The construction of multidimensional membership functions and its application to feasibility problems

Abstract

We present a novel idea of the membership function using logical expressions over inequalities. This is achieved by introducing the multidimensional membership function (distending function) using inequalities by including more variables instead of just one. In this paper, we concentrate on the application of this new approach to different kinds of feasibility problems. This new concept serves as a good tool for describing various kinds of feasibility regions. Another result here is that we present algorithms that can handle linear, nonlinear, convex and non-convex feasibility problems. Usually, in practice only the conjunction operator is used in the case of feasibility problems. A novelty of our result is that we drop this restriction, and based on our construction we will describe regions where other types of operators can also be used. We shall introduce the fundamentals of this new concept and we will show how it can be used in practical applications. Later, this approach may be applied to neural networks as well.