A Bipolar Fuzzy Extension of the MULTIMOORA Method

The aim of this paper is to make a proposal for a new extension of the MULTIMOORA method extended to deal with bipolar fuzzy sets. Bipolar fuzzy sets are proposed as an extension of classical fuzzy sets in order to enable solving a particular class of decision-making problems. Unlike other extensions of the fuzzy set of theory, bipolar fuzzy sets introduce a positive membership function, which denotes the satisfaction degree of the element x to the property corresponding to the bipolar-valued fuzzy set, and the negative membership function, which denotes the degree of the satisfaction of the element x to some implicit counter-property corresponding to the bipolar-valued fuzzy set. By using single-valued bipolar fuzzy numbers, the MULTIMOORA method can be more efficient for solving some specific problems whose solving requires assessment and prediction. The suitability of the proposed approach is presented through an example.

[1]  Wen-Ran Zhang,et al.  Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis , 1994, NAFIPS/IFIS/NASA '94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige.

[2]  Karel Skokan Technological and Economic Development of Economy , 2011 .

[3]  E. Zavadskas,et al.  Project management by multimoora as an instrument for transition economies , 2010 .

[4]  Edmundas Kazimieras Zavadskas,et al.  The MOORA method and its application to privatization in a transition economy , 2006 .

[5]  E. Zavadskas,et al.  The Interval-Valued Intuitionistic Fuzzy MULTIMOORA Method for Group Decision Making in Engineering , 2015 .

[6]  Bernard Roy,et al.  Classement et choix en présence de points de vue multiples , 1968 .

[7]  Dragisa Stanujkic,et al.  An extension of the multimoora method for solving complex decision-making problems based on the use of interval-valued triangular fuzzy numbers , 2015 .

[8]  Muhammad Akram,et al.  A Novel Trapezoidal Bipolar Fuzzy TOPSIS Method for Group Decision-Making , 2018, Group Decision and Negotiation.

[9]  Reza Tavakkoli-Moghaddam,et al.  Pharmacological therapy selection of type 2 diabetes based on the SWARA and modified MULTIMOORA methods under a fuzzy environment , 2018, Artif. Intell. Medicine.

[10]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[11]  F. Smarandache,et al.  THE USE OF THE PIVOT PAIRWISE RELATIVE CRITERIA IMPORTANCE ASSESSMENT METHOD FOR DETERMINING THE WEIGHTS OF CRITERIA , 2018 .

[12]  Weizhang Liang,et al.  Selecting the optimal mining method with extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach , 2019, Neural Computing and Applications.

[13]  Romualdas Ginevičius,et al.  The economy of the Belgian regions tested with multimoora , 2010 .

[14]  Constantin Zopounidis,et al.  Financial Decision Aid Using Multiple Criteria , 2018 .

[15]  T. Baležentis,et al.  Multimoora for the EU member states updated with fuzzy number theory , 2011 .

[16]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[17]  Peter C. Fishburn,et al.  Letter to the Editor - Additive Utilities with Incomplete Product Sets: Application to Priorities and Assignments , 1967, Oper. Res..

[18]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[19]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[20]  Edmundas Kazimieras Zavadskas,et al.  Multimoora Optimization Used to Decide on a Bank Loan to Buy Property , 2011 .

[21]  T. L. Saaty,et al.  Decision making with dependence and feedback , 2001 .

[22]  Mohammad Khalilzadeh,et al.  Ranking and selecting the best performance appraisal method using the MULTIMOORA approach integrated Shannon’s entropy , 2018 .

[23]  Ying Han,et al.  A YinYang bipolar fuzzy cognitive TOPSIS method to bipolar disorder diagnosis , 2018, Comput. Methods Programs Biomed..

[24]  Esra Aytaç Adalı,et al.  The multi-objective decision making methods based on MULTIMOORA and MOOSRA for the laptop selection problem , 2017 .

[25]  Ralph E. Steuer,et al.  On the increasing importance of multiple criteria decision aid methods for portfolio selection , 2018, J. Oper. Res. Soc..

[26]  Ching-Lai Hwang,et al.  Methods for Multiple Attribute Decision Making , 1981 .

