Related papers: On Boolean reliability algebra
The monadic theory of $(\mathbb R,\le)$ with quantification restricted to Borel sets is decidable. The Boolean combinations of $F_\sigma$ sets form an elementary substructure of the Borel sets. Under determinacy hypotheses, the proof…
Aiming for accurate estimation of system reliability of load-sharing systems, a flexible model for such systems is constructed by approximating the cumulative hazard functions of component lifetimes using piecewise linear functions. The…
Observables on effect algebras and their fuzzy versions obtained by means of confidence measures (Markov kernels) are studied. It is shown that, on effect algebras with the (E)-property, given an observable and a confidence measure, there…
An algebraic structure underlying the quantity calculus is proposed consisting in an algebraic fiber bundle, that is, a base structure which is a free Abelian group together with fibers which are one dimensional vector spaces, all of them…
We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classification of transitive Lie algebroids and describe…
We explore the integration of representations from a Lie algebra to its algebraic group in positive characteristic. An integrable module is stable under the twists by group elements. Our aim is to investigate cohomological obstructions for…
Information algebra is algebraic structure for local computation and inference. Given an initial universe set and a parameter set, we show that a soft set system over them is an information algebra. Moreover, in a soft set system, the…
We investigate how classifiers for Boolean networks (BNs) can be constructed and modified under constraints. A typical constraint is to observe only states in attractors or even more specifically steady states of BNs. Steady states of BNs…
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…
A fuzzy mnesor space is a semimodule over the positive real numbers. It can be used as theoretical framework for fuzzy sets. Hence we can prove a great number of properties for fuzzy sets without refering to the membership functions.
Intuitionistic fuzzy Banach algebra is introduced and a few properties of it is studied. The properties of invertible elements and relation among invertible elements, open set, closed set are emphasized. Topological divisors of zero is…
We consider the problem where a set of individuals has to classify $m$ objects into $p$ categories and does so by aggregating the individual classifications. We show that if $m\geq 3$, $m\geq p\geq 2$, and classifications are fuzzy, that…
We show that certain category of bimodules over a finite dimensional quiver algebra known as type B zigzag algebra is a quotient category of the category of type B Soergel bimodules. This leads to an alternate proof of Rouquier's conjecture…
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…
It is known a method for converting a system of Boolean polynomial equations to a single Boolean polynomial equation with less variables. In this paper, we show a formula for systems of Boolean polynomial equations which is based on the…
Given a complete Heyting algebra we construct an algebraic tensor triangulated category whose Bousfield lattice is the Booleanization of the given Heyting algebra. As a consequence we deduce that any complete Boolean algebra is the…
Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables…
This paper presents a study of separation axioms and sobriety of bitopological spaces from the point of view of fuzzy topology via identifying bitopological spaces with topological spaces valued in the Boolean algebra of four elements. A…
In this paper we study affine and bilinear systems on Lie groups. We show that there is an intrinsic connection between the solutions of both systems. Such relation allows us to obtain some preliminary controllability results of affne…
A simple Bayesian approach to nonparametric regression is described using fuzzy sets and membership functions. Membership functions are interpreted as likelihood functions for the unknown regression function, so that with the help of a…