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An essential and quite different class of functions is the triangular norm and its related operators (uninorms, nullnorms, and associative copulas). They are used widely in many disciplines, including fuzzy set theory, probability and statistics, decision sciences, and others. This paper proposes the notion of hybrid Ξ -norm and defines the concepts of Ξ -hybrid ideals, Ξ -hybrid h -ideals in a hemiring . Some equivalent conditions are obtained for a hybrid structure to be a Ξ -hybrid left h -ideal, and it is proved that every imaginable Ξ -hybrid left h -ideal of hemiring is a hybrid left h -ideal, but not conversely by an example. [ABSTRACT FROM AUTHOR]

In a right regular L A -semigroup, the hybrid ideals, hybrid interior ideals, hybrid (1,2)-ideals, hybrid generalized bi-ideals, and hybrid quasi-ideals are all introduced in this work. A right regular L A -semigroup has also been described in terms of its hybrid right and hybrid left ideals. Moreover, we obtain some equivalent conditions in terms of hybrid two-sided ideal, hybrid bi- (respectively, generalized bi-)ideal, hybrid quasi-ideal, hybrid interior ideal and hybrid (1 , 2) -ideal over right regular L A -semigroups. [ABSTRACT FROM AUTHOR]

Fuzzy sets, soft sets, and their generalisations have always been important tools for mathematicians and researchers working with uncertainty. Jun proposed a hybrid structure that combined the concepts of a fuzzy set and a soft set. It should be noted that hybrid structures are a combination of soft set and fuzzy set speculation. Our aim is to explore the concept of hybrid ordered ideals and hybrid interior ideals in ordered semirings, as well as look at some of their related properties, which is one of the important aspects of this paper. In order to investigate the structure theory of hybrid ideals in ordered semirings, we define hybrid composition and hybrid addition. We also establish and characterise the regularity of ordered semirings in terms of hybrid structures. [ABSTRACT FROM AUTHOR]

In this article. we propose the idea of hybrid congruences and hybrid strong ŋ -ideals of hemirings and we build an example that every liybrid strong ŋ-ideal is an hybrid h-ideal. but not conversely. The hybrid hemiring homomorphisins and quotient rings through the hybrid strong 11-ideals are also discussed. In addition. we look into the relationship between hybrid congruence and hybrid strong [1-ideals of hemirings. [ABSTRACT FROM AUTHOR]