This paper introduces a singular value-based method for reducing a given fuzzy rule set. The method conducts singular value decomposition of the rule consequents and generates certain linear combinations of the original membership functions to form new ones for the reduced set. The present work characterizes membership functions by the conditions of sum normalization (SN), nonnegativeness (NN),...

The main purpose of this paper is to use a new way to extend fuzzy implications $I$ from a generalized sublattice $M$ to a bounded lattice $L$, such that the extended implications preserve many of the considered properties of fuzzy implications on $M$.Furthermore, as a special case, we investigate the extension of $(S,N)-$implications. Results indicate that the extended implications preserve ma...

we study interior operators and interior structures in a fuzzy setting.we investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

To the best of our knowledge, till now no one has used fuzzy numbers for solving the linear programming problem with bounded variables. In this paper, a new method for solving a special kind of fuzzy number linear programming problem with bounded variables directly using linear ranking function is proposed. In the proposed method, we represented only the cost coefficients by trapezoidal fuzzy n...

In most practical problems of linear programming problems with fuzzy cost coefficients, some or all variables are restricted to lie within lower and upper bounds. In this paper, the authors propose a new method for solving such problems called the bounded fuzzy primal simplex algorithm. Some researchers used the linear programming problem with fuzzy cost coefficients as an auxiliary problem for...

in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

In this paper, we study countably compact fuzzy sets using the definition of C. K. Wong [10] and obtain its several properties. 1. Introduction The concept of fuzzy set and fuzzy set operations were first introduced by L. A. Zadeh [11] in1965. Several other mathematicians studied fuzzy sets in various areas in mathematics. Firstly, C. L. Chang [2] in 1968 developed the theory of fuzzy topologic...