In the paper a new structure of Multi-Layer Perceptron, able to deal with quaternion-valued signal, is proposed. A learning algorithm for the proposed Quaternion MLP (QMLP) is also derived. Such a neural network allows to interpolate functions of quaternion variable with a smaller number of connections with respect to the corresponding real valued MLP. INTRODUCTION In the last few years, neural...

For simplicity, we follow the rules: X denotes a non empty set, Y denotes a set, S denotes a σ-field of subsets of X, F denotes a function from N into S, f , g denote partial functions from X to R, A, B denote elements of S, r, s denote real numbers, a denotes a real number, and n denotes a natural number. Let X be a non empty set, let f be a partial function from X to R, and let a be a real nu...

Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate non-classical negation such as a paraconsistent one (no paradox arises if the liar is both true and false). We consider a non-Fregean logic which is a revised an...

The role played by real-valued functions in functional analysis is fundamental. One often considers metrics, or seminorms, or linear functionals, to mention some important examples. We introduce the notion of deenable real-valued function in functional analysis: a real-valued function f deened on a structure of functional analysis is deenable if it can be \approximated" by formulas which do not...

Single valued neutrosophic hesitant fuzzy set has three independent parts, namely the truth membership hesitancy function, indeterminacy membership hesitancy function, and falsity membership hesitancy function, which are in the form of sets that assume values in the unit interval [0, 1]. Single valued neutrosophic hesitant fuzzy set is considered as a powerful tool to express uncertain, incompl...

Cellular neural networks (CNNs) are one type of interconnected neural network and differ from the well-known Hopfield model in that each cell has a piecewise linear output function. In this paper, we present a multi-valued CNN model in which each nonlinear element consists of a multi-valued output function. The function is defined by a linear combination of piecewise linear functions. We conduc...

In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of i...

In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced ...

In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...

Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We de...