The notions of pure ideals and pure submodules play an important role in the study of rings and their module categories. In this paper, we introduce right t-pure fuzzy ideals and pure fuzzy submodules of an R-module. We establish their basic properties, and use them to obtain fuzzy theoretic characterizations of right weakly regular rings. Among other results, we prove that a ring R is right we...

The aim of this work is to study an essential property in the framework of fuzzy preference structures, which is the transitivity. In particular, we discuss the relationship between the transitivity of a fuzzy large preference relation R and the transitivity of the fuzzy strict preference relation P obtained from R when every pair of elements can be compared. We consider some of the most import...

We consider randomness extraction by AC circuits. The main parameter, n, is the length of the source, and all other parameters are functions of it. The additional extraction parameters are the min-entropy bound k = k(n), the seed length r = r(n), the output length m = m(n), and the (output) deviation bound = (n). For k ≤ n/ log n, we show that AC-extraction is possible if and only if mr ≤ 1 + p...

A b s t I' act. Maintaining soil productivity is essential if agri­ culture production systems are to be sustainable, thus soil quality is an essential issue. However, there is a paucity of tools for mea­ surement for the purpose ofunderstanding changes in soil quality. Here the possibility of using fuzzy modeling theory as a means to address the problem of soil quality assessment is considered...

The study of theory of fuzzy sets was initiated by Zadeh in 1965. Since then many authors have extended and developed the theory of fuzzy sets in the fields of topology and analysis. The notion of fuzzy metric spaces has very important applications in quantum particle physics. As a result many authors have extended the Banach's Contraction Principle to fuzzy metric spaces and proved fixed ...

Problem (P). Let (Ω ,G ,F,P) be a probability space endowed with the filtration F = (Ft)t∈R+ . Assume that we are given a strictly positive, càdlàg, (P,F)-local martingale N with N0 = 1 and an F-adapted, continuous, increasing process Λ , with Λ0 = 0 and Λ∞ = ∞, and such that Gt := Nte−Λt ≤ 1 for every t ∈ R+. The goal is to construct a random time τ on an extended probability space and a proba...

In this paper we propose the concept of fuzzy projections on subspaces of F(R), obtained from Zadeh’s extension of canonical projections in R, and we study some of the main properties of such projections. Furthermore, we will review some properties of fuzzy projection solution of fuzzy differential equations. As we will see, the concept of fuzzy projection can be interesting for the graphical r...