(1) Let L be a non empty reflexive transitive relational structure and x, y be elements of L. If x ≤ y, then compactbelow(x)⊆ compactbelow(y). (2) For every non empty reflexive relational structure L and for every element x of L holds compactbelow(x) is a subset of CompactSublatt(L). (3) For every relational structure L and for every relational substructure S of L holds every subset of S is a s...

Through changing the equivalence relation of objects to reflexive and symmetric binary relation in the incomplete information system, a cumulative variable precision rough set model is proposed. The basic properties of β lower and β upper cumulative approximation operators are investigated. β upper, and β lower distribution consistent set are explored for defining β upper, and β lower distribut...

In this paper we present a new extension of coupled fixed point theorems in metric spaces endowed with a reflexive binary relation that is not necessarily neither transitive nor antisymmetric. The key feature in this coupled fixed point theorems is that the contractivity condition on the nonlinear map is only assumed to hold on elements that are comparable in the binary relation. Next on the ba...