Some algebraic properties of fuzzy S-acts

M. Haddadi


S-acts, a useful and important algebraic tool, have always been interest to mathematicians, specially to computer scientists. When A. Zadeh introduced the notion of the fuzzy subset in 1965, his idea opened a new direction to reserchers to provide tools in the various elds of mathematics. Here we are going to investigate some algebraic properties of fuzzy S-acts. We rst make an S-act from the fuzzy sub-sets of an S-act A. Then we use this tool to give a characterization for fuzzy S-acts. We then introduce the notion of generated fuzzy S-act by a fuzzy subset of an S-act and give a characterization for the fuzzy actions. And then we dene the notion of indecomposable fuzzy S-act and nd some indecomposable fuzzy actions.


Fuzzy set, Fuzzy acts over fuzzy semigroups.

Full Text:



Belohlavek, Birkho variety theorem and fuzzy logic Arch. Math. Logic 42 (2003), 781-790.

Belohlavek, R., Vychodil, V., Algebras with fuzzy equalities Fuzzy Sets and Systems 157 (2006), 161.201.

Bosnjak. I, R.Madarasz, G.Vojvodic Algebra of fuzzy sets, Fuzzy Sets and Systems 160 (2009), 2979-2988.

Ebrahimi, M.M., M. Mahmoudi, The category of M-sets. Ital. J. Pure Appl. Math. 9 (2001), 123-132.

M. Haddadi Fuzzy acts over fuzzy semigroups and summited

Kilp, M., U. Knauer, A. Mikhalev, Monoids, Acts and Categories, Walter de Gruyter, Berlin, New York, 2000.

Lotfi A. Zadeh Fuzzy sets. Information and Control. 8 (1965), 338-353.


  • There are currently no refbacks.

Copyright (c) 2013 M. Haddadi

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.