Pattern search learning is known for simplicity and faster convergence. However, one of the downfalls of this learning is the premature convergence problem. In this paper, we show how we can avoid the possibility of being trapped in a local pit by the introduction of stochastic value. This improved pattern search is then applied on a recurrent type neuro-fuzzy network (ANFIS) to solve time seri...

We are concerned with the development of a K−step method for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

The aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed every real number r is replaced by a fuzzy number r either triangular fuzzy number or singleton fuzzy set fuzzy point . And then, we will consider that some results re...

In this article we introduce the notion of statistical convergence difference sequences of fuzzy real numbers, c̄ (∆). We study some properties of the statistically convergent and statistically null difference sequence spaces of fuzzy real numbers, like completeness, solidness, sequence algebra, symmetricity, convergence free, nowhere denseness and some inclusion results.

In this paper the concept of strongly (λM )p − Cesáro summability of a sequence of fuzzy numbers and strongly λM− statistically convergent sequences of fuzzy numbers is introduced. Keywords—Fuzzy numbers, statistical convergence, Orlicz space, entire sequence.

Hierarchical structures and uncertainty measures are two main aspects in granular computing, approximate reasoning and cognitive process. Typical hesitant fuzzy sets, as a prime extension of fuzzy sets, are more flexible to reflect the hesitance and ambiguity in knowledge representation and decision making. In this paper, we mainly investigate the hierarchical structures and uncertainty measure...

In this paper the concept of strongly (λM )p − Cesáro summability of a sequence of fuzzy numbers and strongly λM− statistically convergent sequences of fuzzy numbers is introduced. Keywords—Fuzzy numbers, statistical convergence, Orlicz space, gai sequence.

In this paper, a type of fuzzy system structure is applied to heuristic dynamic programming (HDP) algorithm to solve nonlinear discrete-time Hamilton–Jacobi–Bellman (DT-HJB) problems. The fuzzy system here is adopted as a 0-order T–S fuzzy system using triangle membership functions (MFs). The convergence of HDP and approximability of the multivariate 0-order T–S fuzzy system is analyzed in this...

An Uzawa method is presented for solving fuzzy linear systems whose coefficient matrix is crisp and the right-hand side column is arbitrary fuzzy number vector. The explicit iterative scheme is given. The convergence is analyzed with convergence theorems and the optimal parameter is obtained. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of t...

A methodology for the design of fuzzy control laws for tracking control of mechanical systems is described. The approach uses Lyapunov’s stability theory to formulate a class of control laws that guarantee convergence of the tracking errors to within specification limits in presence of bounded parameter uncertainties and input disturbances. The proposed methodology results in control laws that ...