On Covering-Based Rough Intuitionistic Fuzzy Sets

R. Mareay, Ibrahim Noaman, Radwan Abu-Gdairi () and M. Badr
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R. Mareay: Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt
Ibrahim Noaman: Department of Mathematics, Faculty of Science and Arts in Al-Mandaq, AL Baha University, Al Bahah P.O. Box 1988, Saudi Arabia
Radwan Abu-Gdairi: Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13133, Jordan
M. Badr: Department of Mathematics, Faculty of Science, New Valley University, El-Kharja 72511, Egypt

Mathematics, 2022, vol. 10, issue 21, 1-8

Abstract: Intuitionistic Fuzzy Sets ( I F S s ) and rough sets depending on covering are important theories for dealing with uncertainty and inexact problems. We think the neighborhood of an element is more realistic than any cluster in the processes of classification and approximation. So, we introduce intuitionistic fuzzy sets on the space of rough sets based on covering by using the concept of the neighborhood. Three models of intuitionistic fuzzy set approximation space based on covering are defined by using the concept of neighborhood. In the first and second model, we approximate IFS by rough set based on one covering ( C ) by defining membership and non-membership degree depending on the neighborhood. In the third mode, we approximate IFS by rough set based on family of covering ( C i ) by defining membership and non-membership degree depending on the neighborhood. We employ the notion of the neighborhood to prove the definitions and the features of these models. Finlay, we give an illustrative example for the new covering rough I F approximation structure.

Keywords: neighborhood; intuitionistic fuzzy sets; covering lower and upper approximation space; rough intuitionistic fuzzy sets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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