College of Arts and Science, Chiba University, Yayoi-cho, Inage-ku, Chiba 263, Japan
Faculty of Science, Chiba University, Yayoi-cho, Inage-ku, Chiba 263, Japan
Faculty of Education, Chiba University, Yayoi-cho, Inage-ku, Chiba 263, Japan
Abstract:
In this paper we develop a potential theory of fuzzy relations on the positive orthant in a Euclidean space. By introducing a linear structure for fuzzy relations, the existence of a potential and its characterization by fuzzy relational equation are derived under the assumption of contraction and compactness. In the one-dimensional unimodal case, a potential is given explicity. Also, a numerical example is shown to illustrate our approaches.