in this paper we establish several polynomials similar to bernstein's polynomials and several refinements of  hermite-hadamard inequality for convex functions.

Since fuzzy logic was introduced by Lotfi Zadeh in 1965 (41), it has had many successful applications in all fields that one can imagine. The reason is that many real-world applications problems are involved the systems in which at least some parameters are represented by fuzzy numbers rather than crisp numbers and linguistic labels such as small and large are also associated with the fuzzy set...

Mathematical models in science and engineering often contain parameters that are uncertain. These parameters are usually represented by random numbers, fields or processes. However, when the stochastic characteristics of these parameters are not precisely known, an interval representation, or, more generally, a fuzzy representation may be more appropriate. This leads to so-called fuzzy differen...

This study presents an evolutionary neural fuzzy system (NFS) for nonlinear system control. The proposed NFS model uses functional link neural networks (FLNNs) as the consequent part of the fuzzy rules. This study uses orthogonal polynomials and linearly independent functions in a functional expansion of the functional link neural networks. A learning algorithm, which consists of structure lear...

This study presents a new evolutionary learning algorithm to optimize the parameters of the neural fuzzy classifier (NFC). This new evolutionary learning algorithm is based on a hybrid of bacterial foraging optimization and particle swarm optimization. It is thus called bacterial foraging particle swarm optimization (BFPSO). The proposed BFPSO method performs local search through the chemotacti...

Fuzzy techniques have been originally invented as a methodology that transforms the knowledge of experts formulated in terms of natural language into a precise computer-implementable form. There are many successful applications of this methodology to situations in which expert knowledge exist, the most well known is an application to fuzzy control. In some cases, fuzzy methodology is applied ev...

Mathematical models of physical systems often contain parameters with an imprecisely known and uncertain character. It is quite common to represent these parameters by means of random variables. Numerous methods have been developed to compute accurate approximations to solutions of equations with such parameters. This approach, however, may not be entirely justified when the uncertainty is due ...

The theory of fuzzy measures and fuzzy integrals was introduced by S u g e n o [16] and intensively studied. Monographs [15] and [18] are dedicated to this topic. Recently, several classical inequalities were generalized to fuzzy integral. F l o r e sF r a n u l i č and R o m á n-F l o r e s [11] provided a Chebyshev type inequality for fuzzy integral of continuous and strictly monotone functio...

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.