The fuzzy sets defining the linguistic variable values can be seen as a fuzzy partition of the linguistic variable. The membership functions obtained using fuzzy clustering algorithms are defined with respect to the group prototypes, and they cannot be used to define the linguistic variable values. We introduce several criteria to pass from the clustering membership functions to the linguistic ...

This paper attempts to present the new approach to design sufficient number of systematic fuzzy linguistics in matrix form and map the Fuzzy Linguistic Variable Matrix, which contains linguistic terms, into numeric domain using Fuzzy Normal Distribution based on the Parabola-based Membership Function. Existing fuzzy set theory is difficult to design the systematic and sufficient fuzzy linguisti...

is considered, with variable coefficients and a nonconstant delay. Under rather natural assumptions all solutions are positive and bounded. Persistence and extinction conditions are presented for this equation. In the case when there exists a constant positive equilibrium, local asymptotic stability of the constant solution and oscillation about this equilibrium are analyzed. The results are il...

Some recent results for bilinear or multilinear singular integrals operators are presented. The focus is on some of the results that can be viewed as natural counterparts of classical theorems in Calderón-Zygmund theory, adding to the already existing extensive literature in the subject. In particular, two different classes of operators that can be seen as bilinear counterparts of linear Calder...

the purpose of this paper is to introduce the concept of l-fuzzybilinear operators. we obtain a decomposition theorem for l-fuzzy bilinearoperators and then prove that a l-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by s.e.rodabaugh (1991).finally we discuss the continuity of l-fuzzy bilinear operators.

We present a new novel method of automatically generating a multi-variable fuzzy inference system from given sample sets. We rst decompose the sample set, say , into a cluster of sample sets associated with the given input variables, then compute the associated fuzzy rules and membership functions for each variable, independent of the other variables, by solving a single input multiple outputs ...

This work is devoted to the study of solutions around an α-singular point x0 ∈ [a, b] for linear fractional differential equations of the form [Lnα(y)](x) = g(x, α), where [Lnα(y)](x) = y(nα)(x)+ n−1 ∑ k=0 ak(x)y (kα)(x) with α ∈ (0, 1]. Here n ∈ N , the real functions g(x) and ak(x) (k = 0, 1, . . . , n−1) are defined on the interval [a, b], and y(nα)(x) represents sequential fractional deriva...

In this communication we will consider hypothesis-tests for the (fuzzy-valued) mean value of a fuzzy random variable in a population. For this purpose, we will make use of a generalized metric for fuzzy numbers, and we will develop two different approaches for the case of fuzzy random variables taking on a finite number of possible values, both leading to close statistical inferences.

The fuzzy matrix equations AX̃ = Ỹ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the e...

If {qn} is a lacunary sequence of integers, and if for each n, cn(x) and c-n(x) are trigonometric polynomials of degree n, then {Cn(X)} must tend to zero for almost every x whenever {cn(x)ei?nX + c-n(-x)e-i?'nX} does. We conjecture that a similar result ought to hold even when the sequence {f On} has much slower growth. However, there is a sequence of integers {nj } and trigonometric polynomial...