Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making

Hesitant-IFN has been proposed which is a synthesized intuitionistic fuzzy number.Some aggregation operators and their good properties have been studied.Hesitant-IFPR and its complementary form (Hesitant-IFCPR) have been produced.The approximate consistency tests and decision-making steps have been constructed.Two case studies are presented to illustrate the proposed methods and tests. Preference relations are a powerful quantitative decision approach that assists decision makers in expressing their preferences over alternatives. In real-life applications, decision makers may not be able to provide exact preference information with crisp numbers. To solve this problem, a hesitant-intuitionistic fuzzy number (Hesitant-IFN) is proposed in this paper, and a proposal for the hesitant-intuitionistic fuzzy preference relation (Hesitant-IFPR) and its complementary form (Hesitant-IFCPR) for uncertain preference information are presented. Compared with other preference relations, the proposed relations use hesitant fuzzy elements (HFEs) to express the priority intensities of decision makers and produce the corresponding non-priority intensities by a conversion formula. In addition, we have deduced the operational laws and comparative methods of Hesitant-IFNs and used such information to investigate the corresponding aggregation operators and the approximate consistency tests. Next, we have constructed a group decision-making approach under a hesitant-intuitionistic fuzzy environment. Finally, two case studies are presented to illustrate the preference relations, the approximate consistency tests and the group decision method.

[1]  Zeshui Xu,et al.  Multiplicative Consistency of hesitant fuzzy Preference Relation and its Application in Group Decision Making , 2014, Int. J. Inf. Technol. Decis. Mak..

[2]  Janusz Kacprzyk,et al.  A consensus‐reaching process under intuitionistic fuzzy preference relations , 2003, Int. J. Intell. Syst..

[3]  Guo-Jun Wang,et al.  Intuitionistic fuzzy sets and L-fuzzy sets , 2000, Fuzzy Sets Syst..

[4]  Thomas L. Saaty,et al.  On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process , 2007, Math. Comput. Model..

[5]  Zaiwu Gong,et al.  Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations , 2009, Comput. Ind. Eng..

[6]  Zhou Zhen,et al.  A Method for Priorities of Triangular Fuzzy Number Complementary Judgment Matrices , 2005 .

[7]  S. Ovchinnikov,et al.  On strict preference relations , 1991 .

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

[9]  Zeshui Xu,et al.  Methods for fuzzy complementary preference relations based on multiplicative consistency , 2011, Comput. Ind. Eng..

[10]  T. L. Saaty.  A Scaling Method for Priorities in Hierarchical Structures , 1977 .

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

[12]  Li-Wei Lee,et al.  Group decision making with incomplete fuzzy preference relations based on the additive consistency and the order consistency , 2012, Expert Syst. Appl..

[13]  S. Orlovsky.  Decision-making with a fuzzy preference relation , 1978 .

[14]  Ying-Ming Wang,et al.  A goal programming method for obtaining interval weights from an interval comparison matrix , 2007, Eur. J. Oper. Res..

[15]  R. Ramanathan,et al.  Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members' weightages , 1994 .

[16]  Yue Zhao,et al.  The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity , 2011, Expert Syst. Appl..

[17]  Yejun Xu,et al.  Incomplete interval fuzzy preference relations and their applications , 2014, Comput. Ind. Eng..

[18]  Zeshui Xu,et al.  Preference Relations Based on Intuitionistic Multiplicative Information , 2013, IEEE Transactions on Fuzzy Systems.

[19]  Gregory W. Fischer,et al.  Prescriptive decision science: Problems and opportunities , 1989 .

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

[21]  Zhou-Jing Wang,et al.  A note on "Incomplete interval fuzzy preference relations and their applications" , 2014, Comput. Ind. Eng..

[22]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[23]  V. E. Zhukovin,et al.  A decision making model with vector fuzzy preference relation , 1987 .

[24]  Zeshui Xu,et al.  Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives , 2014, Comput. Ind. Eng..

[25]  Zeshui Xu,et al.  Prioritized multi-criteria decision making based on preference relations , 2013, Comput. Ind. Eng..

[26]  Zeshui Xu,et al.  A survey of preference relations , 2007, Int. J. Gen. Syst..

[27]  Zeshui Xu,et al.  Group decision making based on intuitionistic multiplicative aggregation operators , 2013 .

[28]  Yingjun Xu,et al.  On group decision making with four formats of incomplete preference relations , 2011, Comput. Ind. Eng..

[29]  Francisco Herrera,et al.  An optimization-based approach to adjusting unbalanced linguistic preference relations to obtain a required consistency level , 2015, Inf. Sci..

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

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

[32]  Zeshui Xu,et al.  Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations , 2013, Appl. Soft Comput..

[33]  S. Orlovsky.  Decision-making with a fuzzy preference relation , 1978 .

[34]  XuZeshui,et al.  Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making , 2015 .

[35]  Ozan Çakir,et al.  On the order of the preference intensities in fuzzy AHP , 2008, Comput. Ind. Eng..

[36]  Fang Liu,et al.  Acceptable consistency analysis of interval reciprocal comparison matrices , 2009, Fuzzy Sets Syst..

[37]  Z. Xu,et al.  Iterative algorithms for improving consistency of intuitionistic preference relations , 2014, J. Oper. Res. Soc..

[38]  Zeshui Xu,et al.  Hesitant fuzzy information aggregation in decision making , 2011, Int. J. Approx. Reason..

[39]  Vicenç Torra,et al.  On hesitant fuzzy sets and decision , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[40]  Zeshui Xu,et al.  Analytic hierarchy process-hesitant group decision making , 2014, Eur. J. Oper. Res..

[41]  Zeshui Xu,et al.  Group decision making model and approach based on interval preference orderings , 2013, Comput. Ind. Eng..

[42]  Francisco Herrera,et al.  Cardinal Consistency of Reciprocal Preference Relations: A Characterization of Multiplicative Transitivity , 2009, IEEE Transactions on Fuzzy Systems.

[43]  Horace W. Brock,et al.  The Problem of "Utility Weights" in Group Preference Aggregation , 1980, Oper. Res..

[44]  Ying-Ming Wang,et al.  Fuzzy preference relations: Aggregation and weight determination , 2007, Comput. Ind. Eng..

[45]  Wei Zhou,et al.  Two Atanassov intuitionistic fuzzy weighted aggregation operators based on a novel weighted method and their application , 2014, J. Intell. Fuzzy Syst..

[46]  Bernard De Baets,et al.  Cyclic Evaluation of Transitivity of Reciprocal Relations , 2006, Soc. Choice Welf..

[47]  Humberto Bustince,et al.  Mathematical analysis of interval-valued fuzzy relations: Application to approximate reasoning , 2000, Fuzzy Sets Syst..

[48]  Zeshui Xu,et al.  Algorithms for improving consistency or consensus of reciprocal [0, 1]-valued preference relations , 2013, Fuzzy Sets Syst..

[49]  Francisco Herrera,et al.  Group Decision-Making Model With Incomplete Fuzzy Preference Relations Based on Additive Consistency , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).