On the resolution and optimization of a system of fuzzy relational equations with sup-T composition
Fuzzy Optimization and Decision Making
Minimizing a nonlinear function under a fuzzy max-t-norm relational equation constraint
Expert Systems with Applications: An International Journal
On fuzzy relational equations and the covering problem
Information Sciences: an International Journal
Spatial analysis with a tool GIS via systems of fuzzy relation equations
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part II
An efficient algorithm to computing max-min post-inverse fuzzy relation for abductive reasoning
SEMCCO'11 Proceedings of the Second international conference on Swarm, Evolutionary, and Memetic Computing - Volume Part I
Spatial analysis and fuzzy relation equations
Advances in Fuzzy Systems - Special issue on Fuzzy Functions, Relations, and Fuzzy Transforms: Theoretical Aspects and Applications to Fuzzy Systems
Complete solution sets of inf → interval-valued fuzzy relation equations
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
Image matching by using fuzzy transforms
Advances in Fuzzy Systems - Special issue on Fuzzy Functions, Relations, and Fuzzy Transforms 2013
Construction and applications of a modified Fuzzy Relational Model
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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In the literature, a necessary condition for minimal solutions of a fuzzy relational equation with max-product composition shows that each of its components is either zero or the corresponding component's value of the greatest solution. In this paper, we first extend this necessary condition to the situation with max-Archimedean triangular-norm (t-norm) composition. Based on this necessary condition, we then propose rules to reduce the problem size so that the complete set of minimal solutions can be computed efficiently. Furthermore, rather than work with the actual equations, we employ a simple matrix whose elements capture all of the properties of the equations in finding the minimal solutions. Numerical examples with specific cases of the max-Archimedean t-norm composition are provided to illustrate the procedure.