Wewill define a notion for a quasi fuzzy p-normed space, then we use the fixed point alternative theorem to establish Hyers–Ulam– Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p-normed space. Later, we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function, co...

Based on the fully implicational idea, we investigate the interval-valued fuzzy reasoning with multiantecedent rules. First, we construct a class of interval-valued fuzzy implications by means of a type of implications and a parameter on the unit interval, then use them to establish three kinds of fully implicational reasoning methods for the interval-valued fuzzy reasoning with multi-anteceden...

Information fusion introduces special operators ◦ in probability theory and fuzzy theory. Some serious data certify in each cases these two quite distinct techniques. This communication will show that four postulates are the unique aim of these two theories. Evidence theory and fuzzy set theory replace often probabilities in medicine, economy and control. Fuzzy theory is used for example in Jap...

Rule based systems for Fuzzy Control, Fuzzy Supervising and Fuzzy Diagnosis are non-linear multi-input, multi-output systems. The result of the signal processing within the system is a high dimensional characteristic field. For optimizing the behaviour of the system, we have a high number of fiee degrees. The reconstruction of the knowledge base from the characteristic field as starting point i...

We present a categorical approach to the extension of probabilities, i.e. normed σ-additive measures. J. Novák showed that each bounded σ-additive measure on a ring of sets is sequentially continuous and pointed out the topological aspects of the extension of such measures on over the generated σ-ring σ( ): it is of a similar nature as the extension of bounded continuous functions on a complete...

Measures of information based on fuzzy sets have been defined both for finite and for continuous universes. In the continuous case, the measure of information I(f) depends on the concept of nonincreasing rearrangement of the function f . It has been observed that I(f) can be obtained as a limit of discrete distributions π(N) approximating f . We consider the approximation problem in more detail...

In this paper, we deal with the effects of urban landscapes on land prices under uncertainty, represented by fuzzy numbers. To this end, the factors for evaluating urban landscapes are designed using fuzzy numbers. Moreover, we consider 11 factors for utilizing the approach, like as Continuity of external walls, Conformity of colors and materials, Favorable pedestrian space, Decorations and str...

We prove necessary and sufficient conditions for the validity of Jensen type inequalities for generalized Sugeno integral. Our proofs make no appeal to the continuity of neither the fuzzy measure nor the operators. For several choices of operators, we characterize the classes of functions for which the corresponding inequalities are satisfied.

This paper describes optimization of the Takagi-Sugeno fuzzy model. To prove the existence of optimal control, we apply compactness of a set of membership functions in L space and continuity of approximate reasoning and show the existence of a pair of membership functions which minimize the quadratic performance function.