Approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory

作者：Liu Xiaodong^*; Chai Tianyou; Wang Wei; Liu Wanquan

来源：Information Sciences, 2007, 177(4): 1007-1026.

DOI：10.1016/j.ins.2006.07.011

• AFS algebras
• completely distributive lattices
• AFS structures
• preference relations
• sub-preference relations

In this paper, the representations of fuzzy concepts based on raw data have been investigated within the framework of AFS (Axiomatic Fuzzy Set) theory. First, a brief review of AFS theory is presented and a completely distributive lattice, the E(#)I algebra, is proposed. Secondly, two kinds of E(#)I algebra representations of fuzzy concepts are derived in detail, In order to represent the membership functions of fuzzy concepts in the interval [0, 1], the norm of AFS algebra is defined and studied. Finally, the relationships of various representations with their advantages and drawbacks are analyzed.

• 出版日期2007-2-15
• 单位东北大学; 大连理工大学