There exists a calculus for general nondifferentiable functions that englobes a large part of the familiar subdifferential calculus for convex nondifferentiable functions [1]. This development started with F.H. Clarke, who introduced a generalized gradient for functions that are locally Lipschitz, but (possibly) nondifferentiable. Generalized gradients turn out to be the subdifferentials, in th...

In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers which have finite nondifferentiable points. In the previous work, this convolution method only can be ...

A generalized Cohen-Grossberg neural network model with both discrete and neutral time varying delays is considered here. Activation functions and approximately behaved functions are not required to be differentiable. Global robust exponential stability of periodic solution is studied using a suitable Lyapunov functional by constructing a general eigen value problem [GEVP]. More generalized and...

In the present use of fuzzy logic systems tuning of their parameters has become an important issue. Many techniques, mainly based on the application of gradient descent, have been applied to this task generally in order to minimize a quadratic error function. The class of fuzzy logic systems using piecewise linear membership functions (e.g., triangular or trapezoidal) and/or minimum or maximum ...

This article presents some new inequalities of Simpson’s type for differentiable functions by using (α,m)-convexity. Some results concavity are also obtained. These estimates improve on the previously known ones. applications special means real numbers provided.

This contribution deals with fuzzy interval orders which are defined by the use of generalized properties, the Ferrers property and total connectedness, of fuzzy relations. Definitions of the generalized properties involve binary operations including t-norms and t-conorms and, more generally, fuzzy conjunctions and disjunctions. In particular, conditions for n-argument functions to preserve fuz...

In this paper, we use the Riemann-Liouville fractionalintegrals to establish some new integral inequalities related toChebyshev's functional in the case of two differentiable functions.

A method of estimating a variety of curves by a sequence of piecewise polynomials is proposed, motivated by a Bayesian model and an appropriate summary of the resulting posterior distribution. A joint distribution is set up over both the number and the position of the knots de®ning the piecewise polynomials. Throughout we use reversible jump Markov chain Monte Carlo methods to compute the poste...