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Interval-Valued Intuitionistic Fuzzy Soft Rough Approximation Operators and Their Applications in Decision Making Problem

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  • Anjan Mukherjee

    (Tripura University)

  • Abhik Mukherjee

    (ITS Dental College)

Abstract

It has been found that fuzzy sets, rough sets and soft sets are closely related concepts. Many complicated problems in economics, engineering, social sciences, medical science and many other fields involve uncertain data. These problems, which one comes in real life, cannot be solved using classical mathematical methods. There are several well-known theories to describe uncertainty, for instance, fuzzy set theory, rough set theory, and other mathematical tools. But all of these theories have their inherit difficulties as pointed out by D. Molodtsov. In 1999, D. Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainties. The concept of rough sets, proposed by Z. Pawlak as a framework for the construction of approximations of concepts. It is a formal tool for modeling and processing insufficient and incomplete information. Zhou and Wu first proposed the concept of intuitionistic fuzzy rough sets (IFrough sets). The aim of this paper is to introduce the concept of interval-valued intuitionistic fuzzy soft rough sets (IVIFS rough sets). We also investigate some properties of IVIFS rough approximation operators. Some basic operations and properties are studied. Lastly applications have been shown in decision making problems.

Suggested Citation

  • Anjan Mukherjee & Abhik Mukherjee, 2022. "Interval-Valued Intuitionistic Fuzzy Soft Rough Approximation Operators and Their Applications in Decision Making Problem," Annals of Data Science, Springer, vol. 9(3), pages 611-625, June.
    • Handle: RePEc:spr:aodasc:v:9:y:2022:i:3:d:10.1007_s40745-022-00370-3
    DOI: 10.1007/s40745-022-00370-3
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    1. James M. Tien, 2017. "Internet of Things, Real-Time Decision Making, and Artificial Intelligence," Annals of Data Science, Springer, vol. 4(2), pages 149-178, June.
    2. Ashoke Kumar Bera & Dipak Kumar Jana & Debamalya Banerjee & Titas Nandy, 2021. "A Two-Phase Multi-criteria Fuzzy Group Decision Making Approach for Supplier Evaluation and Order Allocation Considering Multi-objective, Multi-product and Multi-period," Annals of Data Science, Springer, vol. 8(3), pages 577-601, September.
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