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
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
A general approach to solving a wide class of fuzzy optimization problems
Fuzzy Sets and Systems
Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh
Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh
A First Course in Fuzzy and Neural Control
A First Course in Fuzzy and Neural Control
The embedding of an ordered groupoid into a poe-groupoid in terms of fuzzy sets
Information Sciences: an International Journal
Fuzzy bi-ideals in ordered semigroups
Information Sciences—Informatics and Computer Science: An International Journal
Toward a generalized theory of uncertainty (GTU)--an outline
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
Q-fuzzy subsets on ordered semigroups
Fuzzy Sets and Systems
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
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Given a set S, a fuzzy subset of S (or a fuzzy set in S) is, by definition, an arbitrary mapping f:S-[0,1] where [0,1] is the usual interval of real numbers. If the set S bears some structure, one may distinguish some fuzzy subsets of S in terms of that additional structure. This important concept of a fuzzy set was first introduced by Zadeh. Fuzzy groups have been first considered by Rosenfeld, fuzzy semigroups by Kuroki. A theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed. Some results on ordered groupoids-semigroups have been already given by the same authors in [N. Kehayopulu, M. Tsingelis, Fuzzy sets in ordered groupoids, Semigroup Forum 65 (2002) 128-132; N. Kehayopulu, M. Tsingelis, The embedding of an ordered groupoid into a poe-groupoid in terms of fuzzy sets, Inform. Sci. 152 (2003) 231-236; N. Kehayopulu, M. Tsingelis, Fuzzy bi-ideals in ordered semigroups, Inform. Sci. 171 (2004) 13-28] where S has been endowed with the structure of an ordered semigroup and defined ''fuzzy'' analogous for several notions that have been proved to be useful in the theory of ordered semigroups. The characterization of regular rings in terms of right and left ideals is well known. The characterization of regular semigroups and regular ordered semigroups in terms of left and right ideals or in terms of left, right ideals and quasi-ideals is well known as well. The characterization of regular le-semigroups (that is lattice ordered semigroups having a greatest element) in terms of right ideal elements and left ideal elements or right, left and quasi-ideal elements is also known. In the present paper we first give the main theorem which characterizes the regular ordered semigroups by means of fuzzy right and fuzzy left ideals. Then we characterize the regular ordered semigroups in terms of fuzzy right, fuzzy left ideals and fuzzy quasi-ideals. The paper serves as an example to show that one can pass from the theory of ordered semigroups to the theory of ''fuzzy'' ordered semigroups. Some of our results are true for ordered groupoids in general.