The concept of the rough set was originally proposed by Pawlak as a formal tool for modelling and processing incomplete information in information systems, then in 1990, Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set theory by means of integrating the classic...

In the traditional fuzzy logic, the expert’s degree of certainty in a statement is described either by a number from the interval [0, 1] or by a subinterval of such an interval. To adequately describe the opinion of several experts, researchers proposed to use a union of the corresponding sets – which is, in general, more complex than an interval. In this paper, we prove that for such set-value...

In this paper are introduced some concepts of interval-valued fuzzy relations and some of their properties: reflexivity, symmetry, T-transitivity, composition and local reflexivity. The existence and uniqueness of T-transitive closure of interval-valued fuzzy relations is proved. An algorithm to compute the T-transitive closure of finite interval-valued fuzzy relations is showed. Some propertie...

The subject of the study was hardware implementations of fuzzy controllers as CMOS analog devices on the base of implementation of fuzzy inference rules as multi-valued logic functions using summing amplifiers as building blocks. Earlier a functional completeness of summing amplifier with saturation in an arbitrary-valued logic was proven that gave a theoretical background for analog implementa...

Fuzzy valued measure is a mapping which maps a σalgebra to a set of fuzzy set with convex compact σlevel defined on banach space (β). In this paper, we investigate the notion of decomposition and representation of fuzzy valued measure (F.V.M) is given in the sequence of singular valued measure. Also we have been studied and develop the notion of integrals with the aid of F.V.M under closed inte...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on...

Dubois. D. , Prade. H. 1980. Fuzzy Sets and Systems. Mathematics in Science and Engineering, Academic Press, New York, 144. Jun. Y. B. , Kavikumar. J. 2011. Bipolar Fuzzy Finite State Machines. Bull. Malays. Sci. Soc. 34 no. 1: 181-188. Kandel. A. , Lee. S. C. Fuzzy Switching and Automata Theory Applications. Edward Arnold Publishers Ltd, London. Lee. K. J. 2000. Bipolar-valued fuzzy sets and t...

Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of generalised interval-valued fuzzy soft set are proposed and their basic properties are studied. The lattice structures of generalised interval-valued fuzzy soft set are also discussed. Furthermore, an application o...

Neural Network based Construction of Fuzzy Graphs Michael R. Berthold and Klaus{Peter Huber Institute for Computer Design and Fault Tolerance (Prof. D. Schmid), University of Karlsruhe, Germany Abstract| Function approximation using example data has gained considerable interest in the past. One interesting application is the approximationof the behaviour of simulationmodels, called metamodellin...