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On fuzzy fantastic filters of lattice implication algebras

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Abstract

Fuzzification of a fantastic filter in a lattice implication algebra is considered. Relations among a fuzzy filter, a fuzzy fantastic filter, and fuzzy positive implicative filter are stated. Conditions for a fuzzy filter to be a fuzzy fantastic filter are given. Using the notion of level set, a characterization of a fuzzy fantastic filter is considered. Extension property for fuzzy fantastic filters is established. The notion of normal/maximal fuzzy fantastic filters and complete fuzzy fantastic filters is introduced, and some related properties are investigated.

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Authors and Affiliations

  1. Department of Mathematics Education, Gyeongsang National University, 660-701, Chinjun (Jinju), Korea

    Young Bae Jun

  2. Department of Mathematics, Cheju National University, 690-756, Cheju, Korea

    Seok Zun Song

Authors
  1. Young Bae Jun
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  2. Seok Zun Song
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Corresponding author

Correspondence to Young Bae Jun.

Additional information

This work was supported by grant R01-2001-000-00004-0 from the Korea. Science and Engineering Foundation.

Y. B. Jun has been an educator and research mathematician since 1982, mostly at the Gyeongsang National University; and a member of the editorial board of Far East Journal of Mathematical Science (India) since 1998, and Quasigroups and Related Systems (Moldova) since 2000. He did postdoctoral work (one year, 1989–90, supported by KOSEF) at the University of Albert in Albert, Canada; and worked for one year (1996–97) as a visiting professor at the Northwest University in Xian, China (supported by LG Yonam Foundation). His research interests focus on the structure theory of BCK/BCI-algebras, Hilbert algebras, (lattice) implication algebras and negatively partially ordered semigroups, and fuzzy and hyper theory of such algebraic structures. Jun is a co-author of the textBCK-algebras with J. Meng which is an approachable introduction to BCK/BCI-algebras.

S. Z. Song has been an educator and research mathematician since 1983, mostly at the Cheju National University; and a visiting professor at Utah State University in USA (1990). Hokkaido University in Japan (1994), Bielefeld University in Germany (1996), Warsaw University in Poland (1998) and Indian Statistical Institute at Delhi (1999). He researches in linear algebra and matrix theory.

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Jun, Y.B., Song, S.Z. On fuzzy fantastic filters of lattice implication algebras. JAMC 14, 137–155 (2004). https://doi.org/10.1007/BF02936104

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  • DOI: https://doi.org/10.1007/BF02936104

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