There are many natural forcing notions adding real numbers, most notably the precursors of this class of forcing notions, namely Cohen and Random forcing. Whereas Random forcing has been deliberately constructed in connection with the σ–algebra of Lebesgue measurable sets and Cohen forcing is represented by the algebra of Borel sets modulo the σ–ideal of meager sets, the other classical forcing...

We consider a multiple-rule, generalized modus ponens inference scheme, with an interpretation based on compositional rule of inference (CRI) and a residuated implication. We show that such a system is equivalent, as far as CRI is concerned, to a system that satis5es the “basic requirement for fuzzy reasoning”, proposed by Turksen and Tian (Fuzzy Sets and Systems 58 (1993) 3–40). We establish a...

The description of the error dynamics (30) in our paper [1] contains an omission that leads to some bounds used in the conditions of Theorem 8 and Corollary 2 in the paper to be incorrectly defined. In what follows, the correct error dynamics and the corresponding conditions are given. Instead of (30) in [1], the error dynamics are actually given by ė = m ∑ i=1 wi(z)[(Ai − LiC +MiAδi)e +Mi(Āδix̂...

In this paper we introduce a generalization of Meir-Keeler contraction forrandom mapping T : Ω×C → C, where C be a nonempty subset of a Banachspace X and (Ω,Σ) be a measurable space with being a sigma-algebra of sub-sets of. Also, we apply such type of random fixed point results to prove theexistence and unicity of a solution for an special random integral equation.