Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part I: fuzzy functions and their applications

References

• Birkhoff G. 1967 Lattice Theory 3rd edn
   Google Scholar
• Bodenhofer U. 2000 A similarity-based generalization of fuzzy orderings preserving the classical axioms Int. J. Uncertainty Fuzziness Knowledge-Based Systems 8 5 593 610
   Google Scholar
• Boixader D. Jacas J. Recasens J. 2000a Fuzzy equivalence relations: advanced material Dubois D. Prade H. Fundmentals of Fuzzy Sets Kluwer Academic Publishers Boston 261 290
   Google Scholar
• Boixader D. Jacas J. Recasens J. 2000b Upper and lower approximations of fuzzy sets Int. J. General Systems 29 555 568
   Google Scholar
• Cerruti U. Höhle U. 1986 An approach to uncertainty using algebras over a monoidal closed category Suppl. Rend. Circ. Matem. Palermo Ser. II 12 47 63
   Google Scholar
• De Baets B. Mesiar R. 1997 Pseudo-metrics and T-equivalences J. Fuzzy Math. 5 471 481
   Google Scholar
• De Baets B. Mesiar R. 2002 Metrics and T-equalities J. Math. Anal. Appl. 267 531 547
   Google Scholar
• Demirci M. 1999a Fuzzy functions and their fundamental properties Fuzzy Sets Systems 106 239 246
   Google Scholar
• Demirci M. 1999b Vague groups J. Math. Anal. Appl. 230 142 156
   Google Scholar
• Demirci M. 2000 Fuzzy functions and their applications J. Math. Anal. Appl. 252 495 517
   Google Scholar
• Demirci M. 2002a Fundamentals of M-vague algebra and M-vague arithmetic operations Int. J. Uncertainty Fuzziness Knowledge-Based Systems 10 1 25 75
   Google Scholar
• Demirci M. 2002b Indistinguishability operators in measurement theory, Part II: Constructions of indistinguishability operators based on probability distributions Int. J. General Systems Submitted for publication
   Google Scholar
• Demirci M. 2003a On many-valued partitions and many-valued equivalence relations Int. J. Uncertainty Fuzziness Knowledge-Based Systems In press
   Google Scholar
• Demirci M. 2003b Constructions of fuzzy functions based on fuzzy equalities Soft Computing 7 3 199 207
   Google Scholar
• Demirci M. 2003c Representations of the extensions of many-valued equivalence relations Int. J. Uncertainty Fuzziness Knowledge-Based Systems In press
   Google Scholar
• Demirci M. 2003d Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, Part II: Vague algebraic notions Int. J. General Systems 32 157 175
   Google Scholar
• Demirci M. 2003e Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, Part III: Constructions of vague algebraic notions and vague arithmetic operations Int. J. General Systems 32 177 201
   Google Scholar
• Demirci M. Recasens J. 2003 Fuzzy groups, fuzzy functions and fuzzy equivalence relations”, Fuzzy Sets and Systems In press
   Google Scholar
• Dubois D. Prade H. 1980 Fuzzy Sets and Systems: Theory and Applications Academic Press New York
   Google Scholar
• Dubois D. Prade H. 1982a Towards fuzzy differential calculus Part 1: Integration of fuzzy mappings Fuzzy Sets Systems 8 1 17
   Google Scholar
• Dubois D. Prade H. 1982b Towards fuzzy differential calculus Part 2: Integration of fuzzy intervals Fuzzy Sets Systems 8 105 116
   Google Scholar
• Dubois D. Prade H. 1982c Towards fuzzy differential calculus Part 3: Differentiation Fuzzy Sets Systems 8 225 233
   Google Scholar
• Dubois D. Prade H. 1983 Unfair coins and necessity measures: Towards a probabilistic interpretation of histogram Fuzzy Sets Systems 10 15 20
   Google Scholar
• Dubois D. Prade H. 1986 Fuzzy Sets and statistical data Eur. J. Operational Res. 25 345 356
   Google Scholar
• Dubois D. Prade H. 1988 Possibility Theory: An Approach to Computerized Processing of Uncertainty Plenum Press New York
   Google Scholar
• Dubois D. Prade H. Sandri S. 1993 On possibility/probability transformations Lowen R. Roubens M. Fuzzy Logic: State of the Art Kluwer Academic Press Dordrecht 103 110
   Google Scholar
• Goetschel R. Voxman W. 1986 Elementary fuzzy calculus Fuzzy Sets Systems 18 31 43
   Google Scholar
