In [23], Zadeh introduced the notion of fuzzy sets and fuzzy set operations. Since then, fuzzy set theory developed by Zadeh and others has evoked great interest among researchers working in different branches of mathematics. Semirings play an important role in studying matrices and determinants. Many aspects of the theory of matrices and determinants over semirings have been studied by Beasley...

In this paper, we present a general framework for the study of interval type-2 rough fuzzy sets by using both constructive and axiomatic approaches. First, several concepts and properties of interval type-2 fuzzy sets are introduced. Then, a pair of lower and upper interval type-2 rough fuzzy approximation operators with respect to a crisp binary relation is proposed. Classical representations ...

This paper reports the evaluation of Fuzzy logic implemented on image, in MATLAB environment, used to implement different functions. In this paper, the in-built functions of MATLAB are implemented on image and the resultant images are displayed using different functions. Fuzzy inference system has been designed for four inputs, one output that tells whether the pixel under consideration is “low...

Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of fuzzy sets and in exploring the multi-modal aspect of fuzzy logic due to the different cognitive, emotional and behavioral angles of assessing truth. We lay here the foundations of...

Recently, the rough set and fuzzy set theory have generated a great deal of interest among more and more researchers. Granular computing (GrC) is an emerging computing paradigm of information processing and an approach for knowledge representation and data mining. The purpose of granular computing is to seek for an approximation scheme which can effectively solve a complex problem at a certain ...

Starting from a unified treatment of uncertainty by combining probability and fuzzy set theory [1], Goodman [2] put forward the equivalence between a fuzzy set and a class of random sets. Falling shadow representation theory was established based on the collection of Wang and Sanchez [3], which is directly related to the concept of probabilistic fuzzy set membership function. The theory shows t...

The treatment of complex systems often requires the manipulation of vague, imprecise and uncertain information. Indeed, the human being is competent in handling of such systems in a natural way. Instead of thinking in mathematical terms, humans describes the behavior of the system by language proposals. In order to represent this type of information, Zadeh proposed to model the mechanism of hum...

in this paper, rst a design is proposed for representing fuzzy polynomials withinput fuzzy and output fuzzy. then, we sketch a constructive proof for existenceof such polynomial which can be fuzzy interpolation polynomial in a set given ofdiscrete points rather than a fuzzy function. finally, to illustrate some numericalexamples are solved.

Graph theory has numerous application to problems in systems analysis, operations research, economics, and transportation. However, in many cases, some aspects of a graph-theoretic problem may be uncertain. For example, the vehicle travel time or vehicle capacity on a road network may not be known exactly. In such cases, it is natural to deal with the uncertainty using the methods of fuzzy sets...