A survey on fuzzy relational equations, part I: classification and solvability |
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| Authors: | Pingke Li Shu-Cherng Fang |
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| Institution: | (1) Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695, USA;(2) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China;(3) Department of Industrial Engineering, Tsinghua University, Beijing, 100084, China |
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| Abstract: | Fuzzy relational equations play an important role in fuzzy set theory and fuzzy logic systems, from both of the theoretical
and practical viewpoints. The notion of fuzzy relational equations is associated with the concept of “composition of binary
relations.” In this survey paper, fuzzy relational equations are studied in a general lattice-theoretic framework and classified
into two basic categories according to the duality between the involved composite operations. Necessary and sufficient conditions
for the solvability of fuzzy relational equations are discussed and solution sets are characterized by means of a root or
crown system under some specific assumptions. |
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| Keywords: | Fuzzy relational equation Solvability Duality Adjointness Triangular norm |
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