Relations on Fs-sets and Some Results

Abstract

In this paper, we define an Fs-binary relation on a pair of Fs-sets and also define a partial order on the collection of all Fs-binary relations between the given pair of Fs-sets and prove that the collection with this given partial order is an infinitely distributive lattice. An Fs-set is a four triple in which first two components are crips sets such that the second component is sub set of first component. The fourth component is a complete Boolean algebra which is also the co-domain of two sub component functions while the third component is a function with combinations of two sub components given in which the first sub component is a complete Boolean valued function with first component as its domain and second sub component is another complete Boolean valued function with the second component as its domain and both sub component functions have fourth component as theirs co-domain and also the first sub component function is more valued than the second sub component function value.The third component which is the combination of two sub components is called the membership function of the given Fs-set. Here, the so called sub components are given within simple brackets after the third component.