INTERVAL LINGUISTIC FUZZY DECISION MAKING IN PERSPECTIVE OF PREFERENCE RELATIONS

Consistency analysis is a crucial topic for preference relations. This paper studies the consistency of interval linguistic fuzzy preference relations (ILFPRs) using the constrained interval linguistic arithmetic and introduces a new consistency definition. Then, several properties of this definition are researched. Meanwhile, the connection between this concept and a previous one is discussed. Following this concept, programming models for judging the consistency and for deriving consistent ILFPRs are constructed, respectively. Considering the case that incomplete ILFPRs may be obtained, a programming model for obtaining missing judgments following the consistency discussion is built. Afterwards, the consensus for group decision making (GDM) is studied and a model for adjusting individual ILFPRs to reach the consensus threshold is established. Consequently, an interactive procedure for GDM with ILFPRs is presented. A practical problem is provided to illustrate the utilization of the new algorithm and comparative discussion is offered.

[1]  Shouzhen Zeng,et al.  A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making , 2018, Int. J. Intell. Syst..

[2]  Fanyong Meng,et al.  An Approach to Uncertain Linguistic Multi-Attribute Group Decision Making Based on Interactive Index , 2015, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[3]  Zeshui Xu,et al.  Exploiting the priority weights from interval linguistic fuzzy preference relations , 2019, Soft Comput..

[4]  Zeshui Xu,et al.  Group decision making based on multiple types of linguistic preference relations , 2008, Inf. Sci..

[5]  Fanyong Meng,et al.  Entropy and similarity measure for Atannasov’s interval-valued intuitionistic fuzzy sets and their application , 2016, Fuzzy Optim. Decis. Mak..

[6]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning - II , 1975, Inf. Sci..

[7]  Gülçin Büyüközkan,et al.  A new GDM based AHP framework with linguistic interval fuzzy preference relations for renewable energy planning , 2014, J. Intell. Fuzzy Syst..

[8]  Zhibin Wu,et al.  A maximizing consensus approach for alternative selection based on uncertain linguistic preference relations , 2013, Comput. Ind. Eng..

[9]  Zeshui Xu,et al.  Incomplete linguistic preference relations and their fusion , 2006, Inf. Fusion.

[10]  Jana Krejcí,et al.  On additive consistency of interval fuzzy preference relations , 2017, Comput. Ind. Eng..

[11]  Luis Martínez-López,et al.  A Consensus Support System Model for Group Decision-Making Problems With Multigranular Linguistic Preference Relations , 2005, IEEE Transactions on Fuzzy Systems.

[12]  Fanyong Meng,et al.  Several Generalized Interval-Valued 2-Tuple Linguistic Weighted Distance Measures and their Application , 2017, Int. J. Fuzzy Syst..

[13]  Zeshui Xu,et al.  An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations , 2006, Decis. Support Syst..

[14]  Qiang Zhang,et al.  An approach to multi-attribute group decision making under uncertain linguistic environment based on the Choquet aggregation operators , 2014, J. Intell. Fuzzy Syst..

[15]  Yueh-Hsiang Chen,et al.  Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP , 2008, Inf. Sci..

[16]  Jin-Han Park,et al.  Uncertain linguistic harmonic mean operators and their applications to multiple attribute group decision making , 2011, Computing.

[17]  Weldon A. Lodwick,et al.  Constrained intervals and interval spaces , 2013, Soft Comput..

[18]  Francisco Herrera,et al.  Theory and Methodology Choice functions and mechanisms for linguistic preference relations , 2000 .

[19]  Francisco Herrera,et al.  Direct approach processes in group decision making using linguistic OWA operators , 1996, Fuzzy Sets Syst..

[20]  Enrique Herrera-Viedma,et al.  A consensus model for group decision making problems with linguistic interval fuzzy preference relations , 2012, Expert Syst. Appl..

[21]  Francisco Herrera,et al.  Group decision making with incomplete fuzzy linguistic preference relations , 2009, Int. J. Intell. Syst..

[22]  Huayou Chen,et al.  On compatibility of uncertain multiplicative linguistic preference relations based on the linguistic COWGA , 2013, Applied Intelligence.

[23]  Francisco Herrera,et al.  A 2-tuple fuzzy linguistic representation model for computing with words , 2000, IEEE Trans. Fuzzy Syst..

[24]  Shyi-Ming Chen,et al.  Autocratic Decision Making Using Group Recommendations Based on the ILLOWA Operator and Likelihood-Based Comparison Relations , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[25]  Yejun Xu,et al.  A Gower Plot-Based Approach to Ascertain and Adjust the Ordinal and Additive Inconsistencies for Fuzzy Linguistic Preference Relations , 2017, International Journal of Fuzzy Systems.

[26]  Z. S. Xu,et al.  Eowa And Eowg Operators For Aggregating Linguistic Labels Based On Linguistic Preference Relations , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[27]  Huayou Chen,et al.  Approaches to group decision making with linguistic preference relations based on multiplicative consistency , 2017, Comput. Ind. Eng..

[28]  Zeshui Xu,et al.  A method based on linguistic aggregation operators for group decision making with linguistic preference relations , 2004, Inf. Sci..

[29]  Fanyong Meng,et al.  A consistency-based approach to group decision making with uncertain multiplicative linguistic fuzzy preference relations , 2018, J. Intell. Fuzzy Syst..

[30]  Jana Krej.  On additive consistency of interval fuzzy preference relations , 2017 .

[31]  Zeshui Xu,et al.  Induced uncertain linguistic OWA operators applied to group decision making , 2006, Inf. Fusion.

[32]  Zeshui Xu,et al.  Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment , 2004, Inf. Sci..

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

[34]  Fanyong Meng,et al.  A consistency and consensus-based method to group decision making with interval linguistic preference relations , 2016, J. Oper. Res. Soc..

[35]  George J. Klir,et al.  Constrained fuzzy arithmetic: Basic questions and some answers , 1998, Soft Comput..

[36]  Zeshui Xu.  Deviation measures of linguistic preference relations in group decision making , 2005 .

[37]  Huayou Chen,et al.  On compatibility of uncertain additive linguistic preference relations and its application in the group decision making , 2011, Knowl. Based Syst..