A novel study on fuzzy ideals and fuzzy filters of ordered *-semigroups

Feng, Xinyang; Tang, Jian; Davvaz, Bijan; Luo, Yanfeng

doi:10.3233/jifs-161740

Cited by 2 publications

(1 citation statement)

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“…For more details, the reader is referred to Jun et al (2009); Shabir and Khan (2011); Xie and Tang (2008). In particular, Feng et al (2017) defined and studied fuzzy ideals and fuzzy filters of ordered * -semigroups, and extended some fuzzy notions of ordered semigroup theory.…”

Section: Introductionmentioning

confidence: 99%

A novel investigation on fuzzy hyperideals in ordered $$*$$-semihypergroups

Tang

Yaqoob

2021

Comp. Appl. Math.

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In this paper, we study the ordered * -semihypergroups in terms of fuzzy subsets in detail and define a unary operation on the set of all the fuzzy subsets of an ordered * -semihypergroup.To begin with, we define and study the fuzzy hyperideals of an ordered * -semihypergroup.In particular, we investigate the properties of fuzzy hyperideals generated by ordered fuzzy points of an ordered * -semihypergroup. Furthermore, we introduce the concepts of prime, weakly prime and semiprime fuzzy hyperideals of ordered * -semihypergroups. Especially, the relationships among these three types of fuzzy hyperideals are established. In the sequel, we give some characterizations of intra-regular ordered * -semihypergroups and semisimple ordered * -semihypergroups in terms of fuzzy hyperideals. Especially, we prove that an ordered * -semihypergroup S is semisimple if and only if every fuzzy hyperideal of S can be expressed as the intersection of all weakly prime fuzzy hyperideals of S containing it.

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Section: Introductionmentioning

confidence: 99%