Communication among Agents: a Set Theoretic Approach

This paper uses the notion of relative sets in relation to fuzzy set theory to provide a mathematical framework to analyze communication among agents. Each relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap’s logic. Two orderings on relative sets are considered; one is an extension of the classical set inclusion ordering while the other is a new ordering of knowledge or information. According to these orderings, we can divide set theoretic problems into two major categories: reasoning problems and communicating problems. In the first category, an agent tries to extract a sound decision through granular reasoning. In this case, a granule represents a concept or a word. In the second category, each granule relates to an agent, and the problem is to compare agents’ knowledge about concepts by their related granules, e.g. a knowledge reduction problem. Then, we concentrate on the second category of problems and try to investigate this kind of problems in the context of fuzzy set theory. In this way, we could provide a basis for modeling and analyzing the relations among machines, which could communicate with each other using words and granules.