Affordable Access

Access to the full text

Characterization of some types of ordered semigroups in terms of fuzzy sets

Authors
  • Kehayopulu, N.1
  • Tsingelis, M.1
  • 1 University of Athens, Department of Mathematics, 157 84 Panepistimiopolis, Athens, Greece , Athens (Greece)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Jan 01, 2008
Volume
29
Issue
1
Pages
14–20
Identifiers
DOI: 10.1134/S1995080208010046
Source
Springer Nature
Keywords
License
Yellow

Abstract

It is well known that the right (left) regular, regular, and intra-regular ordered semigroups play an essential role in studying the structure, especially the decomposition, of ordered semigroups. In the present paper we study some more general classes containing the right regular, left regular, regular and intra-regular ordered semigroups. As an application of our results we get characterizations of right (left) regular, regular and intra-regular ordered semigroups in terms of fuzzy sets. We prove the following: An ordered semigroup S is right (resp. left) regular if and only if for each fuzzy subset f of S we have f ⊆ f2 ° 1 (resp. f ⊆ 1 ° f2). It is regular if and only if for each fuzzy subset f of S we have f ⊆ f ° 1 ° f, and it is intra-regular if and only if f ⊆ 1 ° f2 ° 1 for each fuzzy subset f of S (where 1 is the greatest element of the set of fuzzy subsets of S). Keeping in mind the definitions of right (left) regular, regular, and intra-regular ordered semigroups one can see how similar is the theory of ordered semigroups with the theory of fuzzy ordered semigroups.

Report this publication

Statistics

Seen <100 times