We describe a new method for the fitting of differentiable fuzzy model functions to crisp data. The model functions can be either scalar or multidimensional and need not be linear. The data are n-component vectors. An efficient algorithm is achieved by restricting the fuzzy model functions to sets which depend on a fuzzy parameter vector and assuming that the vector has a conical membership fun...

In this paper we present, propose and examine additional membership functions for the Smoothing Transition Autoregressive (STAR) models. More specifically, we present the tangent hyperbolic, Gaussian and Generalized bell functions. Because Smoothing Transition Autoregressive (STAR) models follow fuzzy logic approach, more fuzzy membership functions should be tested. Furthermore, fuzzy rules can...

In this paper we find sharp inequalities of Jackson-Stechkin type between the best approximations periodic differentiable functions by trigonometric polynomials and generalized moduli continuity m-th order in space L_2. The exact values various n-widths classes from L_2 defined modus $r$-th derivative function f are calculated.

Generalized gradients and subgradients These terms refer to various setvalued replacements for the usual derivative which are used in developing differential calculus for functions which are not differentiable in the classical sense. The subject itself is known as nonsmooth analysis. One of the best-known theories of this type is that of generalized gradients. Another basic construct is the sub...

We consider simple Lyapunov-exponent-based conditions under which the response of a system to a chaotic drive is a smooth function of the drive state. We call this differentiable generalized synchronization ~DGS!. When DGS does not hold, we quantify the degree of nondifferentiability using the Hölder exponent. We also discuss the consequences of DGS and give an illustrative numerical example. @...

generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and   -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. some new results are obtained.

Abstract In this paper, we introduce a new concept of sets and class functions called E -univex functions, respectively. For an -differentiable function, the -univexity is introduced by generalizing several concepts generalized convexity earlier defined into optimization theory. addition, some properties are investigated. Further, also introduced. Then, sufficiency so-called -Karush–Kuhn–Tucker...