Abstract
Resolution of fuzzy relational inequalities (FRIs) plays a significant role in decision-making, image compression and fuzzy control. This paper studies the resolution of a kind of FRIs with Boolean semi-tensor product composition. First, by resorting to the column stacking technique, the equivalent form of FRIs with Boolean semi-tensor product composition is obtained, which is a system of FRIs (SFRIs) with max–min composition. Second, based on the semi-tensor product method, all the solutions to FRIs with Boolean semi-tensor product composition are obtained by finding all possible parameter set solutions. Finally, a general procedure is developed for the resolution of FRIs with Boolean semi-tensor product composition. Two illustrative examples are worked out to show the effectiveness of the obtained new results.
Highlights
Resolution of fuzzy relational equations (FREs) and fuzzy relational inequalities (FRIs) has wide applications in several research fields including decision-making, image compression, fuzzy control and so on [1,2,3,4]
We have investigated the resolution of a kind of FRIs with the Boolean semi-tensor product composition
By using the column stacking operator, we have obtained the equivalent column stacking form of FRIs with Boolean semi-tensor product composition, which has the form of system of fuzzy relational inequalities (SFRIs) with max–min composition
Summary
Resolution of fuzzy relational equations (FREs) and fuzzy relational inequalities (FRIs) has wide applications in several research fields including decision-making, image compression, fuzzy control and so on [1,2,3,4]. All the existing results on the resolution of FREs and FRIs just considered the case where fuzzy matrices have compatible dimensions (see Definition 2 below). It is meaningful to investigate the resolution of FREs and FRIs with Boolean semi-tensor product composition, and apply the obtained results to the study of dimension-varying fuzzy systems. This paper focuses on the resolution of FRIs (see (11) below) and SFRIs (see (12) below) with Boolean semi-tensor product composition, and aims to propose a general procedure to obtain all the solutions. We establish a general procedure for the resolution of FRIs and SFRIs with Boolean semi-tensor product composition, which facilitates the application of fuzzy theory in dimension-varying systems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
