Complex Linear Diophantine Fuzzy Sets over AG-Groupoids with Applications in Civil Engineering

Abstract

Intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and q-rung orthopair fuzzy sets (q-ROFS) are among those concepts which are widely used in real-world applications. However, these theories have their own limitations in terms of membership and non-membership functions, as they cannot be obtained from the whole unit plane. To overcome these restrictions, we developed the concept of a complex linear Diophantine fuzzy set (CLDFS) by generalizing the notion of a linear Diophantine fuzzy set (LDFS). This concept can be applied to real-world decision-making problems involving complex uncertain information. The main motivation behind this paper is to study the applications of CLDFS in a non-associative algebraic structure (AG-groupoid), which has received less attention as compared to associative structures. We characterize a strongly regular AG-groupoid in terms of newly developed CLDF-score left (right) ideals and CLDF-score (0,2)-ideals. Finally, we construct a novel approach to decision-making problems based on the proposed CLDF-score ideals, and some practical examples from civil engineering are considered to demonstrate the flexibility and clarity of the initiated CLDF-score ideals.

Applications of AG-Groupoids in Decision-Making via Linear Diophantine Fuzzy Sets

“…For the interest of the reader, some recent applications of AG-groupoids in decision-making can be found, for example, in [5,6].…”

2-Absorbing Vague Weakly Complete Γ-Ideals in Γ-Rings

“…Nimbhorkar et al [31] suggested a fuzzy weakly 2-absorbing ideal of a lattice. Some notable recent developments in fuzzy set theory can be found, for example, in artificial intelligence [32], supply chain [33], symmetry [34], computational intelligence [35], and some of them use fuzzy set theory in algebraic systems with different applications such as civil engineering [36][37][38][39], etc., where both symmetry and asymmetry have occurred.…”