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

Mathematics

Majed G. Alharbi¹  Muhammad Shabir²  Muhammad Zishan Anwar³  Shahida Bashir³ 

[1] Department of Mathematics, College of Arts and Sciences, Methnab, Qassim University, Buraydah 52571, Saudi Arabia;Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan;Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan;

关键词: intuitionistic fuzzy set;    soft relation;    multigranulation roughness;    decision making;   

DOI  :  10.3390/math9202587

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown