The complexity of Boolean functions
The complexity of Boolean functions
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy relational structures: the state-of-art
Fuzzy Sets and Systems - Special issue: fuzzy relations, part 2
Complexity of identification and dualization of positive Boolean functions
Information and Computation
Solution algorithms for fuzzy relational equations with max-product composition
Fuzzy Sets and Systems
On generating the irredundant conjunctive and disjunctive normal forms of monotone Boolean functions
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
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
Fuzzy Relation Equations (II): The Branch-point-solutions and the Categorized Minimal Solutions
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Algorithm for Solving Max-product Fuzzy Relational Equations
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Solutions of fuzzy relation equations based on continuous t-norms
Information Sciences: an International Journal
On the relation between equations with max-product composition and the covering problem
Fuzzy Sets and Systems
An efficient solution procedure for fuzzy relation equations with max-product composition
IEEE Transactions on Fuzzy Systems
Matrix-pattern-based computer algorithm for solving fuzzy relation equations
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Minimizing a nonlinear function under a fuzzy max-t-norm relational equation constraint
Expert Systems with Applications: An International Journal
Journal of Computational and Applied Mathematics
Minimizing a linear objective function under a fuzzy max-t norm relation equation constraint
Information Sciences: an International Journal
On fuzzy relational equations and the covering problem
Information Sciences: an International Journal
Solution to the covering problem
Information Sciences: an International Journal
Resolution of fuzzy relational equations - Method, algorithm and software with applications
Information Sciences: an International Journal
Resolution of a system of the max-product fuzzy relation equations using LºU-factorization
Information Sciences: an International Journal
| Hi-index | 0.21 |
The problem of solving a system of fuzzy relational equations with max-Archimedean t-norm composition is studied. It is shown that this problem is closely related to the covering problem, which belongs to the class of NP-hard problems. It is proved that there is a one-to-one correspondence between the minimal solutions of the equations and the irredundant coverings, as previously discovered by Markovskii [On the relation between equations with max-product composition and the covering problem, Fuzzy Sets and Systems, 153 (2005) 261-273] for fuzzy relational equations with max-product composition. Since max-product composition is a special case of max-Archimedean t-norm composition, this work extends Markovskii's work to fuzzy relational equations with max-Archimedean t-norm composition. An extension of Markovskii's algorithm is implemented, yielding a processing time linearly proportional to the square of the number of minimal solutions.