Multi-Criteria Decision Making Methods Based on Interval-Valued Intuitionistic Fuzzy Sets

Fuzziness is inherent in decision data and decision making process. In this paper, interval-valued intuitionistic fuzzy set is used to capture fuzziness in multi-criteria decision making problems. The purpose of this paper is to develop a new method for solving multi-criteria decision making problem in interval-valued intuitionistic fuzzy environments. First, we introduce and discuss the concept of interval-valued intuitionistic fuzzy point operators. Using the interval-valued intuitionistic fuzzy point operators, we can reduce the degree of uncertainty of the elements in a universe corresponding to an interval-valued intuitionistic fuzzy set. Then, we define an evaluation function for the decision-making problem to measure the degrees to which alternatives satisfy and do not satisfy the decision-maker's requirement. Furthermore, a series of new score functions are defined for multi-criteria decision making problem based on the interval-valued intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.

[1]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[2]  Zeshui Xu,et al.  Generalized point operators for aggregating intuitionistic fuzzy information , 2010 .

[3]  Shyi-Ming Chen,et al.  Multiattribute decision making based on interval-valued intuitionistic fuzzy values , 2012, Expert Syst. Appl..

[4]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[5]  Zeshui Xu,et al.  Choquet integrals of weighted intuitionistic fuzzy information , 2010, Inf. Sci..

[6]  Michael W. Bridges,et al.  Distinguishing optimism from neuroticism (and trait anxiety, self-mastery, and self-esteem): a reevaluation of the Life Orientation Test. , 1994, Journal of personality and social psychology.

[7]  Jian-Da Wu,et al.  A forecasting system for car fuel consumption using a radial basis function neural network , 2012, Expert Syst. Appl..

[8]  Zun-Quan Xia,et al.  Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets , 2007, J. Comput. Syst. Sci..

[9]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[10]  Zeshui Xu,et al.  A method based on distance measure for interval-valued intuitionistic fuzzy group decision making , 2010, Inf. Sci..

[11]  Xiaohong Chen,et al.  Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making , 2010, Expert Syst. Appl..

[12]  Hiroshi Yokoyama,et al.  Coping availability and stress reduction for optimistic and pessimistic individuals , 2004 .

[13]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

[14]  Deng-Feng Li,et al.  Multiattribute decision making models and methods using intuitionistic fuzzy sets , 2005, J. Comput. Syst. Sci..

[15]  Shu Liu,et al.  Fractional programming methodology for multi-attribute group decision-making using IFS , 2009, Appl. Soft Comput..

[16]  Huawen Liu,et al.  Multi-criteria decision-making methods based on intuitionistic fuzzy sets , 2007, Eur. J. Oper. Res..

[17]  Deng-Feng Li,et al.  Linear programming method for multiattribute group decision making using IF sets , 2010, Inf. Sci..

[18]  Francisco Herrera,et al.  Fuzzy Sets and Their Extensions: Representation, Aggregation and Models , 2008 .

[19]  Uwe Fink,et al.  Fuzzy Sets Decision Making And Expert Systems , 2016 .

[20]  Humberto Bustince,et al.  Vague sets are intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[21]  Deng-Feng Li,et al.  Mathematical Programming Approach to multiattribute Decision Making under Intuitionistic Fuzzy Environments , 2008, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[22]  Ronald R. Yager,et al.  Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making , 2005, Int. J. Syst. Sci..

[24]  Alex M. Andrew,et al.  Uncertainty and Information: Foundations of Generalized Information Theory , 2006 .

[25]  Xiaohong Chen,et al.  Induced intuitionistic fuzzy Choquet integral operator for multicriteria decision making , 2011, Int. J. Intell. Syst..

[26]  Chung-Hsing Yeh,et al.  Simulation-based evaluation of defuzzification-based approaches to fuzzy multiattribute decision making , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[27]  Alexander Strashny.  Asymmetric loss utility: an analysis of decision under risk , 2004 .

[28]  Yong Yang,et al.  Intuitionistic Fuzzy Decision-Making with Similarity Measures and OWA Operator , 2013, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[29]  Guiwu Wei,et al.  Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information , 2009, Knowledge and Information Systems.

