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Weight computation of criteria in a decision-making problem by knowledge measure with intuitionistic fuzzy set and interval-valued intuitionistic fuzzy set

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Abstract

The aim of this study is to propose an objective method for determining weights of criteria (also called attributes) based on a new measure of intuitionistic fuzzy information, called knowledge measure, in a real-world multi-criteria decision-making problem under intuitionistic fuzzy and interval-valued intuitionistic fuzzy environment. To address this issue, we first analyze the existing entropy measures and show that their use in objective weight determination process may lead us to produce unreliable weights of criteria by citing appropriate examples. Then we analyze important properties of knowledge measure of intuitionistic fuzzy set (IFS) and also define knowledge measure for interval-valued intuitionistic fuzzy set. Then a new method to determine the weights of criteria is developed on the basis of knowledge measure where information about criteria weights is completely unknown and partly known. A real-life example is presented to illustrate the proposed weight determination method and a comparative analysis is carried out to indicate the practicality and effectiveness of knowledge-based weight-generation method under both intuitionistic fuzzy and interval-valued intuitionistic fuzzy environment. Finally, we formulate the axioms for knowledge measure associated with IFSs and we also propose families (classes) of knowledge measures.

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Acknowledgments

We are very grateful to the editors and the anonymous reviewers for their insightful and constructive comments and suggestions for the improvement of the manuscript. The first author gratefully acknowledges the financial support provided by the Ministry of Human Resource development, Government of India, and the second author gratefully acknowledges the financial support provided by the Council of Scientific and Industrial Research, New Delhi,India, under Award 09/1023(007)/2011-EMR-I.

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Authors and Affiliations

  1. Department of Mathematics, IIT Patna, Patna, 800013, India

    Satyajit Das, Bapi Dutta & Debashree Guha

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  1. Satyajit Das
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  3. Debashree Guha
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Correspondence to Debashree Guha.

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Communicated by S. Deb, T. Hanne and S. Fong.

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Das, S., Dutta, B. & Guha, D. Weight computation of criteria in a decision-making problem by knowledge measure with intuitionistic fuzzy set and interval-valued intuitionistic fuzzy set. Soft Comput 20, 3421–3442 (2016). https://doi.org/10.1007/s00500-015-1813-3

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