The Similarity Measures for Linguistic q-Rung Orthopair Fuzzy Multi-Criteria Group Decision Making Using Projection Method

The linguistic q-rung orthopair fuzzy sets (Lq-ROFSs) can fully represent linguistic evaluation information by adjusting the parameter $q$ to describe the range of uncertain information. In this paper, we first propose a cosine similarity measure between Lq-ROFSs based on the concept of the cosine similarity measure between intuitionistic fuzzy sets. Considering the cosine similarity measure defined by this method does not satisfy the axiom of similarity measure, we propose the improved similarity measures of Lq-ROFSs according to the corresponding cosine similarity measure and Minkowski distance measure. The improved similarity measures of Lq-ROFSs can deal with the decision information not only from the point of view of algebra but also from the point of view of geometry, which are also proved satisfy the axiom of similarity measure. Furthermore, the similarity measures of Lq-ROFSs based on different linguistic scale functions are defined for considering the semantics of linguistic terms. In addition, we apply the proposed similarity measures of Lq-ROFSs to multi-criteria group decision making problems where the decision makers’ weights are determined by the projection of individual decision on the ideal decision results. Finally, a numerical example is applied to illustrate the feasibility of the proposed method and its effectiveness is verified by comparison with some existing methods. The sensitivity analysis and stability analysis of the proposed method are also given.

[1]  Ronald R. Yager,et al.  Generalized Orthopair Fuzzy Sets , 2017, IEEE Transactions on Fuzzy Systems.

[2]  Jun Ye,et al.  Cosine similarity measures for intuitionistic fuzzy sets and their applications , 2011, Math. Comput. Model..

[3]  Ronald R. Yager,et al.  Fermatean fuzzy sets , 2019, Journal of Ambient Intelligence and Humanized Computing.

[4]  Yuanyuan Liu,et al.  The New Similarity Measure and Distance Measure of a Hesitant Fuzzy Linguistic Term Set Based on a Linguistic Scale Function , 2018, Symmetry.

[5]  Donghai Liu,et al.  Cosine Similarity Measure between Hybrid Intuitionistic Fuzzy Sets and Its Application in Medical Diagnosis , 2018, Comput. Math. Methods Medicine.

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

[7]  Yong Yang,et al.  Some Results for Pythagorean Fuzzy Sets , 2015, Int. J. Intell. Syst..

[8]  H. Lee-Kwang,et al.  Similarity measure between fuzzy sets and between elements , 1994 .

[9]  Peide Liu,et al.  Multiple‐attribute group decision‐making based on power Bonferroni operators of linguistic q‐rung orthopair fuzzy numbers , 2018, Int. J. Intell. Syst..

[10]  Wang Ling-ling,et al.  Improved two-tuple linguistic representation model based on new linguistic evaluation scale , 2010 .

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

[12]  Dengfeng Li,et al.  New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions , 2002, Pattern Recognit. Lett..

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

[14]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..

[15]  Naif Alajlan,et al.  Approximate reasoning with generalized orthopair fuzzy sets , 2017, Inf. Fusion.

[16]  Yuanyuan Liu,et al.  Fermatean fuzzy linguistic set and its application in multicriteria decision making , 2018, Int. J. Intell. Syst..

[17]  Ronald R. Yager,et al.  Pythagorean fuzzy subsets , 2013, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS).

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

[19]  Wei Xing Zheng,et al.  Quasi-Synchronization of Discrete-Time Lur’e-Type Switched Systems With Parameter Mismatches and Relaxed PDT Constraints , 2020, IEEE Transactions on Cybernetics.

[20]  Zheng Pei,et al.  An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers , 2015, Int. J. Comput. Intell. Syst..

[21]  K. Atanassov New operations defined over the intuitionistic fuzzy sets , 1994 .

[22]  Xu Ze-shui A multi-attribute group decision making method based on term indices in linguistic evaluation scales , 2005 .

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

[24]  Xiaohong Chen,et al.  Some cosine similarity measures and distance measures between q‐rung orthopair fuzzy sets , 2019, Int. J. Intell. Syst..

[25]  Harish Garg,et al.  Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision‐making process , 2018, Int. J. Intell. Syst..

[26]  Peide Liu,et al.  Power average operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision making , 2017, J. Intell. Fuzzy Syst..

[27]  Zhen Zhou,et al.  Similarity Measures on Intuitionistic Fuzzy Sets , 2007, FSKD.

[28]  Donghua Zhou,et al.  A Descriptor System Approach to Stability and Stabilization of Discrete-Time Switched PWA Systems , 2018, IEEE Transactions on Automatic Control.

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