Abstract
In this article, we establish the idea of falling fuzzy k -ideals in hemirings through the falling shadow theory and fuzzy sets. We shall express the relations between fuzzy k -ideals and falling fuzzy k -ideals in hemirings. In particular, we shall establish different characterizations of k -hemiregular hemirings in the perfect positive correlation and independent probability space by means of falling fuzzy k -ideals.
Highlights
Semiring theory had been developed by Vandiver in order to generalize rings [1]
By taking inspiration from [30], the notion of falling fuzzy k-ideals of a hemiring is introduced on the basis of the theory of falling shadows and fuzzy sets
This theory is widely applicable in information science and intelligent and fuzzy systems
Summary
Semiring theory had been developed by Vandiver in order to generalize rings [1]. Semirings are used in major applied mathematical fields, like automata and computer sciences [2, 3]. By taking inspiration from [30], the notion of falling fuzzy k-ideals of a hemiring is introduced on the basis of the theory of falling shadows and fuzzy sets. This theory is widely applicable in information science and intelligent and fuzzy systems. This research article is arranged such that the first section briefly describes the history and reviews the literature of fuzzy set theory, ideals in hemirings, and the theory of falling shadows.
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