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Abstract: This paper is to study the rough sets within the context of lattices. We study the special properties of the rough sets which can be constructed by means of the congruences determined by ideals of lattice. Also the properties of the generalized rough sets with respect to ideals of lattice are investigated. Finally we give an example of their application in formal concept analysis. [Copyright &y& Elsevier]

Abstract: In this paper, we intend to study a connection between rough sets and lattice theory. We introduce the concepts of upper and lower rough ideals (filters) in a lattice. Then, we offer some of their properties with regard to prime ideals (filters), the set of all fixed points, compact elements, and homomorphisms. [Copyright &y& Elsevier]

Abstract: In this paper, all cyclic codes with length p s n, (n prime to p) over the ring R = F p + uF p +⋯+ u k−1 F p are classified. It is first proved that Tor j (C) is an ideal of , so that the structure of ideals over extension ring is determined. Then, an isomorphism between R[X]/〈X N −1〉 and a direct sum can be obtained using discrete Fourier transform. The generator polynomial representation of the corresponding ideals over F p + uF p +⋯+ u k−1 F p is calculated via the inverse isomorphism. Moreover, torsion codes, MS polynomial and inversion formula are described. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, by considering the notion of an MV-algebra, we consider a relationship between rough sets and MV-algebra theory. We introduce the notion of rough ideal with respect to an ideal of an MV-algebra, which is an extended notion of ideal in an MV-algebra, and we give some properties of the lower and the upper approximations in an MV-algebra. [Copyright &y& Elsevier]

Abstract: This paper is a continuation of ideas presented by Davvaz [Roughness in rings, Inform. Sci., 164 (2004) 147–163; Roughness based on fuzzy ideals, Inform. Sci., 176 (2006) 2417–2437]. We introduce the notions of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in a ring, and give some properties of such ideals. Also, we discuss the relations between the upper and lower rough prime (primary) ideals and the upper and lower approximations of their homomorphism images. [Copyright &y& Elsevier]

Abstract: The theory of rough set, proposed by Pawlak and the theory of fuzzy set, proposed by Zadeh are complementary generalizations of classical set theory. Many sets are naturally endowed with two binary operations: addition and multiplication. One concept which does this is a ring. This paper concerns a relationship between rough sets, fuzzy sets and ring theory. It is a continuation of ideas presented by Kuroki and Wang [N. Kuroki, P.P. Wang, The lower and upper approximations in a fuzzy group, Inform. Sci. 90 (1996) 203–220]. We consider a ring as a universal set and we assume that the knowledge about objects is restricted by a fuzzy ideal. In fact, we apply the notion of fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring. Some characterizations of the above approximations are made and some examples are presented. [Copyright &y& Elsevier]