Black's Median Voter Theorem is among the more useful mathematical tools available to political scientists for predicting choices of political actors based on their preferences over a finite set of alternatives within an institutional or constitutional setting. If the alternatives can be placed...

Predictions concerning voting outcomes in crisp spatial models rely heavily on the existence of a core, in the absence of which political players choosing among a set of alternatives by majority rule will not be able to arrive at a stable choice. No matter which option they might initially...

In this paper, we prove a fuzzy version of Arrow's Theorem that contains the crisp version. We show that under our definitions, Arrow's Theorem remains intact even if levels of intensities of the players and levels of membership in the set of alternatives are considered.

We use techniques from fuzzy mathematics to develop metrics for measuring how well deaf and hard of hearing preschool students of Omaha Hearing School are closing the gap with respect to language growth.

Given a group G, we show how one can define a vague group structure on G via a chain of subgroups of G. We discuss how a group homomorphism f from a vague group X onto a group Y induces a vague group structure on Y with f satisfying the vague homomorphism property. The notion of Ω-vague groups...

We use for the first time fuzzy mathematics to aid in the determination of which tests of preschool, hard of hearing and deaf children are the best predictors of success when these students are mainstreamed in the public school system. The techniques are those of group decision making and...

In this paper, we present a historical overview of the development of fuzzy mathematics. We mainly concentrate on the evolution of the mathematical representation of fuzziness by means of fuzzy set theory. From the many remaining recently introduced models to represent imprecise and uncertain...

We define vague groups in terms of similarity relations rather than fuzzy equalities. This yields a bijection between the set of all right-invariant similarity relations on a group and the set of all fuzzy subgroups of the group. Under this bijection, right-invariant and left-invariant...

We examine the notion of a vague ring. We develop a method of constructing vague rings which can be used in the construction of other algebraic structures. We make a connection between vague rings and M-adic topologies on rings and also to the solution of nonlinear systems of equations and to...