Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

1. Introduction. Let R be a binary relation on a set X and let aR, cR and sR denote,

Considering a binary operation as a ternary relation permits certain sections of the latter (which are functions) to be used in representing an abstract semigroup as a family of the self-maps of its underlying set under function composition. The idea is thus seen to be entirely similar to the way that the sections of a partial ordering under set inclusion represent the (abstract) partially orde...

This paper presents a series of important results from the theory n-hypergroups. Connections with binary relations and lattices are presented. Special attention is paid to fundamental relation commutative relation. In particular, join n-spaces analyzed.

We consider a new operation on the family of binary relations on integers called Hadamard star. View a binary relation R ⊆ N × N as a mapping of N into the power set of N and let R(n) denote the subset of integers m such that (n,m) ∈ R. Then the Hadamard star of R is the relation which assigns to each integer n the Kleene star of R(n). This is reminiscent of the Hadamard inverse of series with ...

The article discusses the set of square n n binary matrices with the same number of 1’s in each row and each column. An equivalence relation on this set is introduced. Each binary matrix is represented using ordered n-tuples of natural numbers. We are looking for a formula which calculates the number of elements of each factor-set by the introduced equivalence relation. We show a relationship b...

The theory of rough sets is an extension of set theory with two additional unary set-theoretic operators deened based on a binary relation on the universe. These two operators are related to the modal operators in modal logics. By exploring the relationship between rough sets and modal logics, this paper proposes and examines a number of extended rough set models. By the properties satissed by ...

Using the techniques of revealed preference analysis, we study a two-stage model of choice behavior. In the first stage, the decision maker maximizes a menu-dependent binary relation encoding preferences that are imperfectly perceived. In the second, a menu-independent binary relation is maximized over the subset of alternatives that survive the first stage. This structure can support various i...