The fuzzy differential and integral equations are important part of the fuzzy analysis theory. Park et al. [8] have considered the existence of solution of fuzzy integral equation in Banach space and Subrahmaniam and Sudarsanam [12] proved the existence of solution of fuzzy functional equations. An integral equation is called singular if either the range of integration is infinite or the kernel...

We describe in this paper a new approach for pattern recognition using modular neural networks with a fuzzy logic method for response integration. We proposed a new architecture for modular neural networks for achieving pattern recognition in the particular case of human faces and fingerprints. Also, the method for achieving response integration is based on the fuzzy Sugeno integral with some m...

This paper addresses the added value that is provided by using distance-based fuzzy relations in flexible query answering. To use distances and/or concepts of gradual similarity in that domain is not new. Within the last ten years, however, results in the theory of fuzzy relations have emerged that permit a smooth and pragmatic, yet expressive and effective, integration of ordinal concepts too....

A method of fuzzy likelihood-ratio hypothesis testing is applied to binary signal integration. Imprecise parameters of the distribution under each hypothesis are modeled as fuzzy numbers. The false alarm rate and detection rate are therefore also imprecise. The effects of parameter imprecision on integration performance are examined using an example; the method is applied to envelope detection ...

We prove the basic fuzzy Korovkin theorem via a fuzzy Shisha– Mond inequality given here. This determines the degree of convergence with rates of a sequence of fuzzy positive linear operators to the fuzzy unit operator. The surprising fact is that only the real case Korovkin assumptions are enough for the validity of the fuzzy Korovkin theorem, along with a natural realization condition fulfill...

 In order to simulate human beings’ thinking, this study is dedicated to proposing a novel fuzzy neural network (FNN) to cluster the fuzzy data being collected from the fuzzy questionnaires. The proposed FNN is the integration of adaptive resonance theory 2 (ART2) neural network and fuzzy sets theory. It can handle the fuzzy inputs as well as the fuzzy weights. A case study for mobile phone ma...

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...

It is well know that when these concepts arose in PhD disertation of Sugeno in 1974 [1], a lot of works has been done as much in the theoretical branch as in the applied. As we know, the classical measure and the corresponding integral are based on the additivity property, but this property is uncommun in the applied context and could be too restrictive for the appliance. For instance, measurem...

Fuzzy distance is applied on data analysis, classification, and product positioning analysis widely. In this paper, We introduce a fuzzy distance by using graded mean integration representation of generalized fuzzy number and the span of fuzzy number, We also discuss the distance of the linguistic data of “greater or less than x” and “about x”. It is reasonable to say “the fuzzy distance of abo...