Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
New Trends in Preference, Utility, and Choice: From a Mono-approach to a Multi-approach Read chapter Read first chapter

2019 | OriginalPaper | Chapter

New Directions in Ordinal Evaluation: Sugeno Integrals and Beyond

Authors : Miguel Couceiro, Didier Dubois, Hélène Fargier, Michel Grabisch, Henri Prade, Agnès Rico

Published in: New Perspectives in Multiple Criteria Decision Making

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter provides a state-of-the-art account of the use of Sugeno integrals in decision evaluation, when it is difficult to use meaningful figures of merit when assessing the worth of a decision and when only a finite scale of, e.g., linguistic categories, can be used. Here, Sugeno integrals are thought of as idempotent lattice polynomial functions on a finite bounded chain, which makes it possible to assign importance weights to groups of criteria or states. Algebraic and behavioral characterizations of the Sugeno integral are presented and discussed, including the special cases of weighted minima and maxima. Extensions of this framework are also surveyed, namely: lexicographic refinements that increase the discrimination power of this approach; the use of local utility functions in order to cope with criteria having distinct rating scales; and the generalization of the criteria weighting scheme at work in Sugeno integrals. Another kind of extension considered is when ratings belong to a bipolar scale where good and bad figures are explicitly present, thus giving rise to the symmetric Sugeno integral or to the separate evaluation of pros and cons. Moreover, it is pointed out that Sugeno integrals encode decision rules and that this bridge leads to methods for extracting knowledge from qualitative data. The results of empirical studies of the latter are also presented and discussed, accordingly.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Interpretation of Multicriteria Decision Making Models with Interacting Criteria
next chapter Advances and New Orientations in Goal Programming
Footnotes
1
Even ordinal decision methods need to inject some form of bipolarity. Note that multicriteria decision methods based on the merging of outranking relations use concordance and discordance tests between criteria (Roy 1996), where the notion of veto prevents the choice of alternatives that rate too low with respect to some criteria. It can be viewed as an attempt to capture the idea of bipolar preference (Öztürk and Tsoukiás 2008).
 
2
For convenience, we assume that https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-11482-4_7/434584_1_En_7_IEq809_HTML.gif and https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-11482-4_7/434584_1_En_7_IEq810_HTML.gif , for every \(a\in {\tilde{C}}\).
 
3
Here, \(\rho ^0=\varepsilon \) and \(\rho ^1=\rho \).
 
4
The kernel of https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-11482-4_7/434584_1_En_7_IEq841_HTML.gif is defined by https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-11482-4_7/434584_1_En_7_IEq842_HTML.gif .
 
5
\( \phi \) is anonymous if for every \(\sigma =( \alpha _i)_{i\in I}\in {\mathfrak {S}}\) and every permutation \(\pi \) on I, https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-11482-4_7/434584_1_En_7_IEq859_HTML.gif , where \(\sigma \circ \pi =( \alpha _{\pi _i})_{i\in I}\).
 
6
\( \phi \) is internal if for every \(\sigma =( \alpha _i)_{i\in I}\in {\mathfrak {S}}\), \(\min _{i\in I} \alpha _i\leqslant \phi (\sigma )\leqslant \max _{i\in I} \alpha _i\).
 
7
\( \phi \) is monotone if \( \phi (\sigma )\leqslant \phi (\sigma ')\) whenever \(\sigma =( \alpha _i)_{i\in I}\in {\mathfrak {S}}\) and \(\sigma '=(a'_i)_{i\in I}\in {\mathfrak {S}}\) are such that \( \alpha _i\leqslant \alpha '_i\) for every \(i\in I\).
 
8
\( \phi \) is decomposable if for every \( \sigma =( \alpha _i)_{i\in I}\) and \(K\subseteq I\), \( \phi ( \alpha _K)=b\text { implies } \phi ( \alpha _K, \alpha _{I\setminus K})= \phi (|K|\cdot b, \alpha _{I\setminus K})\), where \(|K|\cdot b\) means \(b,b,\ldots , b\) (repeated |K| times).
 
