Abstract
In this paper we define the notions of rough sub-acts and give some properties of such sub-acts and rough fuzzy sub-acts. We discuss approximations of a subset in acts with respect to Green’s relations. Relationship between upper [lower] rough sub-acts [bi-acts] and upper [lower] aproximations of their homomorphic images are discussed. We also discuss approximations with respect to fuzzy congruences.
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References
J. Ahsan, K. Saifullah, and M. Farid Khan, Fuzzy Semirings, Fuzzy Sets and Systems 60, 309 (1993).
J. Ahsan, M. F. Khan, and M. Shabir, Characterization of Monoids by the Properties of Their Fuzzy Subsystems, Fuzzy Sets and Systems 56, 199 (1993).
J. Ahsan, Semirings Characterized by Their Fuzzy Ideals, The Journal of Fuzzy Mathematics 6(1)(1998).
R. Biswas and S. Nanda, Rough Groups and Rough Subgroups, Bull. Polish Acad. Sci. 42(3.1) (1994).
B. Davvaz, Roughness in Rings, Inf. Sci. 164, 147 (2004).
J. M. Howie, An Introduction to Semigroup Theory (Academic press, 1976).
T. B. Iwinski, Algebraic Approach to Rough Sets, Bull. Polish Acad. 35(9–10) (1987).
N. Kuroki, On Fuzzy Semigroups, Inf. Sci. 53, 203 (1991).
N. Kuroki, Rough Ideals in Semigroups, Inf. Sci. 100, 139 (1997).
Mati Kilp, Ulrich Knauer, and Alexander V. Mikhalev, Monoids, Acts and Categories, Walter de Gruter, 2000.
J. N. Mordeson, Rough Set Theory Applied to (Fuzzy) Ideal Theory, Fuzzy Sets and Systems 121(Issue 2), 315 (2001).
T. K. Mukerjee and M. K. Sen, Prime Fuzzy Ideals in Rings, Fuzzy Sets and Systems 32, 337 (1989).
Z. Pawlak, Rough Sets, Int. J. Comp. Sci. 11, 341 (1982).
Z. Pawlak, Rough Sets Theoretical Aspects of Reasoning about Data (Kluwer Academic Publisher, 1991).
A Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl. 35, 512 (1971).
M. Shabir, Fully Fuzzy Prime Semigroups, Int. J. Math. Math. Sci. Issue 1, 163 (2005).
Qi-Mei Xiao, Zhen-Liang Zhang, Rough Prime Ideals and Rough Fuzzy Prime Ideals in Semigroups, Inf. Sci. 176, 725 (2006).
Y. Y. Yao, Constructive and Algebraic Methods of the Theory of Rough Sets, Inf. Sci. 109, 21 (1998).
L. A. Zadeh, Fuzzy sets, Inf. Cont. 8, 267 (1965).
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Submitted by M.M. Arslanov
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Shabir, M., Irfan, M. & Khan, A.A. Rough S-acts. Lobachevskii J Math 29, 98–109 (2008). https://doi.org/10.1134/S199508020802008X
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DOI: https://doi.org/10.1134/S199508020802008X