Indistinguishability operators in measurement theory, part II: Construction of indistinguishability operators based on probability distributions

International Journal of General Systems

Volumn 32, Issue 5, 2003, Pages 431-458

  Demirci, Mustafa ^a  

^a AKDENIZ UNIVERSITY   (Turkey)

Author keywords

Fuzzy equivalence relation; Indistinguishability operator; Measurement theory; Possibility distribution; Probability distribution; Probability possibility transformation

Indexed keywords

FUZZY SETS; PROBABILITY DISTRIBUTIONS;

CONSTRUCTION PROBLEM; INDISTINGUISHABILITY OPERATORS;

MEASUREMENT THEORY;

EID: 14544272490     PISSN: 03081079     EISSN: 15635104     Source Type: Journal    
DOI: 10.1080/0308107031000120310     Document Type: Article

References (47)

1. Baldwin, J.F., Lawry, J. and Martin, T.P. (1996) "Mass Assignment Theory of the probability of fuzzy events", Fuzzy Sets Systems 83, 353-367.
2. Bělohlávek, R. (2000a) "Similarity relations and BK-relational products". Inform. Sci. 126, 287-295.
3. Bělohlávek, R. (2000b) "Similarity relations in concept lattices", J. Logic Computation 10(6), 823-845.
4. Bělohlávek, R. (2002) Fuzzy Relational Systems: Foundations and Principles (Kluwer Academic/Plenum Press, Dordrecht/New York).
5. 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.
6. Boixader, D. and Jacas, J. (1998) "Extensionality based approximate reasoning", Int. J. Approx. Reason. 19, 221-230.
7. Boixader, D., Jacas, J. and Recasens, J. (1997) "Similarity-Based Approach to Defuzzification", Proc. FUZZ'IEEE 97, Barcelona, pp 761-765.
8. De Baets, B. and Mesiar, R. (2002) "Metrics and ℑ- Equalities", J. Math. Anal. Appl. 267, 531-547.
9. Demirci, M. (2000) "Fuzzy functions and their applications", J. Math. Anal. Appl. 252, 495-517.
10. Demirci, M. (2002) "Fundamentals of M-vague algebra and M-vague arithmetic operations", Int. J. Uncertainty Fuzziness Knowledge-Based Systems 10(1), 25-75.
11. Demirci, M. (2003a) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, Part I: Fuzzy functions and their applications", Int. J. General Systems 32(2), 123-155.
12. Demirci, M. (2003b) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, Part II: Vague algebraic notions", Int. J. General Systems 32(2), 157-175.
13. Demirci, M. (2003c) "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(2), 177-201.
14. Demirci, M. (2003d) "Constructions of fuzzy functions based on fuzzy equalities", Soft Computing 7(3), 199-207.
15. Demirci, M. (2003e) "Representations of the extensions of many-valued equivalence relations", Int. J. Uncertainty Fuzziness Knowledge-Based Systems, 11(3), 319-341.
16. Demirci, M. (2003f) "Indistinguishability operators in measurement theory, Part I: Conversions of indistinguish-ability operators with respect to scales", Int. J. General Systems, To appear.
17. De Soto, A.R. and Recasens, J. (2001) "Modelling a linguistic variable as a hierarchical family of partitions induced by an indistinguishability operator", Fuzzy Sets Systems 121, 427-437.
18. Dubois, D. and Prade, H. (1983) "Unfair coins and necessity measures: towards a probabilistic interpretation of histogram", Fuzzy Sets Systems 10, 15-20.
19. Dubois, D. and Prade, H. (1986) "Fuzzy sets and statistical data", Eur. J. Operational Res. 25, 345-356.
20. Dubois, D. and Prade, H. (1988) Possibility Theory: An Approach to Computerized Processing of Uncertainty (Plenum Press, New York).
21. Dubois, D., Prade, H. and Sandri, S. (1993) "On possibility/ probability transformations". In: Lowen, R. and Roubens, M., eds, Fuzzy Logic: State of the Art (Kluwer Academic Publishers, Dordrecht), pp 103-110.