9
\( \phi \) is extremal if for every \(\sigma =( \alpha _i)_{i\in I}\in {\mathfrak {S}}\), \( \phi (\sigma )= \phi \Big (\min _{i\in I} \alpha _i,\max _{i\in I} \alpha _i\Big )\).
 
10
Interpreted in terms of order of magnitude of importance, hence the notation OM in Bonnefon et al. (2008a).
 
Literature
Benferhat, S., Dubois, D., & Prade, H. (1999). Possibilistic and standard probabilistic semantics of conditional knowledge bases. Journal of Logic and Computation, 9, 873–895.CrossRef
Benferhat, S., Dubois, D., Kaci, S., & Prade, H. (2006). Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions. Information Fusion, 7, 135–150.CrossRef
Bennett, C. D., Holland, W. C., & Székely, G. J. (2014). Integer Valued Means. Aequationes Mathematicae, 88, 137–149.CrossRef
Blaszczyński, J., Slowiński, R., & Szelag, M. (2011). Sequential covering rule induction algorithm for variable consistency rough set approaches. Information Sciences, 181(5), 987–1002.CrossRef
Boczek, M., & Kaluszka, M. (2017). On conditions under which some generalized Sugeno integrals coincide: A solution to Dubois’ problem. Fuzzy Sets and Systems, 326, 81–88.CrossRef
Bonnefon, J.-F., Dubois, D., & Fargier, H. (2008a). On the qualitative comparison of decisions having positive and negative features. J. Artificial Intelligence Research, 32, 385–417.
Bonnefon, J.-F., Dubois, D., Fargier, H., & Leblois, S. (2008b). Qualitative heuristics for balancing the pros and cons. Theory and Decision, 65, 71–85.
Borzová-Molnárová, J., Halčinová, L., & Hutník, O. (2015). The smallest semicopula-based universal integrals, part I. Fuzzy Sets and Systems, 271, 1–17.CrossRef
Boutilier, C., Brafman, R. I., Domshlak, C., Hoos, H. H., & Poole, D. (2004). CP-nets: A tool for representing and reasoning with conditional ceteris paribus preference statements. J. Artificial Intelligence Research, 21, 135–191.CrossRef
Bouyssou, D., Marchant, T., & Pirlot, M. (2009). A conjoint measurement approach to the discrete Sugeno integral. In: S. Brams, W. V. Gehrlein, & F. S. Roberts (Eds.) The Mathematics of Preference, Choice and Order; Essays in Honor of Peter C. Fishburn (pp. 85–109). Berlin, London: Springer.
Brabant, Q., Couceiro, M., Dubois, D., Prade, H., Rico, A. (2018). Extracting decision rules from qualitative data via Sugeno Utility functionals. In Medina, J. et al. (Eds.)Proceedings International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU 2018) (pp. 253–265). Springer, CCIS 853.
Cacioppo, J. T., & Berntson, G. G. (1994). Relationship between attitudes and evaluative space: A critical review, with emphasis on the separability of positive and negative substrates. Psychological Bulletin, 115, 401–423.CrossRef
de Campos, L. M., & Bolaños, M. J. (1992). Characterization and comparison of Sugeno and Choquet integrals. Fuzzy Sets and Systems, 52, 61–67.CrossRef
de Campos, L. M., Lamata, M. T., & Moral, S. (1991). A unified approach to define fuzzy integrals. Fuzzy Sets and Systems, 39(1), 75–90.CrossRef
Chateauneuf, A. (1996). Decomposable capacities, distorted probabilities and concave capacities. Mathematical Social Sciences, 31(1), 19–37.CrossRef
Chateauneuf, A., Grabisch, M., & Rico, A. (2008). Modeling attitudes toward uncertainty through the use of the Sugeno integral. J. Math. Econ., 44(11), 1084–1099.CrossRef
Cohen, M., & Jaffray, J. Y. (1980). Rational behavior under complete ignorance. Econometrica, 48(5), 1281–1299.CrossRef
