Abstract
Based on the properties of symmetric difference of sets, a symmetric difference operator for fuzzy sets is defined to be a continuous and associative binary operator on the closed unit interval with some boundary condition. Structures and properties of these operators are investigated in this paper. The main results are: (1) It is proved that a symmetric difference operator is determined by a continuous t-conorm and a strong negation operator on the unit interval. (2) Two models of these operators are discussed. These models are related to the solutions of certain functional equations on the unit interval. In particular, the results presented here provide a partial answer to a problem raised by Alsina, Frank and Schweizer in 2003 about functional equations on the unit interval.
Published Version
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.
