0.024 0.002 0.006 0.048 0.000 Andimeshk 0.037 0.017 0.026 0.045 0.027 0.050 0.036 0.004 0.071 0.036 0.054 0.041 0.066 Ahwaz 0.304 0.345 0.459 0.337 0.433 0.250 0.386 0.503 0.119 0.274 0.240 0.116 0.342 Ize 0.045 0.017 0.022 0.029 0.038 0.042 0.026 0.016 0.024 0.131 0.045 0.093 0.031 Baghmalak 0.026 0.017 0.015 0.029 0.021 0.042 0.013 0.007 0.048 0.017 0.043 0.041 0.018 Bavi 0.014 0.017 0.002 0.004 0.000 0.008 0.002 0.000 0.024 0.002 0.022 0.000 0.000 BandareMahshahr 0.068 0.052 0.066 0.066 0.039 0.033 0.074 0.015 0.048 0.050 0.041 0.011 0.066 123 Mehdi Momeni and Zeinab Mousavi, 2014 Advances in Natural and Applied Sciences, 8(9) August 2014, Pages: 118-127
Behbahan 0.048 0.069 0.047 0.066 0.056 0.058 0.055 0.024 0.024 0.083 0.074 0.057 0.053 Khoramshahr 0.033 0.017 0.022 0.033 0.022 0.042 0.039 0.002 0.024 0.021 0.050 0.009 0.023 Dezfool 0.109 0.069 0.090 0.091 0.083 0.008 0.080 0.020 0.095 0.076 0.124 0.045 0.087 DashteAzadegan 0.016 0.017 0.019 0.029 0.025 0.033 0.022 0.070 0.024 0.012 0.027 0.023 0.020 Ramhormoz 0.025 0.017 0.017 0.025 0.023 0.067 0.011 0.028 0.048 0.031 0.042 0.049 0.031 Shadgan 0.025 0.017 0.013 0.025 0.023 0.017 0.025 0.001 0.048 0.010 0.006 0.108 0.021 Shoosh 0.044 0.017 0.034 0.037 0.033 0.075 0.032 0.147 0.048 0.064 0.017 0.051 0.057 Shooshtar 0.041 0.052 0.036 0.029 0.033 0.033 0.035 0.043 0.024 0.045 0.018 0.035 0.058 MasjedSoleiman 0.020 0.052 0.024 0.029 0.022 0.033 0.028 0.074 0.024 0.043 0.010 0.109 0.034 Lali 0.010 0.017 0.004 0.008 0.011 0.017 0.006 0.008 0.071 0.002 0.030 0.049 0.000 Hendijan 0.010 0.017 0.006 0.008 0.005 0.025 0.011 0.001 0.024 0.002 0.008 0.013 0.000 Ramshir 0.011 0.017 0.011 0.012 0.014 0.008 0.011 0.001 0.024 0.002 0.023 0.040 0.000 Gatoond 0.015 0.017 0.011 0.008 0.010 0.025 0.011 0.000 0.024 0.002 0.035 0.011 0.000 Hoveize 0.008 0.017 0.004 0.004 0.004 0.025 0.009 0.000 0.024 0.002 0.013 0.010 0.000
In the next step, the weight of each index should be determined. For this purpose, the following calculation is used, and the weight of each index (EJ) can be obtained using the following equation: E k n LN(n ) j ij ij D 1 E j j
In this equation, the value of k is obtained from the following equation:
The following equation was used to calculate the normal weight: d W j j d j According to the calculations, the final weight of each of the indexes was obtained using Shannon entropy, the results of which are presented in Table 4.
Table 4: Final Weight of Indexes Using Shannon Entropy. S11 S12 S13 S14 S15 S21 S22 S23 S24 S25 S31 S32 S33 Ej 0.832 0.832 0.893 0.884 0.826 0.936 0.906 0.890 0.779 0.946 0.829 0.645 0.792 Dj 0.168 0.168 0.107 0.116 0.174 0.064 0.094 0.110 0.221 0.054 0.171 0.355 0.208 Wi 0.036 0.036 0.023 0.025 0.037 0.014 0.020 0.023 0.047 0.012 0.036 0.076 0.044 S11 S12 S13 S14 S15 S21 S22 S23 S24 S25 S31 S32 S33 Ej 0.828 0.812 0.692 0.800 0.729 0.885 0.758 0.575 0.944 0.790 0.859 0.909 0.750 Dj 0.172 0.188 0.308 0.200 0.271 0.115 0.242 0.425 0.056 0.210 0.141 0.091 0.250 Wi 0.037 0.040 0.066 0.043 0.058 0.025 0.052 0.091 0.012 0.045 0.030 0.020 0.053
Selecting the Best Option Using VIKOR Technique: In this first study, the weights of decision-making criteria was determined first. In this step, based on the weight of the identified indexes, the cities were ranked using VIKOR technique. VIKOR technique was proposed by Opricovic in 1984. This is another method of multiple-criteria decision making approach for selecting the best option. In TOPSIS technique, the selected option should have the minimum distance from the ideal solution and the farthest from the anti-ideal solution. TOPSIS method introduces two reference points (ideal and anti-ideal), but does not consider the relative importance of the distances or intervals from these two points. VIKOR and TOPSIS methods apply different types of normalization to remove assessment units of criteria, whereas VIKOR method uses linear normalization and TOPSIS method uses vector normalization. The normalized value does not depend on the assessment unit of criterion in VIKOR method, while the normalization values in TOPSIS method may be dependent on the assessment unit of criterion (Huang et al., 2009).
