International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Some Fundamental Concepts in (2, L)-Fuzzy Topology Based on Complete Residuated Lattice-Valued Logic

  • Zeyada, Fathei M. (Department of Mathematics, Faculty of Science, Al-Azhar University) ;
  • Zahran, A.M. (Department of Mathematics, Faculty of Science, Taibah University) ;
  • El-Baki, S.A.Abd (Department of Mathematics, Faculty of Science, Assiut University) ;
  • Mousa, A.K. (Cartography and Geoinformation Department of Geography and Regional Research University of Vienna)
  • Received : 2010.08.03
  • Accepted : 2010.08.25
  • Published : 2010.09.30
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Abstract

In the present paper we introduce and study fundamental concepts in the framework of L-fuzzifying topology(so called(2,L)-fuzzy topology)as L-concepts where L is a complete residuated lattice. The concepts of (2,L)-derived, (2,L)-closure, (2,L)-interior, (2,L)-exterior and (2,L)-boundary operators are studied and some results on above concepts are obtained. Also, the concepts of an L-convergence of nets and an L-convergence of filters are introduced and some important results are obtained. Furthermore, we introduce and study bases and subbases in (2,L)-topology. As applications of our work the corresponding results(see[10-11]) are generalized and new consequences are obtained.

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References

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