the main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. in this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

Turbulent methane flames exhibit a change in Markstein number as the equivalence ratio changes. In this paper, we demonstrate how these changes in Markstein number are related to shifts in the chemistry and transport. We focus on the analysis of simulations of two-dimensional premixed turbulent methane flames at equivalence ratios φ=0.55 and φ=1.00 computed using the GRI-Mech 3.0 mechanism. The...

In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...