Covering rough sets based on neighborhoods: An approach without using neighborhoods

Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the coverings themselves, we introduce unary and composition operations on coverings. A notion of homomorphismis provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin

INTERVAL-VALUED INTUITIONISTIC FUZZY COMPOSITION MATRIX AND ITS APPLICATION FOR CLUSTERING

Abstract. In this paper, the notions of (T, S)-composition matrix and (T, S)-interval-valued intuitionistic fuzzy equivalence matrix are introduced where (T, S) is a dual pair of triangular module. They are the generalization of composition matrix and interval-valued intuitionistic fuzzy equivalence matrix. Furthermore, their properties and characterizations are presented. Then a new method based onα−matrix for clustering is developed. Finally, an example is given to demonstrate our method

A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators

A SD-IITFOWA operator and TOPSIS based approach for MAGDM problems with intuitionistic trapezoidal fuzzy numbers

The aim of this article is to investigate an approach to multiple attribute group decision making (MAGDM) problems in which the information about decision makers (DMs) weights is completely unknown in advance, the attributes are inter-dependent, and the attribute values take the form of intuitionistic trapezoidal fuzzy numbers. First, the concept of similarity degree (SD) for two intuitionistic trapezoidal fuzzy decision matrixes is defined, which measures the level of consensus between individual decision opinion and group decision opinion. Next, we develop some IITFOWA operators to aggregate intuitionistic trapezoidal fuzzy decision matrixes in MAGDM problems. In particular, we present the SD induced IITFOWA (SD-IITFOWA) operator, which induces the order of argument values by utilizing the similarity degree of decision makers. This operator aggregates individual opinion in such a way that more importance is placed on the most similarity one. Then, a SD-IITFOWA operator and TOPSIS method based approach is developed to solve the MAGDM problems with intuitionistic trapezoidal fuzzy numbers. Finally, the developed approach is used to select the right suppliers for a computer company