Transporting many-valued sets along many-valued relations

The transport of L-sets along an L-relation R is considered, with L any residuated lattice, sometimes with further properties as to be a frame or an MV-algebra. Pairs of powerset operators related to R are considered and their basic properties are studied in a comprehensive discussion including some results already known. A few examples and suggestions for application and further development are also given.

[1]  Stephen Ernest Rodabaugh,et al.  Relationship of Algebraic Theories to Powerset Theories and Fuzzy Topological Theories for Lattice-Valued Mathematics , 2007, Int. J. Math. Math. Sci..

[2]  Leon D. Segal,et al.  Functions , 1995 .

[3]  Stephen E. Rodabaugh,et al.  Axiomatic Foundations For Uniform Operator Quasi-Uniformities , 2003 .

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

[5]  Michael A. Erceg,et al.  Functions, equivalence relations, quotient spaces and subsets in fuzzy set theory , 1980 .

[6]  V. I. Ponomarev,et al.  Fundamentals of general topology : problems and exercises , 1984 .

[7]  Cosimo Guido,et al.  Structured lattices and ground categories of L-sets , 2005, Int. J. Math. Math. Sci..

[8]  Cosimo Guido,et al.  Some remarks on fuzzy powerset operators , 2002, Fuzzy Sets Syst..

[9]  D. Mundici,et al.  Algebraic Foundations of Many-Valued Reasoning , 1999 .

[10]  J. Goguen L-fuzzy sets , 1967 .

[11]  Stephen E. Rodabaugh,et al.  POWERSET OPERATOR FOUNDATIONS FOR POINT-SET LATTICE-THEORETIC (POSLAT) FUZZY SET THEORIES AND TOPOLOGIES , 1997 .

[12]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[13]  Ulrich Höhle,et al.  Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory , 1998 .

[14]  Stephen E. Rodabaugh,et al.  Categorical Foundations of Variable-Basis Fuzzy Topology , 1999 .

[15]  C. Guido Powerset Operators Based Approach To Fuzzy Topologies On Fuzzy Sets , 2003 .

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

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

[18]  Jirí Adámek,et al.  Abstract and Concrete Categories - The Joy of Cats , 1990 .

[19]  Radim Belohlávek,et al.  Fuzzy Closure Operators Induced by Similarity , 2003, Fundam. Informaticae.

[20]  Stephen E. Rodabaugh,et al.  Powerset Operator Foundations For Poslat Fuzzy Set Theories And Topologies , 1999 .

[21]  R. Belohlávek Fuzzy Closure Operators , 2001 .

[22]  Radim Belohlávek,et al.  Fuzzy closure operators II: induced relations, representation, and examples , 2002, Soft Comput..

[23]  Wang Guo-jun,et al.  Theory of topological molecular lattices , 1992 .

[24]  Radim Belohlavek,et al.  FUZZY CLOSURE OPERATORS II , 2002 .

[25]  Siegfried Gottwald,et al.  Many-Valued Logic And Fuzzy Set Theory , 1999 .

[26]  K. Hofmann,et al.  A Compendium of Continuous Lattices , 1980 .

[27]  B. Hutton,et al.  Uniformities on fuzzy topological spaces , 1977 .

[28]  U. Höhle Many Valued Topology and its Applications , 2001 .

[29]  Alexander P. Sostak,et al.  A Unified Approach To The Concept Of Fuzzy L-Uniform Space , 2003 .

[30]  Klaas Pieter Hart,et al.  Uniform Spaces, I , 2003 .

[31]  Radim Belohlávek,et al.  Fuzzy Galois Connections , 1999, Math. Log. Q..

[32]  Andrei Popescu,et al.  Non-dual fuzzy connections , 2004, Arch. Math. Log..

[33]  Ulrich Bodenhofer A unified framework of opening and closure operators with respect to arbitrary fuzzy relations , 2003, Soft Comput..

[34]  Radim Belohlávek,et al.  Concept lattices and order in fuzzy logic , 2004, Ann. Pure Appl. Log..

[35]  S. E. Rodabaugh,et al.  Topological and Algebraic Structures in Fuzzy Sets , 2003 .