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Erschienen in:
On the Meaning and the Measuring of ‘Probable’ Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Organizing Families of Aggregation Operators into a Cube of Opposition

verfasst von : Didier Dubois, Henri Prade, Agnès Rico

Erschienen in: Granular, Soft and Fuzzy Approaches for Intelligent Systems

Verlag: Springer International Publishing

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Abstract

The cube of opposition is a structure that extends the traditional square of opposition originally introduced by Ancient Greek logicians in relation with the study of syllogisms. This structure, which relates formal expressions, has been recently generalized to non Boolean, graded statements. In this paper, it is shown that the cube of opposition applies to well-known families of idempotent, monotonically increasing aggregation operations, used in multiple criteria decision making, which qualitatively or quantitatively provide evaluations between the minimum and the maximum of the aggregated quantities. This covers weighted minimum and maximum, and more generally Sugeno integrals on the qualitative side, and Choquet integrals, with the important particular case of Ordered Weighted Averages, on the quantitative side. The main appeal of the cube of opposition is its capability to display the various possible aggregation attitudes in a given setting and to show their complementarity.

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Vorheriges Kapitel On the Meaning and the Measuring of ‘Probable’
Nächstes Kapitel Entropy Measures and Views of Information
Fußnoten
1
This example is specially dedicated to Ron Yager in remembrance of a dinner in Lyon in a traditional restaurant, which took place at the occasion of the CNRS Round Table on Fuzzy Sets organized by Robert Féron [31] in Lyon on June 23–25, 1980 [32]. This Round Table was an important meeting for the development of fuzzy set research, because most of the active researchers of the field were there. Interestingly enough, Robert Féron had the remarkable intuition to invite Gustave Choquet in the steering committee, at a time where no fuzzy set researcher was mentioning Choquet integrals! This meeting also included, as usual, some nice moments of relaxation and good humor. In particular, at the above-mentioned dinner, to which quite a number of people took part (including two of the authors of this paper), Ron enjoyed very much a pigs feet dish. He was visibly very happy with his choice, so Lotfi Zadeh told him, “Ron, you should have been a pig in another life”, to which Ron replied “no, Lotfi, it is in this life”, while continuing to suck pigs’ bones with the greatest pleasure.
 
