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On hybrid k-ideals in semirings

Authors
Elavarasan, B.Muhiuddin, G.Porselvi, K.Jun, Y. B.
Issue Date
Mar-2023
Publisher
IOS PRESS
Keywords
Semiring; hybrid structure; ideal; hybrid product; k-ideal; hybrid k-product; hybrid ideals; hybrid k-ideals
Citation
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, v.44, no.3, pp 4681 - 4691
Pages
11
Indexed
SCIE
SCOPUS
Journal Title
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
Volume
44
Number
3
Start Page
4681
End Page
4691
URI
https://scholarworks.gnu.ac.kr/handle/sw.gnu/68709
DOI
10.3233/JIFS-222335
ISSN
1064-1246
1875-8967
Abstract
Many uncertainties arise in real-world problems, making them impossible to solve using conventional approaches. Researchers all over the world have developed new mathematical theories like fuzzy set theory and rough set theory to better understand the uncertainties that occur in various fields. Soft set theory, which was recently introduced, offers a novel approach to real-world problem solving by removing the need to set the membership function. This is helpful in resolving a variety of issues, and much progress is being made these days. Recently, Jun introduced the concept of a hybrid structure, which blends the concepts of a fuzzy set as well as a soft set. In this paper, we define the hybrid k-sum and hybrid k-product of k-ideals of semiring and investigate their properties. We illustrate with an example that the hybrid sum and hybrid product of two k-ideals are not always hybrid ideals. We also describe semiring regularity constraints in terms of hybrid k-ideal structures.
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