We propose a sound and practical approach, based on a formal method (known as Interval Temporal Logic), to cope with ‘change’ and analyse its effect. The approach allows us to capture a snapshot of system’s behaviour over which various interesting properties, such as liveness, timeliness and safety properties, can be validated compositionally. These properties may include invariants that are re...

We consider a piecewise smooth expanding map of the interval possessing two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed slightly to make the invariant sets merge, we describe how the unique ACIM of the perturbed map can be approximated by a convex combination of the two initial...

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-al...

We extend the notion of matching for one-dimensional dynamical systems to random on an interval. prove that a large family piecewise affine interval property implies any invariant density is constant. further introduce one-parameter produce signed binary expansions numbers in [-1,1]. This has Lebesgue almost every parameter. use this frequency digit 0 associated never exceeds 1/2.

  Fuzzy time series have been developed during the last decade to improve the forecast accuracy. Many algorithms have been applied in this approach of forecasting such as high order time invariant fuzzy time series. In this paper, we present a hybrid algorithm to deal with the forecasting problem based on time variant fuzzy time series and particle swarm optimization algorithm, as a highly effi...