Literatur
1.
2.
Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manage. Sci. 17(4), B-141–B-164 (1970)
3.
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000); Springer, Berlin (2013)
4.
de Campos, L.M., Bolaños, M.J.: Characterization and comparison of Sugeno and Choquet integrals. Fuzzy Sets Syst. 52, 61–67 (1992)MathSciNetCrossRefMATH
5.
Grabisch, M., Labreuche, Ch.: A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. 4OR 6, pp. 1–44 (2008)
6.
7.
8.
Yager. R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)
9.
Yager, R.R., Kacprzyk, J. (eds.): The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer Acad. Publ. (1997)
10.
Yager, R.R., Kacprzyk, J., Beliakov, G. (eds.): Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Studies in Fuzziness and Soft Computing 265, Springer (2011)
11.
Dubois, D., Prade, H., Rico, A.: Qualitative integrals and desintegrals: how to handle positive and negative scales in evaluation. In: Proceedings of 14th IPMU (Information Processing and Management of Uncertainty in Knowledge-Based Systems), vol. 299 of CCIS, pp. 306–316. Springer (2012)
12.
Dubois, D., Prade, H., Rico, A.: Residuated variants of Sugeno integrals: towards new weighting schemes for qualitative aggregation methods. Inf. Sci. to appear
13.
Dubois, D., Prade, H., Rico, A.: On the informational comparison of qualitative fuzzy measures. In: Proceedings of IPMU’14 (Information Processing and Management of Uncertainty in Knowledge-Based Systems), vol. 442 of CCIS, pp. 216–225 (2014)
14.
Dubois, D., Prade, H., Rico, A.: The cube of opposition. A structure underlying many knowledge representation formalisms. In: Proceedings of 24th International Joint Conference on Artificial Intelligence (IJCAI’15), Buenos Aires, Jul. 25–31, pp. 2933–2939 (2015)
15.
Parsons, T.: The traditional square of opposition. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (2008)
16.
17.
Dubois, D., Prade, H.: From Blanché’s hexagonal organization of concepts to formal concept analysis and possibility theory. Logica Univers. 6, 149–169 (2012)MathSciNetCrossRefMATH
18.
Dubois, D., Prade, H.: An introduction to bipolar representations of information and preference. Int. J. Intell. Syst. 23(8), 866–877 (2008)CrossRefMATH
19.
Ciucci, D., Dubois, D., Prade, H.: The structure of oppositions in rough set theory and formal concept snalysis—toward a new bridge between the two settings. In: Beierle, Ch., Meghini, C. (eds.) Proceedings of 8th International Symposium on Foundations of Information and Knowledge Systems (FoIKS’14), Bordeaux, Mar. 3–7, LNCS 8367, pp. 154–173. Springer (2014)
20.
Dubois, D., Prade, H.: Weighted minimum and maximum operations. An addendum to ‘A review of fuzzy set aggregation connectives’. Inf. Sci. 39, 205–210 (1986)MathSciNetCrossRefMATH
21.
Dubois, D., Prade, H.: Possibility theory and its applications: where do we stand? In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 31–60. Springer (2015)
22.
23.
Dubois, D., Prade, H.: Semantics of quotient operators in fuzzy relational databases. Fuzzy Sets Syst. 78, 89–93 (1996)MathSciNetCrossRef
24.
Sugeno, M.: Theory of fuzzy integrals and its applications. Ph.D. Thesis, Tokyo Institute of Technology, Tokyo (1974)
25.
Sugeno, M.: Fuzzy measures and fuzzy integrals: a survey. In: Gupta, M.M., Saridis, G.N., Gaines, B.R. (eds.) Fuzzy Automata and Decision Processes, pp. 89–102. North-Holland (1977)
26.
Yager, R.R.: Measures of assurance and opportunity in modeling uncertain information. Int. J. Intell. Syst. 27(8), 776–797 (2012)CrossRef
27.
Dubois, D., Prade, H., Rico, A.: The cube of opposition and the complete appraisal of situations by means of Sugeno integrals. In: Proceedings of International Symposium on Methodologies for Intelligent Systems (ISMIS’15), Lyon, oct. 21–23, to appear (2015)
28.
Shafer, G.: A Mathematical Theory of Evidence. Princeton University (1976)
29.
Dubois, D., Prade, H.: A set-theoretic view of belief functions. Logical operations and approximation by fuzzy sets. Int. J. Gen. Syst. 12(3), 193–226, (1986). Reprinted in Classic Works of the Dempster-Shafer Theory of Belief Functions. In: Yager, R.R., Liu, L. (eds.) Studies in Fuzziness and Soft Computing, vol. 219, pp. 375–410 (2008)
30.
Chateauneuf, A., Jaffray, J.-Y.: Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Math. Soc. Sci. 17(3), 263–283 (1989). Reprinted in Classic Works of the Dempster-Shafer Theory of Belief Functions. In: Yager, R.R., Liu, L. (eds.) Studies in Fuzziness and Soft Computing, vol. 219, pp. 477–498 (2008)
31.
Auray, J.-P., Prade, H.: Robert Féron: a pioneer in soft methods for probability and statistics. In: Proceedings of 4th International Workshop in Soft Methods in Probability and Statistics (SMPS), Toulouse, Sept. 8–10, pp. 27–32 (2008)
32.
Table Ronde: Quelques Applications Concrètes Utilisant les Derniers Perfectionnements de la Théorie du Flou. BUSEFAL (LSI,Université Paul Sabatier, Toulouse), n\(^{\circ }\)2, 103–105 (1980)
33.
34.
Fodor, J., Marichal, J.-L., Roubens, M.: Characterization of the ordered weighted averaing operators. IEEE Trans. Fuzzy Syst. 3(2), 236–240 (1995)CrossRef
35.
Fodor, J., Yager, R.R.: Fuzzy set-theoretic operators and quantifiers. In: Dubois, D., Prade, H., (eds.) Fundamentals of Fuzzy Sets. The Handbooks of Fuzzy Sets Series, vol.1, pp. 125–193. Kluwer (2000)
36.
Grabisch, M.: On equivalence classes of fuzzy connectives: the case of fuzzy integrals. IEEE Trans. Fuzzy Syst. 3, 96–109 (1995)CrossRef
37.
38.
Metadaten
Titel
Organizing Families of Aggregation Operators into a Cube of Opposition
verfasst von
Didier Dubois
Henri Prade
Agnès Rico
Copyright-Jahr
2017
Buch
Granular, Soft and Fuzzy Approaches for Intelligent Systems

Print ISBN: 978-3-319-40312-0

Electronic ISBN: 978-3-319-40314-4

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-40314-4_2

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