[30]  Jun Ye,et al.  Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment , 2009, Expert Syst. Appl..

[31]  Jun Ye.  Multicriteria decision-making method using the Dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets , 2012 .

[32]  Humberto Bustince,et al.  Construction theorems for intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[33]  Qiang Zhang,et al.  Fuzzy Multiple Attribute Decision Making Based on Interval Valued Intuitionistic Fuzzy Sets , 2006, 2006 IEEE International Conference on Systems, Man and Cybernetics.

[34]  Guiwu Wei,et al.  Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making , 2012, Expert Syst. Appl..

[35]  Hong-yu Zhang,et al.  Multi-Criteria Decision-Making Method Based on induced Intuitionistic Normal Fuzzy Related Aggregation Operators , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[36]  Jian Jhen Chen,et al.  Approach to Group Decision Making Based on Interval-Valued Intuitionistic Judgment Matrices , 2007 .

[37]  Chunqiao Tan,et al.  A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS , 2011, Expert Syst. Appl..

[38]  Zeshui Xu,et al.  Dynamic intuitionistic fuzzy multi-attribute decision making , 2008, Int. J. Approx. Reason..

[39]  Chunqiao Tan,et al.  Generalized intuitionistic fuzzy geometric aggregation operator and its application to multi-criteria group decision making , 2011, Soft Comput..

[40]  Jin-Han Park,et al.  Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems , 2009, Math. Comput. Model..

[41]  Qiang Zhang,et al.  The induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging operator and its application in decision making , 2013, Knowl. Based Syst..

[42]  Zhou-Jing Wang,et al.  A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information , 2011, Expert Syst. Appl..

[43]  K. Atanassov.  Operators over interval valued intuitionistic fuzzy sets , 1994 .

[44]  Michel Grabisch,et al.  Bipolar and bivariate models in multicriteria decision analysis: Descriptive and constructive approaches , 2008, Int. J. Intell. Syst..

[45]  Zeshui Xu,et al.  Intuitionistic preference relations and their application in group decision making , 2007, Inf. Sci..

[46]  Qiang Zhang,et al.  Some Continuous Aggregation Operators with Interval-Valued Intuitionistic Fuzzy Information and their Application to Decision Making , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[48]  Dug Hun Hong,et al.  Multicriteria fuzzy decision-making problems based on vague set theory , 2000, Fuzzy Sets Syst..

[49]  Qiang Zhang,et al.  Approaches to multiple-criteria group decision making based on interval-valued intuitionistic fuzzy Choquet integral with respect to the generalized λ-Shapley index , 2013, Knowl. Based Syst..

[50]  Deng-Feng Li,et al.  Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information , 2011, Appl. Soft Comput..

[51]  G. W. Wei,et al.  Some Geometric Aggregation Functions and their Application to Dynamic Multiple Attribute Decision Making in the Intuitionistic Fuzzy Setting , 2009, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[52]  Deng-Feng Li,et al.  Group Decision Making Methodology Based on the Atanassov's Intuitionistic Fuzzy Set Generalized OWA Operator , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[53]  C. Carver,et al.  Optimism, coping, and health: assessment and implications of generalized outcome expectancies. , 2009, Health psychology : official journal of the Division of Health Psychology, American Psychological Association.

[54]  Ting-Yu Chen,et al.  Bivariate models of optimism and pessimism in multi-criteria decision-making based on intuitionistic fuzzy sets , 2011, Inf. Sci..

[55]  Shyi-Ming Chen,et al.  Handling multicriteria fuzzy decision-making problems based on vague set theory , 1994 .

[56]  Ting-Yu Chen,et al.  An outcome-oriented approach to multicriteria decision analysis with intuitionistic fuzzy optimistic/pessimistic operators , 2010, Expert Syst. Appl..

[57]  Guodong Ye,et al.  An Approach for Multiple Attribute Group Decision Making Based on Intuitionistic Fuzzy Information , 2009, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[58]  H. Simon,et al.  A Behavioral Model of Rational Choice , 1955 .