Multi-criteria game model based on the pairwise comparisons of strategies with Z-numbers

Abstract The Z-number is the most general representation of real-life information with reliability, and it also exhibits the highest descriptive power from the perspective of human cognition. This study focuses on the development of a computationally simple and effective Z-number model to address game problems by systematically comparing pairwise strategies derived from different players. The processing of Z-numbers requires computing fuzzy and probabilistic uncertainties; then, the cloud model is suggested to handle bimodal restriction in Z-numbers. In this manner, a novel concept of asymmetric normal Z-value (ANZ) is proposed. Subsequently, the concordance/discordance index and outranking relations of ANZs are suggested based on classic outranking rules. Next, an innovative game model is established by modeling the outranking relations of strategies of different players under multiple criteria. Finally, an illustrative example concerning enterprise market competition is provided to demonstrate the established model.

[1]  Rafik A. Aliev,et al.  The arithmetic of discrete Z-numbers , 2015, Inf. Sci..

[2]  Samarjit Kar,et al.  A multi-criteria decision making for renewable energy selection using Z-numbers in uncertain environment , 2018 .

[3]  Saeed Zolfaghari,et al.  'Buy n times, get one free' loyalty cards: Are they profitable for competing firms? A game theoretic analysis , 2018, Eur. J. Oper. Res..

[4]  Juan Carlos Leyva López,et al.  A credit ranking model for a parafinancial company based on the ELECTRE-III method and a multiobjective evolutionary algorithm , 2017, Appl. Soft Comput..

[5]  Sankar K. Pal,et al.  Z*-numbers: Augmented Z-numbers for machine-subjectivity representation , 2015, Inf. Sci..

[6]  J. Nash.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[7]  Hong-yu Zhang,et al.  Cloud decision support model for selecting hotels on TripAdvisor.com with probabilistic linguistic information , 2018 .

[8]  Tofigh Allahviranloo,et al.  Two new methods for ranking of Z‐numbers based on sigmoid function and sign method , 2018, Int. J. Intell. Syst..

[9]  B. Roy.  THE OUTRANKING APPROACH AND THE FOUNDATIONS OF ELECTRE METHODS , 1991 .

[10]  R.A. Aliev,et al.  The arithmetic of continuous Z-numbers , 2016, Inf. Sci..

[11]  Christian Esposito,et al.  A coral-reefs and Game Theory-based approach for optimizing elastic cloud resource allocation , 2018, Future Gener. Comput. Syst..

[12]  Yu Luo,et al.  Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers , 2017, J. Intell. Fuzzy Syst..

[13]  Wang Yingming,et al.  Using the method of maximizing deviation to make decision for multiindices , 2012 .

[14]  Jian-qiang Wang,et al.  Outranking Decision-Making Method with Z-Number Cognitive Information , 2018, Cognitive Computation.

[15]  Alexander Gegov,et al.  Interactive TOPSIS Based Group Decision Making Methodology Using Z-Numbers , 2016, Int. J. Comput. Intell. Syst..

[16]  Chao Fu,et al.  Determining attribute weights for multiple attribute decision analysis with discriminating power in belief distributions , 2017, Knowl. Based Syst..

[17]  Elizabeth Chang,et al.  ZBWM: The Z-number extension of Best Worst Method and its application for supplier development , 2018, Expert Syst. Appl..

[18]  Witold Pedrycz,et al.  Functions defined on a set of Z-numbers , 2018, Inf. Sci..

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

[20]  Yong Hu,et al.  An evidential game theory framework in multi-criteria decision making process , 2014, Appl. Math. Comput..

[21]  Deyi Li,et al.  A new cognitive model: Cloud model , 2009 .

[22]  Lotfi A. Zadeh,et al.  A Note on Z-numbers , 2011, Inf. Sci..

[23]  Yu Yang,et al.  SMAA-based model for decision aiding using regret theory in discrete Z-number context , 2018, Appl. Soft Comput..

[24]  Bingyi Kang,et al.  Decision Making Using Z-numbers under Uncertain Environment , 2012 .

[25]  Mubarak Alrashoud.  Multi Attribute Decision Making Using Optimistic/Pessimistic Z-Numbers , 2018, IEEE Access.

[26]  Shu-Ping Wan,et al.  A cosine similarity based QUALIFLEX approach with hesitant fuzzy linguistic term sets for financial performance evaluation , 2018, Appl. Soft Comput..

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

[28]  Yong Deng,et al.  Total utility of Z-number , 2017, Applied Intelligence.

[29]  Orhan Türkbey,et al.  Fuzzy logic based game theory applications in multi-criteria decision making process , 2013, J. Intell. Fuzzy Syst..

[30]  Rafik A. Aliev,et al.  Ranking of Z-Numbers and Its Application in Decision Making , 2016, Int. J. Inf. Technol. Decis. Mak..

[31]  S. Greco,et al.  A robust ranking method extending ELECTRE III to hierarchy of interacting criteria, imprecise weights and stochastic analysis , 2017 .

[32]  Jian-qiang Wang,et al.  Z-VIKOR Method Based on a New Comprehensive Weighted Distance Measure of Z-Number and Its Application , 2018, IEEE Transactions on Fuzzy Systems.

[33]  L. Shapley.  A note on the Lemke-Howson algorithm , 1974 .

[34]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .