The Algebraic Properties of Linguistic Value "Truth" and Its Reasoning

  • Authors:
  • Zheng Pei

  • Affiliations:
  • School of Mathematics & Computer, Xihua University, Chengdu, Sichuan, 610039, China

  • Venue:
  • IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
  • Year:
  • 2007

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Abstract

From logic and algebra point of view, Computing with words is discussed in this paper. By analyzing the semantically ordering relation of linguistic variable Truth, orderings on linguistic hedges Hand atomic evaluating syntagm Tr= {true, false} are obtained, respectively. Let Hbe finite chain, then Lukasiewicz product algebra of T= H×Trof Truthis obtained, and term-set T(X) of Truthis embedded into an algebra Γof type Δ= { ï戮驴 , ï戮驴 , ï戮驴,ï戮驴L}. In some cases, Γcan be applied in linguistic decision directly, also as truth domain of logic statements. Different with other truth domain, here truth values are linguistic terms rather than numerals (or symbolic).