New insights into rough approximations of a fuzzy set inspired by soft relations with decision making applications

Rani Sumaira Kanwal; Saqib Mazher Qurashi; Rizwan Gul; Alaa M. Abd El-latif; Tareq M. Al-shami; Faiza Tufail; Rani Sumaira Kanwal; Saqib Mazher Qurashi; Rizwan Gul; Alaa M. Abd El-latif; Tareq M. Al-shami; Faiza Tufail

doi:10.3934/math.2025444

AIMS Mathematics

2025, Volume 10, Issue 4: 9637-9673. doi: 10.3934/math.2025444

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Research article

New insights into rough approximations of a fuzzy set inspired by soft relations with decision making applications

1.
Department of Mathematics, Government College Women University, Faisalabad 38000, Pakistan
2.
Department of Mathematics, Government College University, Faisalabad 3800, Pakistan
3.
Department of Mathematics, Quaid-i-Azam University, Islamabad 44230, Pakistan
4.
Mathematics Department, College of Science, Northern Border University, Arar 91431, Saudi Arabia
5.
Department of Mathematics, Sana'a University, P.O.Box 1247 Sana'a, Yemen
6.
Jadara University Research Center, Jadara University, Jordan

Received: 21 January 2025 Revised: 02 March 2025 Accepted: 05 March 2025 Published: 25 April 2025
MSC : 03E72, 18B40

In the fields of mathematics and information sciences, binary relations are vital. Fuzzy sets (FSs), rough sets (RSs), and soft sets (SSs) are mathematical strategies that effectively handle ambiguous and imprecise data in practical situations. This work presents various properties of the roughness of fuzzy sets regarding foresets (F-sets) and aftersets (A-sets) using soft binary relations (SBRs). Initially, two pairs of fuzzy soft sets (FSSs) are obtained by approximating a fuzzy subset using an SBR, and their distinctive axiomatic systems are explored. Additionally, two types of fuzzy topologies that result from soft reflexive relations (SRRs) are examined. Numerous similarity relations allied with SBRs are also investigated. In addition, we present the accuracy measure and roughness measure for a fuzzy subset based on the mass assignment of the fuzzy subset through soft relations. Next, we outline a decision-making (DM) approach within the context of the proposed method. In addition, we provide two algorithms and decision phases. Ultimately, an applied example is used to evaluate the reliability of the decision processes. An extensive comparison study confirms the proposed method's feasibility and superiority over current DM methods.
- fuzzy set,
- rough set,
- soft set,
- decision-making,
- soft relation,
- accuracy measure,
- roughness measure
Citation: Rani Sumaira Kanwal, Saqib Mazher Qurashi, Rizwan Gul, Alaa M. Abd El-latif, Tareq M. Al-shami, Faiza Tufail. New insights into rough approximations of a fuzzy set inspired by soft relations with decision making applications[J]. AIMS Mathematics, 2025, 10(4): 9637-9673. doi: 10.3934/math.2025444

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Abstract

In the fields of mathematics and information sciences, binary relations are vital. Fuzzy sets (FSs), rough sets (RSs), and soft sets (SSs) are mathematical strategies that effectively handle ambiguous and imprecise data in practical situations. This work presents various properties of the roughness of fuzzy sets regarding foresets (F-sets) and aftersets (A-sets) using soft binary relations (SBRs). Initially, two pairs of fuzzy soft sets (FSSs) are obtained by approximating a fuzzy subset using an SBR, and their distinctive axiomatic systems are explored. Additionally, two types of fuzzy topologies that result from soft reflexive relations (SRRs) are examined. Numerous similarity relations allied with SBRs are also investigated. In addition, we present the accuracy measure and roughness measure for a fuzzy subset based on the mass assignment of the fuzzy subset through soft relations. Next, we outline a decision-making (DM) approach within the context of the proposed method. In addition, we provide two algorithms and decision phases. Ultimately, an applied example is used to evaluate the reliability of the decision processes. An extensive comparison study confirms the proposed method's feasibility and superiority over current DM methods.

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