Information Sciences: an International Journal
Fuzzy generalized bi-ideals in semigroups
Information Sciences: an International Journal
Fuzzy semiprime quasi-ideals in semigroups
Information Sciences: an International Journal
The embedding of an ordered groupoid into a poe-groupoid in terms of fuzzy sets
Information Sciences: an International Journal
TL-filters of integral residuated l-monoids
Information Sciences: an International Journal
Lattice implication ordered semigroups
Information Sciences: an International Journal
The characterizations of h-hemiregular hemirings and h-intra-hemiregular hemirings
Information Sciences: an International Journal
Fuzzy radicals and prime fuzzy ideals of ordered semigroups
Information Sciences: an International Journal
Fuzzy ideals and semiprime fuzzy ideals in semigroups
Information Sciences: an International Journal
Characterizations of ordered semigroups by the properties of their fuzzy ideals
Computers & Mathematics with Applications
Characterizations of regular ordered semigroups in terms of (α,β)-fuzzy generalized bi-ideals
Information Sciences: an International Journal
Regular ordered semigroups in terms of fuzzy subsets
Information Sciences: an International Journal
Ordered semigroups characterized by interval valued ε, ε $\vee$ q-fuzzy bi-ideals
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Characterizations of regular ordered semigroups by generalized fuzzy ideals
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Characterizations of non-associative ordered semigroups by their fuzzy bi-ideals
Theoretical Computer Science
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Given a set S, a fuzzy subset of S is, by definition, an arbitrary mapping f : S → [0,1] where [0,1] is the unit segment of the real line. If the set S bears some structure, one may distinguish some fuzzy subsets of S in terms of that additional structure. This important concept was first introduced by Zadeh. Fuzzy groups have been first considered by Rosenfelt, fuzzy semigroups by Kuroki. A theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed. In the present paper we endow S with the structure of an ordered semigroup and define "fuzzy" analogous for several notions that have been proved to be useful in the theory of ordered semigroups. We define the fuzzy bi-ideals in ordered semigroups and we give the main theorem which characterizes the bi-ideals in terms of fuzzy bi-ideals. Then we characterize the left and right simple, the completely regular, and the strongly regular ordered semigroups by means of fuzzy bi-ideals. We also study the decomposition of left and right simple ordered semigroups and of ordered semigroups having the property a ≤ a2 for all a, in terms of fuzzy bi-ideals. This decomposition is uniquely defined.