Two extensions of classical Shepard operators to the fuzzy case are presented. We study Shepard-type interpolation/approximation operators for functions with domain and range in the fuzzy number’s space and max-product approximation operators. Error estimates are obtained in terms of the modulus of continuity.

In this paper we introduce the notion of levelwise convergence of sequence of fuzzy random variables. We derive equivalent conditions for left quasi uniform convergence of fuzzy random variables. Conditions are obtained for eventually equi-right continuity for the sequence of fuzzy random variables. A necessary and sufficient condition is obtained under which for a sequence of fuzzy random vari...

In this paper, numerical solution of nonlinear fuzzy Hammerstein integral equations is studied by fuzzy B-spline series. An error bound for the method is found based on modulus of continuity and it is proved that the proposed algorithm is numerically stable. Finally, theoretical results are illustrated by some numerical examples.

This paper presents an approach to formally model Takagi–Sugeno– Kang (TSK) fuzzy systems without the use of any external components. In order to keep the model continuity, the formal simulation model for a TSK fuzzy system is comprised of three types of reusable sub-models involving primitive operations. Thus, the model can be executed even on limited computational platforms, such as embedded ...

The concept of upper and lower semicontinuity of fuzzy mappings introduced by Bao and Wu [Y.E. Bao, C.X. Wu, Convexity and semicontinuity of fuzzy mappings, Comput. Math. Appl., 51 (2006) 1809–1816] is redefined by using the concept of parameterized triples of fuzzy numbers. On the basis of the linear ordering of fuzzy numbers proposed by Goetschel and Voxman [R. Goetschel, W. Voxman, Elementar...

Ever since the introduction of fuzzy sets by L. A. Zadeh [14], the fuzzy concept has invaded almost all branches of Mathematics. The concept of fuzzy topological space was introduced and developed by C.L. Chang [3] and since then many fuzzy topologists [1,6-13] have extended various notions in classical topology to fuzzy topological spaces. The concept of somewhat continuous functions was intro...

In a previous paper, we proposed an axiomatic model for measuring self-contradiction in the framework of Atanassov fuzzy sets. This way, contradiction measures that are semicontinuous and completely semicontinuous, from both below and above, were defined. Although some examples were given, the problem of finding families of functions satisfying the different axioms remained open. The purpose of...