The lower and upper approximations are basic concepts in rough set theory, and the approximations will change dynamically over time. Incremental methods for updating approximations in rough set theory and its extension has been received much attention recently. This paper presents an approach for incrementally updating approximations of fuzzy rough sets in dynamic fuzzy decision systems when a ...

The notion of three-way decisions was originally introduced by the needs to explain the three regions of probabilistic rough sets. Recent studies show that rough set theory is only one of possible ways to construct three regions. A more general theory of three-way decisions has been proposed, embracing ideas from rough sets, interval sets, shadowed sets, three-way approximations of fuzzy sets, ...

In recent years, many researchers have focused on applying the fuzzy set theory to generate fuzzy rules from training instances to deal with the Iris data classification problem. In this paper, we propose a new method to automatically generate weighted fuzzy rules from training instances by using genetic algorithms to handle the Iris data classification problem, where the attributes appearing i...

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (∈,∈ ∨ q)-fuzzy filters of pseudo BL-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these ge...

The primary goal of this paper is to price European options in the Merton’s framework with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes a...

In this paper we develop the general framework for text representation based on fuzzy set theory. This work is extended from our original ideas [5],[4], in which a document is represented by a set of fuzzy concepts. The importance degree of these fuzzy concepts characterize the semantics of documents and can be calculated by a specified aggregation function of

the intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by atanassov in 1983. the aim of this paper is to develop an effective methodology for solving matrix games with payoffs of atanassov’s triangular intuitionistic fuzzy numbers (tifns). in this methodology, the concepts and ranking order relations of atanassov’s tifns are defined. a pair of bi-object...

Many researchers have combined rough set theory and fuzzy set theory in order to easily approach problems of imprecision and uncertainty. Covering-based rough sets are one of the important generalizations of classical rough sets. Naturally, covering-based fuzzy rough sets can be studied as a combination of covering-based rough set theory and fuzzy set theory. It is clear that Pawlak’s rough set...

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...

In much of human reasoning, the form of reasoning is approximate rather than exact as in "A red apple is ripe and this apple is more or less red. Then this apple is more or less ripe.' L.A. Zadeh and E.H. Mamdani suggested methods for such a fuzzy reasoning as an application of fuzzy set theory. The method involves an inference rule and a conditional proposition which contains fuzzy concepts. I...