The usefulness of fuzzy input fuzzy output functions and their interpolation/approximation by different operators in fuzzy control motivate their deeper theoretical study. We obtain some properties of fuzzy B-spline series such as variation and uncertainty diminishing property. We also propose spline approximation of fuzzy input fuzzy output functions. Key–Words: Fuzzy numbers, Fuzzy splines, A...

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory...

Parsimony is very important in system modeling as it is closely related to model interpretability. In this paper, a scheme for constructing accurate and parsimonious fuzzy models by generating distinguishable fuzzy sets is proposed, in which the distinguishability of input space partitioning is measured by a so-called “local” entropy. By maximizing this entropy measure the optimal number of mer...

the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.

8 This work deals with the simulation of fuzzy random variables, which can be used 9 to model various realistic situations, where uncertainty is not only present in form 10 of randomness but also in form of imprecision, described by means of fuzzy sets. 11 Utilizing the common arithmetics in the space of all fuzzy sets only induces a conical 12 structure. As a consequence, it is difficult to di...

In this paper the concepts of sectional intuitionistic fuzzy continuous mapping, l -intuitionistic fuzzy compact sets and asymptotic intuitionistic fuzzy normal structure are introduced. Schauder type and Baillon and Schoneberg type fixed point theorems are also established in an intuitionistic fuzzy n -normed linear space.

The approximation space definition has evolved in rough set theory over the last 15 years. The aim was to build a unified framework for concept approximations. We present an overview of this evolution together with some operations on approximation spaces that are used in searching for relevant approximation spaces. Among such operations are inductive extensions and granulations of approximation...

motivated by samet et al. [nonlinear anal., 75(4) (2012), 2154-2165], we introduce the notions of $alpha$-$phi$-fuzzy contractive mapping and $beta$-$psi$-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. the presented theorems extend, generalize and improve the corresponding results given in the literature.

The main purpose of this paper is to consider the new kind of approximation which is called as t-best coapproximation in fuzzy n-normed spaces. The set of all t-best coapproximation define the t-coproximinal, t-co-Chebyshev and F-best coapproximation and then prove several theorems pertaining to this sets. Keywords—Fuzzy-n-normed space, best coapproximation, co-proximinal, co-Chebyshev, F-best ...