The goal of this study is to introduce a statistical method regarding the analysis of specific latent data for regression analysis of the discrete data and to build a relation between a probit regression model (related to the discrete response) and normal linear regression model (related to the latent data of continuous response). This method provides precise inferences on binary and multinomia...

We study the problem of finding a maximal transitive relation contained in a given binary relation. Given a binary relation of size m defined on a set of size n, we present a polynomial time algorithm that finds a maximal transitive sub-relation in time O(n + nm). We also study the problem of finding a maximum transitive relation contained in a binary relation. For the class of triangle-free re...

Galois connection in crisp binary relations has proved to be useful for several applications in computer science. Unfortunately, data is not always presented as a crisp binary relation but may be composed of fuzzy values, thus forming a fuzzy binary relation. This paper aims at defining the notion of fuzzy galois connection corresponding to a fuzzy binary relation in two steps: firstly by defin...

Abstract relation types (ART) are developed to represent, describe and establish a computational framework for a system. An abstract relation type is closely related to and builds upon two fundamental ideas. The first idea is the binary relation and structural modeling techniques developed by John N. Warfield. The second idea is the concept of abstract data types. These two ideas are combined t...

In this lecture, binary granular computing (granular computing on binary relations) is re-examined. Two definitions for approximations in Rough Set Theory (one is from equivalence relation and the other from point-based topology view) were no longer equal under binary relation, the latter will have the better performance, especially when the universe is infinite. However, the point-based defini...

fuzzy relation inequalities based on max-f composition are discussed, where f is a binary aggregation on [0,1]. for a fixed fuzzy relation inequalities system $ a circ^{f}textbf{x}leqtextbf{b}$, we characterize all matrices $ a^{'} $ for which the solution set of the system $ a^{' } circ^{f}textbf{x}leqtextbf{b}$ is the same as the original solution set. similarly, for a fixed matrix ...