Abstract
The fuzzy relational equations with min-implication composition are considered, where the implication operation involved is the residuum with respect to the minimum operation. The solution set of such a system of equations, whenever nonempty, can be characterized by a minimum solution and finitely many maximal solutions. It is shown that a system of fuzzy relational equations with min-implication composition can be reformulated in polynomial time into a system of 0-1 mixed integer linear inequalities, and consequently, the structure of its solution set can be revealed in a succinct manner. Besides, it is shown that the determination of all maximal solutions is polynomially reducible to the transversal hypergraph generation problem, of which some practically well-performed algorithms are available.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.