Step One: Forming the Decision Matrix: Like other methods of selecting the best or superior option based on multi-criteria decision making techniques, the decision matrix is formed first. Decision matrix or scoring choices matrix based on criteria is provided in Table 2, the weight of each index was determined by entropy method. Decision matrix is shown by m and each of its elements by m . ij
124 Mehdi Momeni and Zeinab Mousavi, 2014 Advances in Natural and Applied Sciences, 8(9) August 2014, Pages: 118-127
Step Two: Preparation of Descaled Matrix: In the second step, descaling decision matrix is done using linear normalization method. The descaled n matrix is shown by N and each of its elements by ij . Each is calculated by dividing each corresponding element in the first matrix to the sum of the elements of the corresponding column as follows:
Thus, the output of the VIKOR technique for the descaled matrix N is given in Table 3.
Step Three: Determining the Positive and Negative Ideal Points: For each criteria, the best and the worst options are determined among all options, respectivelyf_j^* and f_j^- . If the criterion is positive, f_j ^ * is the maximum amount of the column and f_j ^ - is the minimum amount of the column. If all f_j ^ * are bound, it will give the optimal combination with the highest score (the positive ideal point) and for all f_j ^ - , it will give the worst score (the negative ideal point) would be. In this matrix, allcriteria are positive. So we will have: f_j^*=0.309, 0.311, 0.230, 0.236, 0.322, 0.111, 0.170, 0.138, 0.329, 0.148, 0.308, 0.467, 0.348, 0.304, 0.370, 0.460, 0.339, 0.433, 0.250, 0.386, 0.503, 0.119, 0.274, 0.240, 0.116, 0.342 f_j^-=0.007, 0.007, 0.009, 0.005, 0.007, 0.007, 0.019, 0.000, 0.004, 0.006, 0.007, 0.002, 0.000, 0.008, 0.000, 0.000, 0.000, 0.000, 0.008, 0.002, 0.000, 0.024, 0.002, 0.006, 0.000, 0.000
Step Four: Calculating the Suitability Value (S) and the Regret Value (R) for each Option: Suitability value (S) indicates the relative distance of i thoption from the positive ideal solution (the best composition), and the amount of (R) represents the maximum discomfort ofi thoption because of being far from the positive ideal solution.
Therefore, we will have:
Table 5: The Amounts of Suitability and Regret. City Amount of suitability (S) Amount of regret (R) Abadan 0.827 0.090 Omidie 0.931 0.085 Andika 0.983 0.091 Andimeshk 0.878 0.090 Ahwaz 0.046 0.046 Ize 0.871 0.088 Baghmalak 0.921 0.090 Bavi 0.983 0.091 BandareMahshahr 0.851 0.088 Behbahan 0.827 0.087 Khoramshahr 0.916 0.090 Dezfool 0.667 0.087 DashteAzadegan 0.917 0.078 Ramhormoz 0.913 0.086 Shadgan 0.924 0.091 Shoosh 0.844 0.073 Shooshtar 0.867 0.083 MasjedSoleiman 0.896 0.077 Lali 0.967 0.089 Hendijan 0.982 0.091 Ramshir 0.969 0.091 Gatoond 0.968 0.091 Hoveize 0.991 0.091
Step Five: Calculating VIKOR Index: Thus, the next step is calculating VIKOR index (Q) for each option.
125 Mehdi Momeni and Zeinab Mousavi, 2014 Advances in Natural and Applied Sciences, 8(9) August 2014, Pages: 118-127
- S = maxSi, S* = minSi - R = maxRi, R* = minRi S* = 0.462; S-=0.990; R*= 0.046, R- = 0.091 As a result:
Similarly, the Q value for the other variables is determined. These calculations are presented in Table 6.
