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http://dx.doi.org/10.5391/IJFIS.2010.10.3.230

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)

Publication Information

International Journal of Fuzzy Logic and Intelligent Systems / v.10, no.3, 2010 , pp. 230-241 More about this Journal

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.

Keywords

L-fuzziying topology; convergence of nets; convergence of filters; bases; subbases and Complete residuated lattice;

Citations & Related Records

Reference

1	T. Kubiak, On Fuzzy Topologies, Ph.D. Thesis, Adam Mickiewicz University, Poznan, Poland, 1985.
2	J. Pavelka, On fuzzy logic II, Z. Math. Logic Gvundlagen Math, vol.25, pp. 119–134 , 1979. DOI
3	K.I. Rosenthal, Quantales and their applications, Pitman Research Notes in Mathematics 234 (Longman, Burnt Mill, Harlow 1990).
4	A.P. Sostak, On fuzzy topological structure, Suppl. Rend. Circ. Mat. Palermo vol.2, no.11, pp. 89–103, 1985.
5	M.S. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, vol.39, pp. 302–321, 1991.
6	M.S. Ying, A new approach for fuzzy topology (II), Fuzzy Sets and Systems, vol. 47, pp. 221–232, 1992. DOI ScienceOn
7	M.S. Ying, Fuzzifying topology based on complete residuated Lattice-valued logic(I), Fuzzy Sets and Systems, vol. 56, pp. 337–373, 1993. DOI ScienceOn
8	Y. Yue and Fu-Gui Shi, On (L,M)-fuzzy quasi-uniform spaces, Fuzzy Sets and Systems, vol.158, pp. 1472–1485, 2007. DOI ScienceOn
9	L.A. Zadeh, Fuzzy sets, Inform. Control, vol.8, pp.338–353, 1965. DOI
10	A.M. Zahran, Fathei M. Zeyada, M. Azab Abd-Allah and M.M. Khalaf, Separation axioms in L-fuzzifying topology, Far East Journal of Mathematical Sciences(FJMS). vol. 21 no. 2. pp. 227–249.
11	Fathei M. Zeyada, M. Azab Abd-Allah and M.M. Khalaf, Short Communication: A comment on and a characterization of the concept of complete residuated lattice, Journal of Nonlinear Sciences and Applications vol. 1, no.2, pp.202–204, 2008.
12	G. Birkhoff, Lattice theory, 3rd ed., AMS Providence, RI, 1967.
13	U. Hohle, Upper semicontinuous fuzzy sets and applications, J. Math. Anal. Appl,vol 78, pp. 659–673,1980. DOI
14	U. Hohle, Characterization of L-topologies by L-valued neighborhoods, in: U. Hohle, S.E. Rodabaugh (Eds.), The Handbooks of Fuzzy Sets Series, Vol. 3 Kluwer Academic Publishers, Dordrecht, pp.389.432, 1999.
15	U. Hohle and A.P. Sostak, Axiomatic foundations of fixed-basis fuzzy topology, The Handbooks of Fuzzy Sets Series, Vol. 3 Kluwer Academic Publishers, Dordrecht, pp.123–272, 1999.
16	J.L. Kelley, General topology, Van Nostrand, New York, 1955.