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Keywords = CLDF-score (0,2)-ideals

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19 pages, 1727 KiB  
Article
Complex Linear Diophantine Fuzzy Sets over AG-Groupoids with Applications in Civil Engineering
by Hao Guan, Faisal Yousafzai, Muhammad Danish Zia, Murad-ul-Islam Khan, Muhammad Irfan and Kostaq Hila
Symmetry 2023, 15(1), 74; https://doi.org/10.3390/sym15010074 - 27 Dec 2022
Cited by 8 | Viewed by 2712
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 [...] Read more.
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. Full article
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