Table 6: The suitability, and regret values and Q index. City Amount of suitability (S) Amount of regret (R) Q index Abadan 0.827 0.090 0.909 Omidie 0.931 0.085 0.903 Andika 0.983 0.091 0.992 Andimeshk 0.878 0.090 0.932 Ahwaz 0.046 0.046 0.000 Ize 0.871 0.088 0.904 Baghmalak 0.921 0.090 0.949 Bavi 0.983 0.091 0.996 BandareMahshahr 0.851 0.088 0.895 Behbahan 0.827 0.087 0.866 Khoramshahr 0.916 0.090 0.956 Dezfool 0.667 0.087 0.789 DashteAzadegan 0.917 0.078 0.818 Ramhormoz 0.913 0.086 0.903 Shadgan 0.924 0.091 0.962 Shoosh 0.844 0.073 0.718 Shooshtar 0.867 0.083 0.847 MasjedSoleiman 0.896 0.077 0.800 Lali 0.967 0.089 0.972 Hendijan 0.982 0.091 0.993 Ramshir 0.969 0.091 0.987 Gatoond 0.968 0.091 0.988 Hoveize 0.991 0.091 1.000
Sixth Step: Arranging the Options Based on the Values of Q, R, S: In this step, the options are arranged based on the values of Q, R, S in three groups, from small to large. The best option is the one which has the smallest Q, provided that the following two conditions are true: Condition one: If A1 and A2 options among m options have the first and second rankings, the following equation must be satisfied:
Condition two: A1 option must have the top ranking at least in one of the groups R or S. If the first condition does not hold, both options would be the best option. If the latter condition does not hold, both A1 and A2 options are selected as the best option.
Table 7: Calculating VIKOR Index. City S S ranking R R ranking Q Q ranking Abadan 0.827 3 0.090 16 0.909 12 Omidie 0.931 16 0.085 6 0.903 10 Andika 0.983 22 0.091 17 0.992 20 Andimeshk 0.878 9 0.090 14 0.932 13 Ahwaz 0.046 1 0.046 1 0.000 1 Ize 0.871 8 0.088 10 0.904 11 Baghmalak 0.921 14 0.090 13 0.949 14 Bavi 0.983 21 0.091 21 0.996 22 BandareMahshahr 0.851 6 0.088 11 0.895 8 Behbahan 0.827 4 0.087 8 0.866 7 Khoramshahr 0.916 12 0.090 15 0.956 15 Dezfool 0.667 2 0.087 9 0.789 3 DashteAzadegan 0.917 13 0.078 4 0.818 5 Ramhormoz 0.913 11 0.086 7 0.903 9 Shadgan 0.924 15 0.091 18 0.962 16 Shoosh 0.844 5 0.073 2 0.718 2 Shooshtar 0.867 7 0.083 5 0.847 6 MasjedSoleiman 0.896 10 0.077 3 0.800 4 126 Mehdi Momeni and Zeinab Mousavi, 2014 Advances in Natural and Applied Sciences, 8(9) August 2014, Pages: 118-127
Lali 0.967 17 0.089 12 0.972 17 Hendijan 0.982 20 0.091 19 0.993 21 Ramshir 0.969 19 0.091 20 0.987 18 Gatoond 0.968 18 0.091 22 0.988 19 Hoveize 0.991 23 0.091 23 1.000 23
Therefore, based on VIKOR calculations, Ahwaz and Shoosh are ranked first and second. Now, the first condition is checked:
Thus, the first condition is satisfied. The second condition is satisfied based on the point that the best option must be recognized as the top ranking at least in one of the groups R or S. Thus, because both conditions are true, the optimal solution (compromised) is that Ahwaz is selected as the best or superior option.
Conclusion: This study aimed at assessing the degree of development of the citiesin Khoozestan province. By comparing the ranking of development of the cities, it is found out that there is economic, social, environmental, cultural and physical or framework imbalancesamong cities of the province. According to the calculations done using Shannon entropy and VIKOR models and , Ahvaz city is the developed city, and Shoosh, Dezfool , MasjedSoleiman , Dashte Azadegan, Shooshtar, Behbahan, Bandare Mahshahr, Ramhormoz, Omidie, ize, and Abadan are moderately developed, and Andimeshk, Baghmalak, Khoramshahr, Shadgan, Lali, Ramshir, Gatoond, Andika, Hendijan, Bavi, and Hoveize are far from development. These inequalities because of the lack of corresponding development in the cities are consistent with the needs of their population. These inequalities and disparities are due to natural, economic, and political factors and failures of planning system and the growth pole (i.e. Ahvaz city). Ahwaz has maintained its superiority due to bureaucratic-political centralization and being the growth pole in all indexes and it absorbs facilities, services, and expert specialist human services from the surrounding cities and is the economic, political and population center and it is the crucial city in order to provide the background for development due to its natural, climatic, and human resources. Achieving social and environmental ideal and justice is not possible without analyzing and understanding the inequalities and disparities of the present situation and the history of cities and regions. Thus, any kind of planning for the development of cities and regions requires precise and accurate assessment of the degree of development of the cities, areas, and regions using standard methods and models acceptable by researchers. In that way, using trustful statistical data and combining comprehensive and valid indexes, environmental, economic, social, cultural, and physical or framework dimensions of development are measured and the levels of development in cities and regions are ranked quantitatively and correspondingly a model for proper planning is provided. According to the results, the following recommendations are offered: In codifying and formulating policies of allocating resources by management and planning organization and other administrative centers, special attention must be paid to cities that have a low level of development or are far from development. Planning approach must change from polar to spatial mode.
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