Gen. Math. Notes, Vol. 17, No. 2, August, 2013, pp. 76-80
ISSN 2219-7184; Copyright © ICSRS Publication, 2013
www.i-csrs.org
Available free online at http://www.geman.in
On Some Ideals of Fuzzy Points Semigroups
E.H. Hamouda
Department of Basic Sciences, Faculty of Industrial Education
Beni-Suef University, Beni-Suef, Egypt
E-mail: ehamouda70@gmail.com
(Received: 20-5-13 / Accepted: 30-6-13)
Abstract
Kim [Int. J. Math. & Math. Sc. 26:11 (2001), 707-712.] Considered the
semigroup of the fuzzy points of a semigroup . In this paper, we discuss the
relation between some ideals of and the subset
of .
Keywords: Fuzzy set; Semigroup; Fuzzy point; Minimal ideal.
1 Introduction
Zadeh [9] introduced the concept of a fuzzy set for the first time and this concept
was applied by Rosenfeld [8] to define fuzzy subgroups and fuzzy ideals. Based
on this crucial work, Kuroki [3, 4, 5, 6] defined a fuzzy semigroup and various
kinds of fuzzy ideals in semigroups and characterized them. Authors in [1]
investigated the existence of a fuzzy kernel and minimal fuzzy ideals in
semigroups. They showed that a subset of a semigroup is minimal ideal if and
only if the characteristic function of , C
, is minimal fuzzy ideal of . In [2],
Kim considered the semigroup of the fuzzy points of a semigroup , and
discussed the relation between the fuzzy interior ideals and the subsets of . In
this paper, we discuss the relation between some ideals of and the subset C
of .