This paper shows a proposal for Type-reduction of an Interval Type-2 fuzzy set composed from α-cuts done over its primary membership functions. The definition of available Type-reduction methods for Interval Type-2 fuzzy sets are based on an homogeneous subdivision of the universe of discourse, so we propose an approximation algorithm for Type-reduction of an Interval type-2 fuzzy set through i...

The notion of a fuzzy set, a natural extension of a classical set, was defined in 1965 by L.A. Zadeh; see [16]. Since that time, the fuzzy set theory has been deeply developed and it has influenced many fields of applications and therefore we can find results in branches like: fuzzy time series, fuzzy modeling, fuzzy graph theory and finally, the most often one fuzzy control. In general, the fu...

In this paper, we present a general framework for the study of interval type-2 rough fuzzy sets by using both constructive and axiomatic approaches. First, several concepts and properties of interval type-2 fuzzy sets are introduced. Then, a pair of lower and upper interval type-2 rough fuzzy approximation operators with respect to a crisp binary relation is proposed. Classical representations ...

The paper investigates the method of a fuzzy system design through its approximation with neural networks. It concentrates on further simplification by replacement of a Gaussian radial basis function with its linear and piecewise linear approximation. Different approximating possibilities are tested on four controllers chosen as benchmarks.

A new complex neuro-fuzzy self-learning approach to the problem of function approximation is proposed, where complex fuzzy sets are used to design a complex neuro-fuzzy system as the function approximator. Particle swarm optimization (PSO) algorithm and recursive least square estimator (RLSE) algorithm are used in hybrid way to adjust the free parameters of the proposed complex neuro-fuzzy syst...

In practical situations, interval-valued fuzzy sets are frequently encountered. In this paper, firstly, we present shadowed sets for interpreting and understanding interval fuzzy sets. We also provide an analytic solution to computing the pair of thresholds by searching for a balance of uncertainty in the framework of shadowed sets. Secondly, we construct errorsbased three-way approximations of...

A measure of s k c e s s for any learning algorithm is how u s e ful it is in a variety of learning situations. Those learning algorithms that support universal function approximation can theoretically h e applied to a very large and interesting class of learning problems. Many kinds of neural network architectures have already been shown to support universal approximation. In this paper, we wi...

the main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. we develop the theory of t-bestsimultaneous approximation in quotient spaces. then, we discuss the relationshipin t-proximinality and t-chebyshevity of a given space and its quotientspace.

In this paper, a due date assignment scheduling problem with precedence constraints and controllable processing times in uncertain environment is investigated, in which the basic processing time of each job is assumed to be the symmetric trapezoidal fuzzy number, and the linear resource consumption function is used.The objective is to minimize the crisp possibilistic mean (or expected) value of...