In this paper, we investigated the notion of a linear Diophantine fuzzy set (LDFS) by using the concept of a score function to build the LDF-score left (right) ideals and LDF-score (0,2)-ideals in an AG-groupoid. We used these newly developed LDF-score ideals to characterize an AG-groupoid. We then use the proposed structure in multiattribute decision-making by considering bridge design selection and artificial intelligence-based chatbot selection.

This work addresses the issue of similarity measures between two temporal complex Atanassov’s intuitionistic fuzzy sets, many measures of similarity between complex Atanassov’s intuitionistic fuzzy sets. What was proposed before did not consider the abstention group influence, which may lead to counterintuitive results in some cases. A new structure of temporal complex Atanassov’s intuitionistic fuzzy sets is obtained. This set is formally generalized from a conventional Atanassov’s intuitionistic complex fuzzy sets. Here we analyze the limitations of the existing similarity measures. Then, a new similarity measure of temporal complex Atanassov’s intuitionistic fuzzy sets is proposed and several numeric examples are given to demonstrate the validity of the proposed measure. Finally, the proposed similarity measure is applied to pattern recognition and medical diagnosis.

The main purpose of this article is to utilize mathematical tools to rank alternatives for a decision making problem. In this regard, we developed different types of interval-valued intuitionistic fuzzy (IVIF) score ideals through unit-valued score (accuracy) functions. We used IVIF-score left (right) ideals to characterize an intra-regular class of an ordered Abel-Grassmann's-grououpoid (AG-groupoid) which is a semilattice of left simple AG-groupoids. We also established a connection between IVIF-score (0, 2)-ideals and IVIF-score left (right) ideals. Finally, we demonstrated how to use the interval valued intuitionistic fuzzy score $ (0, 2) $-ideals to identify the most suitable alternative in a decision making problem, and also explain how it can be applied to a problem of selecting a warehouse.

The concept of (∈,∈∨qk)-fuzzy hyperideal of an ordered LA-semihypergroup is introduced by the ordered fuzzy points, and related properties are investigated. We study the relations between different (∈,∈∨qk)-fuzzy hyperideal of an ordered LA-semihypergroup. Furthermore, we study some results on homomorphisms of (∈,∈∨qk)-fuzzy hyperideals.