Related papers: Intuitionistic Fuzzy Banach Algebra
In an earlier paper, Dawson and the second author asked whether or not a Banach function algebra with dense invertible group can have a proper Shilov boundary. We give an example of a uniform algebra showing that this can happen, and…
A Banach algebra A is self-induced if the multiplication is an isomorphism from the A-balanced projective tensor-square of A to A. The class of self-induced Banach algebras is a natural generalization of unital Banach algebras, providing a…
This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers have fuzzy…
After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. In this paper, we apply the concept…
In this chapter, we study Information Geometry from a particular non-parametric or functional point of view. The basic model is a probabilities subset usually specified by regularity conditions. For example, probability measures mutually…
The class of radial fuzzy systems is introduced. The fuzzy systems in this class use radial functions to implement membership functions of fuzzy sets and exhibit a shape preservation property in antecedents of their rules. The property is…
In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact…
Fusion of Artificial Neural Networks (ANN) and Fuzzy Inference Systems (FIS) have attracted the growing interest of researchers in various scientific and engineering areas due to the growing need of adaptive intelligent systems to solve the…
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…
We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces.…
In this paper we consider systems which consist of binary components with known reliabilities. We discuss their algebraic properties and define the corresponding algebraic structure, which we call the reliability algebra. We prove that the…
Soft set theory serves as a mathematical framework for handling uncertain information, and hesitant fuzzy sets find extensive application in scenarios involving uncertainty and hesitation. Hesitant fuzzy sets exhibit diverse membership…
In this paper, the formulation of Quantum Mechanics in terms of fuzzy logic and fuzzy sets is explored. A result by Pykacz, that establishes a correspondence between (quantum) logics (lattices with certain properties) and certain families…
In a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a…
We construct a topology on a given algebraically closed field with a distinguished subfield which is also algebraically closed. This topology is finer than Zariski topology and it captures the sets definable in the pair of algebraically…
A new seemingly weak axiomatic formulation of information algebras is given. It is shown how such information algebras can be embedded into set (information) algebras. In set algebras there is a natural relation of conditional independence…
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus,…
In the current paper a new Trapezoidal Fuzzy Model for Assessment is developed. This model is a variation of a special form of the commonly used in Fuzzy Mathematics Center of Gravity technique.
In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy…
After a concise introduction to the square of opposition, in particular, and, Aristotelian Diagrams, in general, I describe how one can create a mathematical universe to host these objects. Since these objects assume that the underlying…