Abstract
The sustaining degree is generalized to the two-dimensional sustaining degree, and based on it a new symmetric implicational method is proposed and investigated. To begin with, some properties of such two kinds of sustaining degrees are carefully discussed. Furthermore, the symmetric implicational principles are improved. Aiming at the FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems, unified forms of the new method are obtained for R-implications and (S, N)-implications. Following that, optimal solutions of the new method are obtained for eleven R- and (S, N)-implications, and four specific examples are shown which include two continuous ones and two discrete ones. Finally, it is pointed out that the new method contains related symmetric implicational methods and full implication methods as its particular cases.
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.
