A totally ordered monoid, or tomonoid for short, is a monoid endowed with a compatible total order. We deal in this paper with tomonoids that are finite and negative, where negativity means that the monoidal identity is the top element. Examples can be found, for instance, in the context of finite-valued fuzzy logic. By a Rees coextension of a negative tomonoid S, we mean a negative tomonoid T ...

In the elementary case of finitely many events, we generalise to Gödel (propositional infinite-valued) logic — one of the fundamental fuzzy logics in the sense of Hájek — the classical correspondence between partitions, quotient measure spaces, and push-forward measures. To achieve this end, appropriate Gödelian analogues of the Boolean notions of probability assignment and partition are needed...

The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this paper to the general non-involutive case, i. e. to MTL-algebras. To this end we describe the radical of MTL-algebras and characterize perfect MTL-algebras as those for which the quotient by the radical is isomorphic to the two-element Boolean algebra, and a special class of bipartite MTL-algebras, B...

In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon 4] shows that the Rayleigh quotient | i.e., the tridiagonal matrix produced by the Lanczos recursion | contains fully accurate approximations to the Ritz values in spite...

Direct-sequence Code-division multiple-access (DS-CDMA) has emerged as proper format for communication systems. As a result of multiple-access interference (MAI), inter-symbol interference (ISI), narrowband interference (NBI) and nonlinearities in channels, DS-CDMA systems can suffer deterioration in performance . New techniques to suppress narrow-band and multiple-access interference for sprea...

Granular neural networks(GNNs) as a new calculation system structure based on Granular Computing(GrC) and artificial neural network can be able to deal with all kinds of granular information of the real world. This article has made the summary on the development and the present situation of GNNs. Firstly, it introduces the basic model of GrC: word calculation model based on fuzzy sets theory, r...

Let us consider the Analytic Hierarchy Process in which the labels are structured as graded numbers. To obtain the scoring that corresponds to the best alternative, or the ranking of the alternatives, we need to use a total order for the graded numbers involved in the problem. In this article, we consider a definition of such a total order, which is based upon two subjective aspects: the degree...

The purpose of this paper is to introduce and discuss the concept of T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal in a commutative ring . Our main aim in this paper is, generalization of theorems which have been proved in [6, 7, 11]. At first, T-rough sets introduced by Davvaz in [6]. By using the paper, we define a concept of T-rough ideal , T-rough quotient ideal an...

Granular neural networks(GNNs) as a new calculation system structure based on Granular Computing(GrC) and artificial neural network can be able to deal with all kinds of granular information of the real world. This article has made the summary on the development and the present situation of GNNs. Firstly, it introduces the basic model of GrC: word calculation model based on fuzzy sets theory, r...