Introduction A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?”. Such a problem, called a stability problem of the functional equation, was formulated by Ulam [1] in 1940. In the next year, Hyers [2] gave a partial solution of Ulam’s probl...

A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?” Such a problem, called a stability problem of the functional equation, was formulated by Ulam 1 in 1940. In the next year, Hyers 2 gave a partial solution of Ulam’s problem for the case of...

the traditional event tree analysis uses a single probability to represent each top event. however, it is unrealistic to evaluate the occurrence of each event by using a crisp value without considering the inherent uncertainty and imprecision a state has. the fuzzy set theory is universally applied to deal with this kind of phenomena. the main purpose of this study is to construct an easy metho...

In this paper, a hesitant fuzzy multiple attribute group decision making problem where there exists prioritization relationships over the attributes and decision makers is studied. First, some Einstein operations on hesitant fuzzy elements and their properties are presented. Then, several generalized hesitant fuzzy prioritized Einstein aggregation operators, including the generalized hesitant f...

The main result is to show that the space of nonmonotonic fuzzy measures on a measurable space (X,X) with total variation norm is separable if and only if the -algebra X is a finite set. Our result is related to fuzzy analysis, functional spaces and discrete mathematics. © 2007 Elsevier B.V. All rights reserved.

a fuzzy observer based scheme for synchronizing two hyperchaoticoscillators via a scalar transmitted signal for cryptographic application isproposed. the takagi-sugeno fuzzy model exactly represents chaotic systems.based on the general fuzzy model, the fuzzy observer of a chaotic system isdesigned on the basis of the n-shift multiple state based key encryption algorithm.the scalar transmitted s...

In sensory analysis a panel of assessors gives scores to blocks of sensory attributes for profiling products, thus yielding a three-way table crossing assessors, attributes and products. In this context, it is important to evaluate the panel performance as well as to synthesize the scores into a global assessment to investigate differences between products. Recently, a combined approach of fuzz...

Recently, many works have appeared dealing with the distributivity of fuzzy implications over t-norms, tconorms and uninorms (see [2, 3, 4, 5, 12, 13, 14]). These equations have a very important role to play in efficient inferencing in approximate reasoning, especially fuzzy control systems (see [6]). In this work we present some results connected with two functional equations describing the di...