Fuzzy ideals of ordered semigroups with fuzzy orderings

• Autorzy: Xiaokun Huang , Qingguo Li
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to introduce the notions of ∈, ∈ ∨qk-fuzzy ideals of a fuzzy ordered semigroup with the ordering being a fuzzy relation. Several characterizations of ∈, ∈ ∨qk-fuzzy left (resp. right) ideals and ∈, ∈ ∨qk-fuzzy interior ideals are derived. The lattice structures of all ∈, ∈ ∨qk-fuzzy (interior) ideals on such fuzzy ordered semigroup are studied and some methods are given to construct an ∈, ∈ ∨qk-fuzzy (interior) ideals from an arbitrary fuzzy subset. Finally, the characterizations of generalized semisimple fuzzy ordered semigroups in terms of ∈, ∈ ∨qk-fuzzy ideals (resp. ∈, ∈ ∨qk-fuzzy interior ideals) are developed.

Słowa kluczowe

EN

Fuzzy set, (∈, ∈ ∨qk)-Fuzzy ideal; (∈, ∈ ∨qk)-Fuzzy interior ideal; Generalized semisimple fuzzy ordered semigroup

Kategorie tematyczne

• 08A72: Fuzzy algebraic structures
• 03E72: Fuzzy set theory
• 06F05: Ordered semigroups and monoids

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 841-856

Daty

wydano

2016-01-01

otrzymano

2016-03-03

zaakceptowano

2016-09-13

online

2016-11-14

Twórcy

autor

Xiaokun Huang

• College of Mathematics and Econometrics, Hunan University, Changsha 410082, China and College of Mathematics, Honghe University, Mengzi 661199,

autor

Qingguo Li

• College of Mathematics and Econometrics, Hunan University, Changsha 410082,

Identyfikatory

DOI

10.1515/math-2016-0076