In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal element...

The notion of a subtractive category, recently introduced by the author, is a “categorical version” of the notion of a (pointed) subtractive variety of universal algebras, due to A.Ursini. We show that a subtractive variety C, whose theory contains a unique constant, is abelian (i.e. C is the variety of modules over a fixed ring), if and only if the dual category Cop of C, is subtractive. More ...

We prove that any simpliication order over arbtrary terms is an extension of an order by weight, by considering a related monadic term algebra called the spine. We show that any simpliication order on the spine lifts to an order on the full term algebra. Conversely a simpliication ordering on the term algebra deenes a weight function on the spine, which in turn can be lifted to a weight order o...

We prove that any simpliication order over arbtrary terms is an extension of an order by weight, by consideringa related monadic term algebra called the spine. We show that any simpliication order on the spine lifts to an order on the full term algebra. Conversely a simpliication ordering on the term algebra deenes a weight function on the spine, which in turn can be lifted to a weight order on...

Foundations should be designed for the needs of mathematics and not vice versa. We propose a technique for doing this that exploits the correspondence between category theory and logic and is potentially applicable to several mathematical disciplines. This method is applied to devising a new paradigm for general topology, called Abstract Stone Duality. We express the duality between algebra and...

We deene a family of graphs whose monadic theory is (in linear space) reducible to the monadic theory S2S of the complete ordered binary tree. This family contains strictly the context-free graphs investigated by Muller and Schupp, and also the equational graphs deened by Courcelle. Using words as representations of vertices, we give a complete set of representatives by preex rewriting of ratio...

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtain...

We present a way to organize a constructive development of the theory of Banach algebras, inspired by works of Cohen, de Bruijn and Bishop [15, 14, 4, 19]. We illustrate this by giving elementary proofs of Wiener’s result on the inverse of Fourier series and Wiener’s Tauberian Theorem. In a sequel to this paper we show how this can be used in a localic, or point-free, description of the spectru...

This paper describes a cost-effective fuzzy control system applied to a small spark-ignition internal-combustion engine to achieve regulation of the fuel injection system. It determines the amount of fuel required from a fuzzy algorithm using engine speed and manifold air pressure as input values. The fuzzy control parameters were a collection of comprehensible rules and fuzzy-set membership fu...