Various expanded rough set models based on tolerance relations enlarge the application fields of rough set theory. Through generating tolerance relations to fuzzy tolerance relations and combining with dominance relations, a tolerance class of a fuzzy tolerance relation is further decomposed into a positive fuzzy tolerance class, a negative fuzzy tolerance class and a purely fuzzy tolerance cla...

In this paper we modify some previous definitions of fuzzy Turing machines to define the notions of accepting and rejecting degrees of inputs, computationally. We use a BFS-based search method and obtain an upper level bound to guarantee the existence of accepting and rejecting degrees. We show that fuzzy, generalized fuzzy and classical Turing machines have the same computational power. Next, ...

The uncertain nonlinear systems can bemodeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations.We use the neural networks to approximate the coefficients of the fuzzy equations.The approximation theory for ...

Systems of linear equations, with uncertainty on the parameters, play a major role in various problems in economics and finance. Fuzzy system of linear equations has been discussed in [1] using LU decomposition when the matrix A in Ax = b is a crisp matrix. Also the Adomian decomposition method and iterative methods have been studied in [2, 6] for fuzzy system of linear equations. In this paper...

To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough se...

In this paper, we considered decision processes in which one decision is made in each process. We incorporate the utility function concept into the decision process, derived the utility function in fuzzy events and by the max-product operation obtained the utility possibility measure of the fuzzy events. In cases with numerous decision processes, the optimum action can be determined from the re...

Ever since the first hybrid fuzzy rough set model was proposed in the early 1990?s, many researchers have focused on the definition of the lower and upper approximation of a fuzzy set by means of a fuzzy relation. In this paper, we review those proposals which generalize the logical connectives and quantifiers present in the rough set approximations by means of corresponding fuzzy logic operati...

The paper discusses integration in possibility theory, both in an ordinal and in a numerical (behavioral) context. It is shown that in an ordinal context, the fuzzy integral has an important part in at least three areas: the extension of possibility measures to larger domains, the construction of product measures from marginals and the definition of conditional possibilities. In a numerical (be...