Improving Consensus in Group Decision Making with Intuitionistic Reciprocal Preference Relations: A Granular Computing Approach

Intuitionistic reciprocal preference relations constitute a flexible and simple representation of decision makers' preference on a set of alternative options, while at the same time allow to accommodate degrees of hesitation inherent to all decision making processes. In this study, we present an approach to support the objective of reaching consensus in group decision making. By using intuitionistic reciprocal preference relations to model the assessments expressed by the decision makers, we propose the concept of a granular intuitionistic reciprocal preference relation in which each pairwise comparison is formed as an interval (information granule) in place of a single numeric value. This provides the flexibility that is required to improve the quality of consensus. With the purpose of illustrating and testing the performance of this approach, an experimental example is provided.

[1]  Salman Mohagheghi,et al.  Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems , 2008, IEEE Transactions on Evolutionary Computation.

[2]  Francesco Orciuoli,et al.  Linguistic fuzzy consensus model for collaborative development of fuzzy cognitive maps: a case study in software development risks , 2017, Fuzzy Optim. Decis. Mak..

[3]  Enrique Herrera-Viedma,et al.  A New Consensus Model for Group Decision Making Problems With Non-Homogeneous Experts , 2014, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[4]  Witold Pedrycz,et al.  Analytic Hierarchy Process (AHP) in Group Decision Making and its Optimization With an Allocation of Information Granularity , 2011, IEEE Transactions on Fuzzy Systems.

[5]  Luis Martínez-López,et al.  An Adaptive Consensus Support Model for Group Decision-Making Problems in a Multigranular Fuzzy Linguistic Context , 2009, IEEE Transactions on Fuzzy Systems.

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

[7]  Xuefeng Zheng,et al.  A dynamic rule extraction based on information granularity model for complete data , 2014, 2014 IEEE International Conference on Granular Computing (GrC).

[8]  Andrzej Bargiela,et al.  An Optimization of Allocation of Information Granularity in the Interpretation of Data Structures: Toward Granular Fuzzy Clustering , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[9]  Witold Pedrycz,et al.  An improvement of multiplicative consistency of reciprocal preference relations: A framework of granular computing , 2017, 2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC).

[10]  Enrique Herrera-Viedma,et al.  A framework for context-aware heterogeneous group decision making in business processes , 2016, Knowl. Based Syst..

[11]  Enrique Herrera-Viedma,et al.  Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks , 2010, Soft Comput..

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

[13]  Huchang Liao,et al.  Isomorphic Multiplicative Transitivity for Intuitionistic and Interval-Valued Fuzzy Preference Relations and Its Application in Deriving Their Priority Vectors , 2018, IEEE Transactions on Fuzzy Systems.

[14]  Zbigniew Michalewicz,et al.  Stability Analysis of the Particle Swarm Optimization Without Stagnation Assumption , 2016, IEEE Transactions on Evolutionary Computation.

[15]  J. Kacprzyk.  Group decision making with a fuzzy linguistic majority , 1986 .

[16]  Enrique Herrera-Viedma,et al.  Integrating experts' weights generated dynamically into the consensus reaching process and its applications in managing non-cooperative behaviors , 2016, Decis. Support Syst..

[17]  Witold Pedrycz,et al.  Clustering Granular Data and Their Characterization With Information Granules of Higher Type , 2015, IEEE Transactions on Fuzzy Systems.

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

[19]  Ido Millet,et al.  The Effectiveness of Alternative Preference Elicitation Methods in the Analytic Hierarchy Process , 1997 .

[20]  Bernard De Baets,et al.  Fuzzy Preference Modelling: Fundamentals and Recent Advances , 2008, Fuzzy Sets and Their Extensions: Representation, Aggregation and Models.

[21]  Francisco Herrera,et al.  Linguistic measures based on fuzzy coincidence for reaching consensus in group decision making , 1997, Int. J. Approx. Reason..

[22]  C. Hwang,et al.  Group Decision Making Under Multiple Criteria: Methods and Applications , 1986 .

[23]  Witold Pedrycz,et al.  Granular Encoders and Decoders: A Study in Processing Information Granules , 2017, IEEE Transactions on Fuzzy Systems.

[24]  J. Bezdek,et al.  A fuzzy relation space for group decision theory , 1978 .

[25]  Witold Pedrycz,et al.  A review of soft consensus models in a fuzzy environment , 2014, Inf. Fusion.

[26]  Min Deng,et al.  Study of Partial Discharge Localization Using Ultrasonics in Power Transformer Based on Particle Swarm Optimization , 2008, IEEE Transactions on Dielectrics and Electrical Insulation.

[27]  Marc Roubens,et al.  Fuzzy sets and decision analysis , 1997, Fuzzy Sets Syst..

[28]  Etienne E. Kerre,et al.  On the relationship between some extensions of fuzzy set theory , 2003, Fuzzy Sets Syst..

[29]  Enrique Herrera-Viedma,et al.  A Selection Process Based on Additive Consistency to Deal with Incomplete Fuzzy Linguistic Information , 2010, J. Univers. Comput. Sci..

[30]  Francisco Herrera,et al.  A model of consensus in group decision making under linguistic assessments , 1996, Fuzzy Sets Syst..

[31]  Guan-Jun Zhang,et al.  Acoustic localization of partial discharge sources in power transformers using a particle-swarm-optimization-route-searching algorithm , 2017, IEEE Transactions on Dielectrics and Electrical Insulation.

[32]  Yucheng Dong,et al.  The interactive consensus reaching process with the minimum and uncertain cost in group decision making , 2017, Appl. Soft Comput..

[33]  Francisco Chiclana,et al.  Consistency of 2D and 3D distances of intuitionistic fuzzy sets , 2012, Expert Syst. Appl..

[34]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.