Design of fuzzy logic controllers based on generalized T-operators
Fuzzy Sets and Systems - Special memorial volume on fuzzy logic and uncertainly modelling
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Solution algorithms for fuzzy relational equations with max-product composition
Fuzzy Sets and Systems
Optimization of fuzzy relation equations with max-product composition
Fuzzy Sets and Systems
Resolution of composite fuzzy relation equations based on Archimedean triangular norms
Fuzzy Sets and Systems
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
New algorithms for solving fuzzy relation equations
Mathematics and Computers in Simulation
Some specific types of fuzzy relation equations
Information Sciences—Informatics and Computer Science: An International Journal
System of fuzzy relation equations as a continuous model of IF-THEN rules
Information Sciences: an International Journal
Solutions of fuzzy relation equations based on continuous t-norms
Information Sciences: an International Journal
Infinite fuzzy relation equations with continuous t-norms
Information Sciences: an International Journal
Fuzzy relational equations with generalized connectives and their applications
Fuzzy Sets and Systems
On the relation between equations with max-product composition and the covering problem
Fuzzy Sets and Systems
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Fuzzy Systems
Adaptive diagnostic system based on fuzzy relations
Cybernetics and Systems Analysis
Minimizing a linear objective function under a fuzzy max-t norm relation equation constraint
Information Sciences: an International Journal
Novel approximate solving algorithm for fuzzy relational equations
Mathematical and Computer Modelling: An International Journal
Solution to the covering problem
Information Sciences: an International Journal
Resolution of a system of the max-product fuzzy relation equations using LºU-factorization
Information Sciences: an International Journal
Some properties of infinite fuzzy relational equations with sup-inf composition
Information Sciences: an International Journal
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This work considers fuzzy relation equations with max-product composition. The critical problem in solving such equations is to determine the minimal solutions when an equation is solvable. However, this problem is NP-hard and difficult to solve [A.V. Markovskii, On the relation between equations with max-product composition and the covering problem, Fuzzy Sets and Systems 153 (2005) 261-273]. This work first examines the attributes of a solvable equation and characteristics of minimal solutions, then reduces the equation to an irreducible form, and converts the problem into a covering problem, for which minimal solutions are correspondingly determined. Furthermore, for theoretical and practical applications, this work presents a novel method for obtaining minimal solutions. The proposed method easily derives a minimal solution, and obtains other minimal solutions from this predecessor using a back-tracking step. The proposed method is compared with an existing algorithm, and some applications are described in detail.