• Guang-Quan Z. 1991 Fuzzy continuous function and its properties Fuzzy Sets Systems 43 159 171
   Google Scholar
• Hisdal E. 1978 Conditional possibilities, independence and noninteraction Fuzzy Sets Systems 1 283 297
   Google Scholar
• Hisdal E. 1979 Possibilistically dependent variables and a general theory of fuzzy sets Gupta M.M. Ragade R.K. Yager R.R. Advances in Fuzzy Set Theory and Applications North-Holland Publishing Company Amsterdam 215 234
   Google Scholar
• Höhle U. 1988 Quotients with respect to similarity relations Fuzzy Sets Systems 27 31 44
   Google Scholar
• Höhle U. 1995 Commutative, residuated 1-monoids Höhle U. Klement E.P. Non-Classical Logics and Their Applications to Fuzzy Subsets Kluwer Academic Press Dordrecht 53 106
   Google Scholar
• Höhle U. 1998a Classification of subsheaves over GL-algebra Buss S.R. Hăek P. Pudlăk P. Logic Colloquium'98 Lecture Notes in Logic 13, Springer-Verlag Berlin 238 261
   Google Scholar
• Höhle U. 1998b Many-valued equalities, singletons and fuzzy partitions Soft Computing 2 134 140
   Google Scholar
• Höhle U. 1999 The Poincaré paradox and non-classical logics Dubois D. Prade H. Klement E.P. Fuzzy Sets, Logics and Reasoning about Knowledge Kluwer Academic Press Dordrecht 7 16
   Google Scholar
• Höhle U. Šostak A.P. 1999 Axiomatic foundations of fixed-basis fuzzy topology Höhle U. Rodabaugh S.E. Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory Kluwer Academic Publishers Boston 123 272
   Google Scholar
• Joslyn C. Possibilistic Processes for Complex Systems Modelling Ph.D. Thesis, State University of New York Binghamton
   Google Scholar
• Joslyn C. 1997 Measurement of possibilistic histograms from interval data Int. J. General Systems 26 9 33
   Google Scholar
• Kaufmann A. Gupta M.M. 1988 Fuzzy Mathematical Models in Engineering and Management Science Elsevier Science Amsterdam
   Google Scholar
• Klawonn F. 1995 Fuzzy control on the basis of equality relations-with an example from idle speed control IEEE Trans. Fuzzy Systems 3 336 350
   Google Scholar
• Klawonn F. 2000 Fuzzy points, fuzzy relations and fuzzy functions Novăk V. Perfilieva I. Discovering World with Fuzzy Logic Physica-Verlag Heidelberg 431 453
   Google Scholar
• Klawonn F. Castro J.L. 1995 Similarity in Fuzzy Reasoning Mathware Soft Computing 2 197 228
   Google Scholar
• Klawonn F. 1997 Constructing a fuzzy controller from data Fuzzy Sets Systems 85 177 193
   Google Scholar
• Klir G.J. 1990 A principle of uncertainty and information invariance Int. J. General Systems 17 249 275
   Google Scholar
• Klir G.J. Geer J.F. 1993 Information-preserving probability–possibility transformations: Recent developments Lowen R. Roubens M. Fuzzy Logic: State of the Art Kluwer Academic Press Dordrecht 417 428
   Google Scholar
• Klir G.J. Parviz B. 1992 Probability–possibility transformations: A comparison Int. J. General Systems 21 291 310
   Google Scholar
• Klir G.J. Wang B. 1992 Fuzzy Measure Theory Plenum Press New York
   Google Scholar
• Novăk V. 1986 Fuzzy Sets and Their Applications Adam Hilger Bristol
   Google Scholar
• Ogata K. 1990 Modern Control Engineering Prentice-Hall New Jersey
   Google Scholar
• Oussalah M. 2000 On the probability/possibility transformations: A comparative analysis Int. J. General Systems 29 5 671 718
   Google Scholar
• Sudkamp T. 1992 On probability/possibility transformations Fuzzy Sets Systems 51 73 81
   Google Scholar
• Valverde L. 1985 On the structure of F-indistinguishability operators Fuzzy Sets Systems 17 313 328
   Google Scholar
• Wonneberger S. 1994 Generalization of an invertible mapping between probability and possibility Fuzzy Sets Systems 64 229 240
   Google Scholar
• Yue Z. Zhong Q. Guangyuan W. 1998 Solving process for a system of first-order fuzzy differential equations Fuzzy Sets Systems 95 333 347
   Google Scholar
• Zadeh L.A. 1965 Fuzzy sets Inform. Control 8 338 353
   Google Scholar
• Zadeh L.A. 1978 Fuzzy sets as a basis for a theory of possibility Fuzzy Sets Systems 1 3 28
   Google Scholar