[27]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[28]  Marc Roubens,et al.  Multiple criteria decision making , 1994 .

[29]  C. B. E. Costa,et al.  MACBETH — An Interactive Path Towards the Construction of Cardinal Value Functions , 1994 .

[30]  Edmundas Kazimieras Zavadskas,et al.  A new additive ratio assessment (ARAS) method in multicriteria decision‐making , 2010 .

[31]  T. L. Saaty Modeling unstructured decision problems — the theory of analytical hierarchies , 1978 .

[32]  S. Meysam Mousavi,et al.  Selecting project-critical path by a new interval type-2 fuzzy decision methodology based on MULTIMOORA, MOOSRA and TPOP methods , 2018, Comput. Ind. Eng..

[33]  Edmundas Kazimieras Zavadskas,et al.  Multicriteria assessment of unfinished construction projects , 2015 .

[34]  Edmundas Kazimieras Zavadskas,et al.  State of art surveys of overviews on MCDM/MADM methods , 2014 .

[35]  Zhang-peng Tian,et al.  Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets , 2015, Int. J. Syst. Sci..

[36]  Shouzhen Zeng,et al.  MULTIMOORA-IFN: A mcdm method based on intuitionistic fuzzy number for performance management , 2015 .

[37]  Shankar Chakraborty,et al.  A study on the ranking performance of some MCDM methods for industrial robot selection problems , 2016 .

[38]  Dragisa Stanujkic,et al.  Selection of candidates in the mining industry based on the application of the SWARA and the MULTIMOORA methods , 2015 .

[39]  Abraham Charnes,et al.  Cone ratio data envelopment analysis and multi-objective programming , 1989 .

[40]  Alvydas Balezentis,et al.  MULTIMOORA-FG: A Multi-Objective Decision Making Method for Linguistic Reasoning with an Application to Personnel Selection , 2012, Informatica.

[41]  Ralph E. Steuer,et al.  Multiple Criteria Decision Making, Multiattribute Utility Theory: The Next Ten Years , 1992 .

[42]  Shouzhen Zeng,et al.  Group multi-criteria decision making based upon interval-valued fuzzy numbers: An extension of the MULTIMOORA method , 2013, Expert Syst. Appl..

[43]  Muhammad Akram,et al.  Multi-Criteria Decision-Making Methods in Bipolar Fuzzy Environment , 2018, International Journal of Fuzzy Systems.

[44]  Manik Chandra Das,et al.  Decision making under conflicting environment: a new MCDM method , 2012, Int. J. Appl. Decis. Sci..

[45]  A. Gabus,et al.  World Problems, An Invitation to Further Thought within the Framework of DEMATEL , 1972 .

[46]  Joseph G. Ecker,et al.  Finding all efficient extreme points for multiple objective linear programs , 1978, Math. Program..

[47]  Dragisa Stanujkic,et al.  A Neutrosophic Extension of the MULTIMOORA Method , 2017, Informatica.

[48]  Kalyanmoy Deb,et al.  Multiple Criteria Decision Making, Multiattribute Utility Theory: Recent Accomplishments and What Lies Ahead , 2008, Manag. Sci..

[49]  Salvatore Greco,et al.  Robust Ordinal Regression , 2014, Trends in Multiple Criteria Decision Analysis.

[50]  Mehmet Sahin,et al.  Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making , 2018, Neural Computing and Applications.

[51]  Atul Kumar Sahu,et al.  Application of modified MULTI-MOORA for CNC machine tool evaluation in IVGTFNS environment: an empirical study , 2016, Int. J. Comput. Aided Eng. Technol..

[52]  K R MacCrimmon,et al.  Decisionmaking among Multiple-Attribute Alternatives: A Survey and Consolidated Approach , 1968 .

[53]  F. Smarandache A Unifying Field in Logics: Neutrosophic Logic. , 1999 .

[54]  Mohammad Kazem Sayadi,et al.  Extension of MULTIMOORA method with interval numbers: An application in materials selection , 2016 .

[55]  Edmundas Kazimieras Zavadskas,et al.  From a centrally planned economy to multi-objective optimization in an enlarged project management : the case of China , 2011 .