A complex valued neural network is a neural network, which consists of complex valued input and/or weights and/or thresh olds and/or activation functions. Complex-valued neural networks have been widening the scope of applications not only in electronics and informatics, but also in social systems. One of the most important applications of the complex valued neural network is in image and visio...

In this paper, a fully complex-valued radial basis function (FC-RBF) network with a fully complex-valued activation function has been proposed, and its complex-valued gradient descent learning algorithm has been developed. The fully complex activation function, sech(.) of the proposed network, satisfies all the properties needed for a complex-valued activation function and has Gaussian-like cha...

We show that every inner divisor of the operator-valued coordinate function, zIE, is a Blaschke-Potapov factor. also introduce notion “rational” function and then Δ two-sided rational if only it can be represented as finite product; this extends to functions well-known result proved by V.P. Potapov for matrix-valued functions.

In this paper, -subgradients for convex set-valued maps are defined. We prove an existence theorem for -subgradients of convex set-valued maps. Also, we give necessary optimality conditions for an -solution of a convex set-valued optimization problem (CSP). Moreover, using the single-valued function induced from the set-valued map, we obtain theorems describing the -subgradient sum formula for ...

This paper addresses the problem of probabilistic reasoning as it applies to Truth Maintenance Systems. A Belief Maintenance System hal! been constructed which manages a current set of probabilistic beliefs in much the same way that a TMS manages a set of true/false beliefs. Such a system may be thought of as a generalization of a. Truth Maintenance System. It enables one to reason using normal...

Bilattices and d-frames are two different kinds of structures with a four-valued interpretation. Whereas d-frames were introduced with their topological semantics in mind, the theory of bilattices has a closer connection with logic. We consider a common generalisation of both structures and show that this not only still has a clear bitopological semantics, but that it also preserves most of the...

This paper looks at logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so that a soundness of the procedure is guaranteed in terms of 3-valued logic model theory.

It is shown in this paper that a model of multiplevalued logic over the field of complex numbers is the most appropriate for the representation of the genetic code as a multiple-valued function. The genetic code is considered as a partially defined multiple-valued function of three variables. The genetic code is the four-letter nucleic acid code, and it is translated into a 20-letter amino acid...

Motivated by the need for effectively summarising, modelling, and forecasting distributional characteristics of intra-daily returns, as well recent work on histogram-valued time-series in area symbolic data analysis, we develop a model quantile-function-valued (QF-valued) daily summaries returns. We call this dynamic quantile function (DQF) model. Instead histogram, propose to use g-and-h summa...