Related papers: On Boolean reliability algebra
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…
A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered,…
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof…
Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…
In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…
A semicoherent system can be described by its structure function or, equivalently, by a lattice polynomial function expressing the system lifetime in terms of the component lifetimes. In this paper we point out the parallelism between the…
We prove two results intended to streamline proofs about cellularity that pass through mutual algebraicity. First, we show that a countable structure $M$ is cellular if and only if $M$ is $\omega$-categorical and mutually algebraic. Second,…
Items in a test are often used as a basis for making decisions and such tests are therefore required to have good psychometric properties, like unidimensionality. In many cases the sum score is used in combination with a threshold to decide…
In this paper, we deal with soft MTL-algebras based on fuzzy sets. By means of $\in$-soft sets and q-soft sets, some characterizations of (Boolean, G- and MV-) filteristic soft MTL-algebras are investigated. Finally, we prove that a soft…
We introduce shift algebras as certain crossed product algebras based on general function spaces and study properties, as well as the classification, of a particular class of modules depending on a set of matrix parameters. It turns out…
In this paper we discuss the existence of a control measure for a family of measures on a Boolean algebra. We obtain a necessary and sufficient condition and several related results, including a new criterion for weak compactness for…
A strongly Fregean algebra is an algebra such that the class of its homomorphic images is Fregean and the variety generated by this algebra is congruence modular. To understand the structure of these algebras we study the prime intervals…
We consider Stone algebras with a distinguished element $e$ satisfying the identity $e \to x = \neg \neg x$ for all elements $x$ of the algebra. We provide an adjunction between the category of such algebras and that of Boolean algebras.
This paper puts forth a class of algebraic structures, relativized Boolean algebras (RBAs), that provide semantics for propositional logic in which truth/validity is only defined relative to a local domain. In particular, the join of an…
This paper proposes a new fuzzy assessing procedure with application in management decision making. The proposed fuzzy approach build the membership functions for system characteristics of a standby repairable system. This method is used to…
Classical machine learning classifiers tend to be overconfident can be unreliable outside of the laboratory benchmarks. Properly assessing the reliability of the output of the model per sample is instrumental for real-life scenarios where…
This paper consider the problem of determining the reliability of a software system which can be decomposed in a number of modules. We have derived the expression of the reliability of a system using the Markovian model for the transfer of…
Fault tree analysis is a vital method of assessing safety risks. It helps to identify potential causes of accidents, assess their likelihood and severity, and suggest preventive measures. Quantitative analysis of fault trees is often done…
We discuss the construction of component importance measures for binary coherent reliability systems from known stochastic dependence measures by measuring the dependence between system and component failures. We treat both the…
Fuzzy logic is a way to argue with boolean predicates for which we only have a confidence value between 0 and 1 rather than a well defined truth value. It is tempting to interpret such a confidence as a probability. We use Markov kernels,…