Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision Making

Muhammad Zishan Anwar, Shahida Bashir, Muhammad Shabir and Majed G. Alharbi
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Muhammad Zishan Anwar: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
Shahida Bashir: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
Muhammad Shabir: Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Majed G. Alharbi: Department of Mathematics, College of Science and Arts, Almithnab, Qassim University, Buridah 51931, Saudi Arabia

Mathematics, 2021, vol. 9, issue 20, 1-22

Abstract: Multigranulation rough set (MGRS) based on soft relations is a very useful technique to describe the objectives of problem solving. This MGRS over two universes provides the combination of multiple granulation knowledge in a multigranulation space. This paper extends the concept of fuzzy set Shabir and Jamal in terms of an intuitionistic fuzzy set (IFS) based on multi-soft binary relations. This paper presents the multigranulation roughness of an IFS based on two soft relations over two universes with respect to the aftersets and foresets. As a result, two sets of IF soft sets with respect to the aftersets and foresets are obtained. These resulting sets are called lower approximations and upper approximations with respect to the aftersets and with respect to the foresets. Some properties of this model are studied. In a similar way, we approximate an IFS based on multi-soft relations and discuss their some algebraic properties. Finally, a decision-making algorithm has been presented with a suitable example.

Keywords: intuitionistic fuzzy set; soft relation; multigranulation roughness; decision making (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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