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A survey on fuzzy relational equations, part I: classification and solvability

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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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  1. Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, 27695, USA

    Pingke Li & Shu-Cherng Fang

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Shu-Cherng Fang

  3. Department of Industrial Engineering, Tsinghua University, Beijing, 100084, China

    Shu-Cherng Fang

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Li, P., Fang, SC. A survey on fuzzy relational equations, part I: classification and solvability. Fuzzy Optim Decis Making 8, 179–229 (2009). https://doi.org/10.1007/s10700-009-9059-0

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