Chapter

Fuzzy Systems and Knowledge Discovery

Volume 3613 of the series Lecture Notes in Computer Science pp 160-166

Fuzzy Ultra Filters and Fuzzy G-Filters of MTL-Algebras

  • Xiao-hong ZhangAffiliated withCarnegie Mellon UniversityFaculty of Science, Ningbo University
  • , Yong-quan WangAffiliated withCarnegie Mellon UniversityInformation Technology Center, East China University of Politics and Law
  • , Yong-lin LiuAffiliated withCarnegie Mellon UniversityDepartment of Mathematics, Nanping Teachers College

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Abstract

The concepts of fuzzy ultra filters and fuzzy G-filters of MTL-algebras are introduced. Some examples are given and the following main results are proved: (1) a fuzzy filter of MTL-algebra is fuzzy ultra filter if and only if it is both a fuzzy prime filter and fuzzy Boolean filter; (2) a fuzzy filter of MTL-algebra is fuzzy Boolean filter if and only if it is both a fuzzy G-filter and fuzzy MV-filter.