We distinguish three types of uncertainty: the probabilistic, the quantum and the fuzzy uncertainty. In these three contexts, we use diierent mathematical models to describe the event structures | the Boolean, the quantum and the fuzzy logics. We deene states in a uniform way as valuations. Let us ask the following question: If a; b are two elements of a (Boolean, quantum, fuzzy, resp.) logic L...

In this paper, we introduced the concepts of roughness and fuzziness in ordered ternary semigroups. We proved that the lower and upper approximation of an ordered ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal) in an ordered ternary semigroup is an ordered ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal)....

the aim of this paper is to introduce $(l,m)$-fuzzy closurestructure where $l$ and $m$ are strictly two-sided, commutativequantales. firstly, we define $(l,m)$-fuzzy closure spaces and getsome relations between $(l,m)$-double fuzzy topological spaces and$(l,m)$-fuzzy closure spaces. then, we introduce initial$(l,m)$-fuzzy closure structures and we prove that the category$(l,m)$-{bf fc} of $(l,m...

‎The distinguishing number (resp. index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$‎ ‎such that $G$ has an vertex labeling (resp. edge labeling) with $d$ labels that is preserved only by a trivial‎ ‎automorphism‎. ‎For any $n in mathbb{N}$‎, ‎the $n$-subdivision of $G$ is a simple graph $G^{frac{1}{n}}$ which is constructed by replacing each edge of $G$ with a path of length $n$...

To the memory of my mother Abstract We consider the variety of (p + 1)-tuples of matrices A j (resp. M j) from given conju-gacy classes c j ⊂ gl(n, C) (resp. C j ⊂ GL(n, C)) such that A 1 +. .. + A p+1 = 0 (resp. M 1. .. M p+1 = I). This variety is connected with the weak Deligne-Simpson problem: give necessary and sufficient conditions on the choice of the conjugacy classes c j ⊂ gl(n, C) (res...

It is well known that the right (left) regular, regular, and intra-regular ordered semigroups play an essential role in studying the structure, especially the decomposition, of ordered semigroups. In the present paper we study some more general classes containing the right regular, left regular, regular and intra-regular ordered semigroups. As an application of our results we get characterizati...

Let L : T M → R be a Tonelli Lagrangian function (with M compact and connected and dim M ≥ 2). The tiered Aubry set (resp. Mañé set) A T (L) (resp. N T (L)) is the union of the Aubry sets (resp. Mañé sets) A(L + λ) (resp. N (L + λ)) for λ closed 1-form. Then : 1. the set N T (L) is closed, connected and if dim H 1 (M) ≥ 2, its intersection with any energy level is connected and chain transitive...

let $r$ be an associative ring with identity. an element $x in r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if there exist $g in g$, $n in mathbb{z}$ and $r in r$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). a ring $r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if every element of $r$ is $mathbb{z}g$-regular (resp. strongly $...

We develop efficient Monte Carlo methods for estimating the failure probability of a system. An example of the problem comes from an approach for probabilistic safety assessment of nuclear power plants known as riskinformed safety-margin characterization, but it also arises in other contexts, e.g., structural reliability, catastrophe modeling, and finance. We estimate the failure probability us...