An intrinsic fuzzy set on the universe of discourse of predicate formulas

  • Authors:

  • Guo-Jun Wang;Xiao-Yan Qin;Xiang-Nan Zhou

  • Affiliations:

  • Institute of Mathematics, Shaanxi Normal University, Xi'an 710062, China and Research Center for Science, Xi'an Jiaotong University, Xi'an 710049, China;Institute of Mathematics, Shaanxi Normal University, Xi'an 710062, China and Department of Mathematics, Shanxi Teachers University, Linfen 041000, China;Institute of Mathematics, Shaanxi Normal University, Xi'an 710062, China and Department of Mathematics, Hunan University, Changsha 410082, China

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2006

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Abstract

We construct and study a new intrinsic fuzzy subset @t on the crisp set F of all first-order logic formulas in two-valued logic. In order to define this fuzzy set, we need to introduce a number of other new concepts, such as the relative satisfiability degree, the least and the largest interpretations, and the average validity degree of a formula. One of the main results proved in this paper is that all the membership degrees of this fuzzy set form a dense subset of [0,1]. This new intrinsic fuzzy set will be used to develop a kind of fuzzy deductive reasoning of Pavelka's type.