Stratified L-ordered convergence structures

In this paper, a new kind of lattice-valued convergence structures on a universal set, called stratified L-ordered convergence structures, are presented by modifying the axiom for stratified L-generalized convergence structures in the fuzzy setting so as to make use of the intrinsic fuzzy inclusion order on the fuzzy power set. The category of stratified L-ordered convergence spaces described here is shown to be a reflective full subcategory in the category of stratified L-generalized convergence spaces, and hence it is topological and Cartesian-closed. As preparation, a further investigation of stratified L-filters is presented from the viewpoint that latticed-valued filters should be compatible with the intrinsic fuzzy inclusion order on the fuzzy power set.

[1]  Ulrich Höhle,et al.  Probabilistic topologies induced by L-fuzzy uniformities , 1982 .

[2]  R. Belohlávek.  Fuzzy Relational Systems: Foundations and Principles , 2002 .

[3]  Bobby Schmidt,et al.  Fuzzy math , 2001 .

[4]  Yong-Ming Li,et al.  Limit structures over completely distributive lattices , 2002, Fuzzy Sets Syst..

[5]  Qi-Ye Zhang,et al.  Continuity in quantitative domains , 2005, Fuzzy Sets Syst..

[6]  Lei Fan,et al.  A New Approach to Quantitative Domain Theory , 2001, MFPS.

[7]  J. Goguen.  L-fuzzy sets , 1967 .

[8]  Gunther Jäger,et al.  On fuzzy function spaces. , 1999 .

[9]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[10]  Gunther Jäger.  Even continuity and equicontinuity in fuzzy topology , 2001, Fuzzy Sets Syst..

[11]  Wei Yao,et al.  On many-valued stratified L-fuzzy convergence spaces , 2008, Fuzzy Sets Syst..

[12]  Wei Yao,et al.  Quantitative domains via fuzzy sets: Part I: Continuity of fuzzy directed complete posets , 2010, Fuzzy Sets Syst..

[13]  Gunther Jäger,et al.  A CATEGORY OF L-FUZZY CONVERGENCE SPACES , 2001 .

[14]  Luoshan Xu,et al.  Characterizations of fuzzifying topologies by some limit structures , 2001, Fuzzy Sets Syst..

[15]  Mustafa Demirci,et al.  A theory of vague lattices based on many-valued equivalence relations - I: general representation results , 2005, Fuzzy Sets Syst..

[16]  R. Lowen.  Convergence in fuzzy topological spaces , 1977 .

[17]  Michael Wagenknecht,et al.  Computational aspects of fuzzy arithmetics based on Archimedean t-norms , 2001, Fuzzy Sets Syst..

[18]  H. Poppe.  Brehmer, S./Apelt, H., Analysis (I. Folgen, Reihen, Funktionen). Berlin. VEB Deutscher Verlag der Wissenschaften. 1974. 207 S. (Studienbücherei) , 1979 .

[19]  Gunther Jäger,et al.  Pretopological and topological lattice-valued convergence spaces , 2007, Fuzzy Sets Syst..

[20]  Alexander P. Sostak,et al.  Axiomatic Foundations Of Fixed-Basis Fuzzy Topology , 1999 .

[21]  Gerhard Preub,et al.  SEMIUNIFORM CONVERGENCE SPACES , 1995 .

[22]  D. Kent,et al.  Convergence functions and their related topologies , 1964 .

[23]  Gunther Jäger,et al.  Subcategories of lattice-valued convergence spaces , 2005, Fuzzy Sets Syst..

[24]  Mustafa Demirci,et al.  A theory of vague lattices based on many-valued equivalence relations - II: complete lattices , 2005, Fuzzy Sets Syst..

[25]  E. Lowen,et al.  A Topological Universe Extension of FTS , 1992 .

[26]  Robert Lowen,et al.  The categorical topology approach to fuzzy topology and fuzzy convergence , 1991 .

[27]  Horst Herrlich,et al.  Abstract and concrete categories , 1990 .

[28]  Dexue Zhang,et al.  An enriched category approach to many valued topology , 2007, Fuzzy Sets Syst..

[29]  Ulrich Höhle,et al.  Non-classical logics and their applications to fuzzy subsets : a handbook of the mathematical foundations of fuzzy set theory , 1995 .