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Generalization of extent analysis method for solving multicriteria decision making problems involving intuitionistic fuzzy numbers

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Abstract

Analytic hierarchy process (AHP) is a widely used multicriteria decision making method. Chang’s extent analysis method (EAM) is appeared as a very popular fuzzy AHP approach. The aim of this paper is to generalize the EAM in intuitionistic fuzzy settings for effective modeling of imprecision and uncertainty inherent in nature. In this paper, special triangular intuitionistic fuzzy degree of possibility is defined for comparing two or more triangular intuitionistic fuzzy numbers (TIFNs) and some relevant theorems are introduced generating intuitionistic fuzzy numbers as weights of criteria or performance scores of alternatives. Based on TIFNs, a conversion scale for linguistic variables is proposed for generating a triangular intuitionistic fuzzy preference relation. The EAM is then generalized in intuitionistic fuzzy settings by proposing generalized intuitionistic fuzzy EAM using TIFNs and its arithmetic for deriving crisp priority vector from the triangular intuitionistic fuzzy preference relation. The advanced approach is validated through two numerical examples.

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Acknowledgements

The authors express their sincere gratitude to the reviewers for their constructive comments and suggestions in improving the quality of the manuscript. The authors are thankful to University of Kalyani for providing partial financial support through DST-PURSE program in carrying out the proposed research work.

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Authors and Affiliations

  1. Department of Mathematics, University of Kalyani, Kalyani, 741235, India

    Animesh Biswas

  2. Department of Mathematics, Acharya Jagadish Chandra Bose College, Kolkata, 700020, India

    Samir Kumar

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  1. Animesh Biswas
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  2. Samir Kumar
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Correspondence to Animesh Biswas.

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Biswas, A., Kumar, S. Generalization of extent analysis method for solving multicriteria decision making problems involving intuitionistic fuzzy numbers. OPSEARCH 56, 1142–1166 (2019). https://doi.org/10.1007/s12597-019-00413-z

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