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http://dx.doi.org/10.11568/kjm.2013.21.2.171

FUZZY SEMIGROUPS IN REDUCTIVE SEMIGROUPS  

Chon, Inheung (Department of Mathematics Seoul Women's University)
Publication Information
Korean Journal of Mathematics / v.21, no.2, 2013 , pp. 171-180 More about this Journal
Abstract
We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ and find a faithful representation (or anti-representation) of S by transformations of S. Also we show that a fuzzy semigroup S in a weakly reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ is isomorphic to the semigroup consisting of all pairs of inner right and left translations of S and that S can be embedded into the semigroup consisting of all pairs of linked right and left translations of S with the property that S is an ideal of the semigroup.
Keywords
fuzzy semigroup; reductive semigroup; weakly reductive semigroup; linked; translational hull;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 J.M. Anthony and H. Sherwood, Fuzzy groups redefined, J. Math. Anal. Appl. 69 (1979), 124-130.   DOI
2 I. Chon, Fuzzy ideals generated by fuzzy subsets in semigroups, (To appear Commun. Korean Math. Soc.).
3 A.H. Clifford and G.B. Preston, The algebraic theory of semigroups Vol. 1, American mathematical society, Providence, Rhode Island, 1961.
4 P. Da, Fuzzy multiplication semigroup, Fuzzy Sets and Systems 105 (1999), 171-176.   DOI   ScienceOn
5 N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems 5 (1981), 203-215.   DOI   ScienceOn
6 N. Kuroki, Fuzzy semiprime ideals in semigroups, Fuzzy Sets and Systems 8 (1982), 71-79.   DOI   ScienceOn
7 N. Kuroki, On Fuzzy semigroups, Information Sciences 53 (1991), 203-236.   DOI   ScienceOn
8 N. Kuroki, Fuzzy semiprime quasi-ideals in semigroups, Information Sciences 75 (1993), 201-211.   DOI   ScienceOn
9 A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971), 512-517   DOI
10 S. Sessa, On fuzzy subgroups and fuzzy ideals under triangular norms, Fuzzy Sets and Systems 13 (1984), 95-100.   DOI   ScienceOn
11 L.A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353.   DOI