Some Results on Fs-Binary Relations of Different Kinds

Abstract

Y. Vaddiparthi et al. introduced Fs-binary rela tions on a pair of Fs-sets in a research article, “Some Modifica tions on Binary Relations on Fs-sets-Consequences,” and proved the collection of all Fs-binary relations with suitable partial orders is an infinitely distributive lattice. In this paper, we introduce various kinds of Fs-binary relations, viz. increasing Fs-binary relation, decreasing Fs-binary relation and preserving Fs-binary relation and prove any non-empty collection of all increasing (decreasing) Fs-binary relations on a pair of Fs-sets is a ∨-complete lattice (∧-complete lattice) with the same partial order and also prove that the collection of all preserving Fs binary relations with the same partial order is an infinitely distributive sublattice of the infinitely distributive lattice of all Fs-binary relations on the same pair of Fs-sets with the same partial order. Also, lastly, we define composition between suitable Fs-binary relations and introduce (1) a category of Fs binary relations. (2) a category of increasing Fs-binary relations (3) a category of decreasing Fs-binary relations and (4) a category of preserving Fs-binary relations and prove some related results.