An empirical test of some measurement-theoretic axioms for fuzzy sets

Fuzzy Sets and Systems

Volumn 158, Issue 12, 2007, Pages 1348-1359

  Desimpelaere, C ^a   Marchant, T ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Fuzzy set theory; Measurement theoretic axioms; Testing axioms

Indexed keywords

DATA REDUCTION; PROBLEM SOLVING; SOCIAL SCIENCES; SYSTEMS ENGINEERING; THEOREM PROVING;

MEASUREMENT-THEORETIC AXIOMS; TESTING AXIOMS;

FUZZY SETS;

EID: 34247156628     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2007.02.011     Document Type: Article

References (28)

1. Bilgiç T., and Türksen I.B. Measurement-theoretic justification of connectives in fuzzy set theory. Fuzzy Sets and Systems 76 (1995) 289-308
2. Bilgiç T., and Türksen I.B. Measurement-theoretic frameworks for fuzzy set theory. In: Martin T., and Ralsecu A. (Eds). Fuzzy Logic in Artificial Intelligence: Towards Intelligent Systems (1997), Springer, Berlin 252-265
3. Bilgiç T., and Türksen I.B. Measurement of membership functions: theoretical and empirical work. In: Dubois D., and Prade H. (Eds). Fundamentals of Fuzzy Sets, The Handbook of Fuzzy Sets vol. 7 (2000), Kluwer Academic Press, Dordrecht 195-232
4. Bollman-Sdorra P., Wong S.K.M., and Yao Y.Y. A measure-theoretic axiomatization of fuzzy sets. Fuzzy Sets and Systems 60 (1993) 295-307
5. Carbone E., and Hey J.D. which error story is best. Journal of Risk and Uncertainty 20 2 (2000) 161-176
6. Fishburn P.C. Nontransitive preferences in decision theory. J. Risk and Uncertainty 4 (1991) 113-134
7. Gelman A., and Rubin D.B. Inference from iterative simulation using multiple sequences. Statist. Sci. 7 (1992) 457-511
8. Harless D.W., and Camerer C.F. The predictive utility of generalized expected utility theories. Econometrica 62 (1994) 1251-1290
9. Iverson G., and Falmagne J.-C. Statistical issues in measurement. Math. Social Sci. 10 (1985) 131-153
10. Karabatsos G. The Rasch model, additive conjoint measurement, and new models of probabilistic measurement theory. J. Appl. Measurement 2 (2001) 389-423
11. Karabatsos G. The exchangeable multinomial model as an approach to testing deterministic axioms of choice and measurement. J. Math. Psychology 49 (2005) 51-69
12. Karabatsos G., and Sheu C.-F. Testing measurement theory axioms with Markov Chain Monte Carlo. Paper Presented at the 34th Annual Meeting of the Society for Mathematical Psychology (2001), Brown University, Providence, Rhode Island
13. Karabatsos G., and Ullrich J.R. Enumerating and testing conjoint measurement models. Math. Social Sci. 43 (2002) 485-504
14. Krantz D.H., Luce R.D., Suppes P., and Tversky A. Foundations of Measurement vol. 1 (1971), Academic Press, New York
15. Luce R.D. Utility of Gains and Losses: Measurement Theoretical and Experimental Approaches (2000), Lawrence Erlbaum, Mahwah, NJ
16. Maassen H., and Bezembinder T. Generating random weak orders and the probability of a Condorcet winner. Social Choice and Welfare 19 (2002) 517-532
17. Marchant T. The measurement of membership by comparison. Fuzzy Sets and Systems 148 (2004) 157-177
18. Marchant T. The measurement of membership by subjective ratio estimation. Fuzzy Sets and Systems 148 (2004) 179-199
19. Myung J.I., Karabatsos G., and Iverson G. A Bayesian approach to testing decision making axioms. J. Math. Psych. 49 (2005) 205-225
20. Norwich A.M., and Türksen I.B. The fundamental measurement of fuzziness. In: Yager R. (Ed). Fuzzy Sets and Possibility Theory: Recent Developments (1982), Pergamon, Oxford
21. Roberts F.S. Measurement Theory: with Applications to Decision Making, Utility, and the Social Sciences (1979), Addison-Wesley Publishing Company, Reading, MA
22. Schwartz D.G. Layman's probability theory: a calculus for reasoning with linguistic likelihood. Inform. Sci. 126 (2000) 71-82
23. F. Tamburini, C. De Santis, E. Zamuner, Identifying phrasal connectives in Italian using quantitative methods, in: S. Nuccorini (Ed.), Phrases and Phraseology, Berlin, Peter Lang, 2002, pp. 45-64.
24. Türksen I.B. Measurement of membership functions and their acquisition. Fuzzy Sets and Systems 40 (1991) 5-38
25. Türksen I.B. Breakdown of classical equivalences in fuzzy theory. Proc. Fifth Internat. Symp. on Intelligent Manufacturing Systems, May 29-31, 2006 (2006), Sakarya University 1-8
26. Tversky A. Intransitivity of preferences. Psychological Rev. 76 (1969) 31-48
27. Zadeh L.A. Fuzzy sets. Inform. and Control 8 (1965) 338-353
28. Zimmermann H.-J., and Zysno P. Latent connectives in human decision making. Fuzzy Sets and Systems 4 (1980) 37-51