Convergence and fixed points by fuzzy orders

A general approach to fixed point theory is proposed which is related to the notion of fuzzy ordering. This approach extends both the fixed point theorems in metric spaces and the ones in ordered sets.

[1]  Melvin Fitting,et al.  Metric Methods Three Examples and a Theorem , 1994, J. Log. Program..

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

[3]  L. Valverde.  On the structure of F-indistinguishability operators , 1985 .

[4]  Paulo Ribenboim,et al.  Logic programming and ultrametric spaces , 1999 .

[5]  Ulrich Bodenhofer,et al.  Representations and constructions of similarity-based fuzzy orderings , 2003, Fuzzy Sets Syst..

[6]  Ulrich Höhle,et al.  Partial ordering in L-underdeterminate sets , 1985, Inf. Sci..

[7]  Cristina Coppola.  Distance and closeness measures in information spaces , 2006 .

[8]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[9]  Anthony Karel Seda.  Quasi-Metrics and the Semantics of Logic Programs , 1997, Fundam. Informaticae.

[10]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[11]  Michael B. Smyth,et al.  Quasi Uniformities: Reconciling Domains with Metric Spaces , 1987, MFPS.

[12]  K. Deimling.  Fixed Point Theory , 2008 .

[13]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

[14]  V. Novák,et al.  Mathematical Principles of Fuzzy Logic , 1999 .

[15]  C. Marsala,et al.  Linguistic modifiers and measures of similarity or resemblance , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[16]  Jan J. M. M. Rutten,et al.  Elements of Generalized Ultrametric Domain Theory , 1996, Theor. Comput. Sci..

[17]  Bernard De Baets,et al.  A compendium of fuzzy weak orders: Representations and constructions , 2007, Fuzzy Sets Syst..

[18]  Anthony Karel Seda.  Quasi-Metrics and Fixed Points in Computing , 1996, Bull. EATCS.

[19]  B. Baets,et al.  Metrics and T-Equalities , 2002 .

[20]  Melvin Fitting,et al.  Fixpoint Semantics for Logic Programming a Survey , 2001, Theor. Comput. Sci..

[21]  Giangiacomo Gerla,et al.  Fuzzy Logic: Mathematical Tools for Approximate Reasoning , 2001 .