22. Gerla, G. (2001) Fuzzy Logic: Mathematical Tools for Approximate Reasoning (Kluwer Academic Publishers, Dordrecht).
23. Höhle, U. (1988) "Quotients with respect to similarity relations", Fuzzy Sets Systems 27, 31-44.
24. Höhle, U. (1996) "On the fundamentals of fuzzy set theory", J. Math. Anal. Appl. 201, 786-826.
25. Höhle, U. (1999) "The Poincaré paradox and non-classical logics", In: Dubois, D., Pade, H. and Klement, E.P., eds, Fuzzy Sets, Logics and Reasoning about Knowledge (Kluwer Academic Publishers, Dordrecht), pp 7-16.
26. Höhle, U. and Šostak, A.P. (1999) "Axiomatic foundations of fixed-basis fuzzy topology", In: Höhle, U. and Rodabaugh, S.E., eds. Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory (Kluwer Academic Press, Boston), pp 123-272.
27. Höppner, F., Klawonn, F. and Eklund, P. (2002) "Learning indistinguishability from data", Soft Computing 6, 6-13.
28. Klawonn, F. (1994) "Fuzzy sets and vague environments", Fuzzy Sets Systems 66, 207-221.
29. Klawonn, F. (2000) "Fuzzy points, fuzzy relations and fuzzy functions", In: Novâk, V. and Perfilieva, I., eds, Discovering World with Fuzzy Logic (Physica-Verlag, Heidelberg) pp 431-453.
30. Klawonn, F. and Castro, J.L. (1995) "Similarity in fuzzy reasoning", Mathware Soft Computing 2, 197-228.
31. Klawonn, F. and Kruse, R. (1993) "Equality relations as a basis for fuzzy control". Fuzzy Sets Systems 54, 147-156.
32. Klawonn, F. and Kruse, R. (1997) "Constructing a fuzzy controller from data", Fuzzy Sets Systems 85, 177-193.
33. Klawonn, F., Gebhardt, J. and Kruse, R. (1995) "Fuzzy control on the basis of equality relations-with an example from idle speed control", IEEE Trans. Fuzzy Systems 3, 336-350.
34. Klement, E.P., Mesiar, R. and Pap, E. (2000) Triangular Norms, Trends in Logic (Kluwer Academic Publishers, Dordrecht) Vol. 8.
35. Klir, G.J. (1990) "A principle of uncertainty and information invariance". Int. J. General Systems 17, 249-275.
36. Klir, G.J. and Geer, J.F. (1993) "Information-preserving probability-possibility transformations: recent developments". In: Lowen, R. and Roubens, M., eds, Fuzzy Logic: State of the Art (Kluwer Academic Publishers, Dordrecht), pp 417-428.
37. Klir, G.J. and Parviz, B. (1992) "Probability-possibility transformations: a comparison", Int. J. General Systems 21, 291-310.
38. Klir, G.J. and Wang, Z. (1992) Fuzzy Measure Theory (Plenum Press, New York).
39. Lassere, V.G., Mauris, L. and Foullay, L. (1997) A Simple Probability-Possibility Transformation for Measuring Error Representation: A Truncated Triangular Transformation Proc. IFSA Congress, Prague.
40. Novǎk, V. (1986) Fuzzy Sets and Their Applications (Adam Hilger, Bristol).
41. Oussalah, M. (2000) "On the probability/possibility transformations: a comparative analysis", Int. J. General Systems 29(5), 671-718.
42. Pradera, A., Trillas, E. and Castineira, E. (2002) "On the aggregation of some classes of fuzzy relations", In: Magdalena, L., Bouchon-Meunier, B., Gutiérrez-Rios, J. and Yager, R.R., eds. Technologies for Constructing Intelligent Systems 2: Tools, Studies in Fuzziness and Soft Computing (Springer-Verlag, Berlin) pp 125-136.
43. Sudkamp, T. (1992) "On probability-possibility transformations" , Fuzzy Sets Systems 51, 73-81.
44. Valverde, L. (1985) "On the structure of F-indistinguishability operators", Fuzzy Sets Systems 17, 313-328.
45. Wonneberger, S. (1994) "Generalization of an invertible mapping between probability and possibility". Fuzzy Sets Systems 64, 229-240.
46. Zadeh, L.A. (1965) "Fuzzy sets", Inform. Control 8, 338-353.
47. Zadeh, L.A. (1978) "Fuzzy sets as a basis for a theory of possibility", Fuzzy Sets Systems 1, 3-28.