The idea of intuitionistic fuzzy sets (IFSs) is a reasonable soft computing construct for resolving ambiguity and vagueness encountered in decision-making situations. Cases like pattern recognition, diagnostic analysis, etc. have been explored based on intuitionistic fuzzy pairs via similarity-distance measures. Many similarity and distance techniques have been proposed and used to solve decision-making situations. Though the existing similarity measures and their distance counterparts are somewhat significant, they possess some weakness in terms of accuracy and their alignments with the concept of IFSs which needed to be strengthened to enhance reliable outputs. As a consequent, this paper introduces a novel similarity-distance technique with better performance rating. A comparative analysis is presented to showcase the advantages of the novel similarity-distance over similar existing approaches. Some attributes of the similarity-distance technique are presented. Furthermore, the applications of the novel similaritydistance technique in sundry decision-making situations are explored.

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The idea of composition relations on Fermatean fuzzy sets based on the maximum-extreme values approach has been investigated and applied in decision making problems. However, from the perspective of the measure of central tendency, this approach is not reliable because of the information loss occasioned by the use of extreme values. Based on this limitation, we introduce an enhanced Fermatean fuzzy composition relation with a better performance rating based on the maximum-average approach. An easy-to-follow algorithm based on this approach is presented with numerical computations. An application of Fermatean fuzzy composition relations is discussed in diagnostic analysis where diseases and patients are mirrored as Fermatean fuzzy pairs characterized with some related symptoms. To ascertain the veracity of the novel Fermatean fuzzy composition relation, a comparative analysis is presented to showcase the edge of this novel Fermatean fuzzy composition relation over the existing Fermatean fuzzy composition relation.

Fuzzy multigroup is an application of fuzzy multiset to group theory. Although, a lots have been done on the theory of fuzzy multigroups, some group's theoretic notions could still be investigated in fuzzy multigroup context. Certainly, the idea of commutator is one of such group's theoretic notions yet to be studied in the environment of fuzzy multigroups. Hence, the aim of this article is to establish the notion of commutator in fuzzy multigroup setting. A number of some related results are obtained and characterized. Among several results that are obtained, it is established that, if $A$ and $B$ are fuzzy submultigroups of a fuzzy multigroup $C$, then $[A, B]\subseteq A\cup B$ holds. Some homomorphic properties of commutator in fuzzy multigroup context are discussed. The notion of admissible fuzzy submultisets $A$ and $B$ of $C\in FMG(X)$ under an operator domain $\mathcal{D}$ is explicated, and it is shown that $(A,B)$ and $[A,B]$ are $\mathcal{D}$-admissible.