k-Fuzzy Ideals of Ternary Semirings



The notion of k-fuzzy ideals of semirings was intro-duced by Kim and Park in 1996. In 2003, Dutta and Kar introduced a notion of ternary semirings. This structure is a generalization of ternary rings and semirings. The main purpose of this paper is to introduce and study k-fuzzy ideals in ternary semirings analogous to k-fuzzy ideals in semirings considered by Kim and Park.

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    • "Moreover, they were studied in various kinds of ternary algebraic systems. For example, Kavikumar and Khamis [10] studied fuzzy ideals and fuzzy quasiideals in ternary semirings, Kavikumar, Khamis and Jun [11] studied fuzzy bi-ideals in ternary semirings, Chinram and Malee studied L-fuzzy ideals [1] and k-fuzzy ideals [15] in ternary semirings, Davvaz [3] studied fuzzy hyperideals in ternary semihyperrings and Chinram and Saelee [2] studied fuzzy ideals and fuzzy filters of ordered ternary semigroups, etc. Rough ideals in semigroups were studied by Kuroki [12]. In [22], Xiao and Zhang studied rough prime ideals and rough fuzzy prime ideals. "
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    ABSTRACT: A ternary semigroup is a nonempty set together with a ternary multiplication which is associative. Any semi-group can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup. The notion of fuzzy sets was introduced by Zadeh in 1965 and that of rough sets by Pawlak in 1982. Applications of the fuzzy set theory and rough set theory have been found in various fields. The theory of fuzzy sets and rough sets were studied in various kinds of algebraic systems. In this paper, we study rough, fuzzy and rough fuzzy bi-ideals of ternary semigroups. Index Terms—bi ideals, rough bi-ideals, fuzzy bi-ideals, rough fuzzy bi-ideals, ternary semigroups.


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