Fuzzy-valued transitive inclusion measure, similarity measure and application to approximate reasoning

  • Authors:

  • Hong-Ying Zhang;Wen-Xiu Zhang

  • Affiliations:

  • Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaan'xi, P.R. China;Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaan'xi, P.R. China

  • Venue:
  • RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
  • Year:
  • 2007

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Abstract

In fuzzy set theory, inclusion measure indicates the degree to which a given fuzzy set is contained in another fuzzy set. Many inclusion measures taking values in [0,1] have been made in the literature. This paper proposes a series of fuzzy-valued inclusion measures which, by a relation view, are reflexive, antisymmetric and T -transitive where T is a left-continuous triangular norm; In addition, they possess most of the axiomatic properties which are postulated by Sinha and Dougherty for an inclusion measure. Fuzzy-valued similarity measures are also defined by the fuzzy-valued inclusion measures; They have T -transitivity and properties introduced by Liu for a similarity measure. Lastly two methods for inference in approximate reasoning based on the fuzzy-valued inclusion measure and the fuzzy-valued similarity measure are studied.