Symmetric difference operators on fuzzy sets

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• 作者：Zhiqiang Shen ^{zhiqiangshen7@gmail.com} ; Dexue Zhang ; ^{dxzhang@scu.edu.cn}
• 关键词：Symmetric difference operator ; t-Norm ; t-Conorm ; Strong negation ; Associativity
• 刊名：Fuzzy Sets and Systems
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：308
• 期：Complete
• 页码：1-26
• 全文大小：450 K
• 卷排序：308

文摘

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.