Introduction: Communicative approximations are equivalence relations. For considering Communicative approximation, new constructs are necessary including “rough points” and “rough intervals”. “Communication about quantities is defined on a shared conventional space, which constitutes a tessellation on the real number line”. The uncertainty which results from measurement error (±η) is defined on...

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to ...

This paper presents different approaches to the problem of fuzzy rules extraction by using fuzzy clustering as the main tool. Within these approaches we describe six methods that represent different alternatives in the fuzzy modeling process and how they can be integrated with a genetic algorithms. These approaches attempt to obtain a first approximation to the fuzzy rules without any assumptio...

Algebraic structures and lattice structures of rough sets are basic and important topics in rough sets theory. In this paper we pointed out that a basic problem had been overlooked, that is the closeness of union and intersection operations of rough approximation pairs, i.e. (lower approximation, upper approximation). We present that the union and intersection operations of rough approximation ...

In this paper, we advocate that the use of concepts from Soft Computing theory, in particular from fuzzy systems, can be quite useful in the modeling and coordination of collaborative activities. The tolerance of imprecision, uncertainty, and approximation, which is the core of such technology, may provide a more subjective model for such activities, closer to human reasoning. We introduce a fu...

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 ...

in a fuzzy metric space (x;m; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. it is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.

We prove that some important properties of convex subsets of vector topological spaces remain valid in the space of fuzzy numbers endowed with the Euclidean distance. We use these results to obtain a characterization of fuzzy number-valued Lipschitz functions. This fact helps us to find the best Lipschitz constant of the trapezoidal approximation operator preserving the value and ambiguity intr...