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A potential of fuzzy relations with a linear structure: The contractive case |
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| Authors: | Yuji Yoshida Masami Yasuda Jun-ichi Nakagami Masami Kurano |
| Affiliation: | 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. |
| Keywords: | Fuzzy potential linear structure fuzzy relation fuzzy relational equation contraction property |
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