Couceiro, M., Dubois, D., Prade, H., & Rico, A. (2017a). Enhancing the expressive power of Sugeno integrals for qualitative data analysis. In Kacprzyk, J. et al. (Eds.) Advances in Fuzzy Logic and Technology 2017 (Proc. EUSFLAT 2017). Advances in Intelligent Systems and Computing (Vol. 641, pp. 534–547). Springer
Couceiro, M., Dubois, D., Prade, H., & Waldhauser, T. (2016). Decision-making with sugeno integrals—Bridging the gap between multicriteria evaluation and decision under uncertainty. Order, 33(3), 517–535.CrossRef
Couceiro, M., Foldes, S., & Lehtonen, E. (2006). Composition of post classes and normal forms of Boolean functions. Discrete Mathematics, 306, 3223–3243.CrossRef
Couceiro, M., & Grabisch, M. (2013). On the poset of computation rules for nonassociative calculus. Order, 30(1), 269–288.CrossRef
Couceiro, M., & Grabisch, M. (2017). On integer-valued means and the symmetric maximum. Aequationes Mathematicae, 91(2), 353–371.CrossRef
Couceiro, M., Lehtonen, E., Marichal, J.-L., & Waldhauser, T. (2011). An algorithm for producing median normal form representations for Boolean functions. In The Proceedings of the Reed-Muller Workshop 2011 (pp. 49–54).
Couceiro, M., & Marichal, J.-L. (2010a). Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices. Fuzzy Sets and Systems, 161(5), 694–707.
Couceiro, M., & Marichal, J.-L. (2010b). Representations and characterizations of polynomial functions on chains. Journal of Multiple-Valued Logic and Soft Computing, 16(1–2), 65–86.
Couceiro, M., & Marichal, J.-L. (2012). Polynomial functions over bounded distributive lattices. Journal of Multiple-Valued Logic and Soft Computing, 18, 247–256.
Couceiro, M., Mercuriali, P., Péchoux, R., & Saffidine, A. (2017b). Median based calculus for lattice polynomials and monotone Boolean functions. In 47th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2017) (pp. 37–42 ). IEEE Computer Society
Couceiro, M., Waldhauser, T. (2011). Axiomatizations and factorizations of Sugeno utility functionals. International Journal Uncertainity Fuzziness Knowledge Based Systems, 19(4), 635–658
Couceiro, M., & Waldhauser, T. (2014). Pseudo-polynomial functions over finite distributive lattices. Fuzzy Sets and Systems, 239, 21–34.CrossRef
Deschamps, R., & Gevers, L. (1978). Leximin and utilitarian rules: a joint characterization. J. of Economic Theory, 17, 143–163.CrossRef
Doyle, J., & Thomason, R. (1999). Background to qualitative decision theory. The AI Magazine, 20(2), 55–68.
Dubois, D. (1986). Belief structures, possibility theory and decomposable confidence measures on finite sets. Computers and Artificial Intelligence, 5(5), 403–416.
Dubois, D., Durrieu, C., Prade, H., Rico, A., & Ferro, Y. (2015). Extracting Decision Rules from Qualitative Data Using Sugeno Integral: A Case-Study. ECSQARU, 2015, 14–24.
Dubois, D., & Fargier, H. (2009a). Making Discrete Sugeno Integrals More Discriminant. International Journal of Approximate Reasoning, 50, 880–898.
Dubois, D., Fargier, H. (2009b). Capacity refinements and their application to qualitative decision evaluation. In C. Sossai & G. Chemello (Eds.) Symbolic and quantitative approaches to reasoning with uncertainty (ECSQARU 2009) (pp. 311–322). Springer, LNAI 5590.
Dubois, D., Fargier, H. (2010). Qualitative bipolar decision rules: Toward more expressive settings. dans: preferences and decisions—Models and applications. In S. Greco, R. M. Peirera, M. Squillante, R. R. Yager, & J. Kacprzyk (Eds.) Studies in fuzziness and soft computing (Vol. 257, pp. 139–158). Springer.
Dubois, D., Fargier, H., & Prade, H. (1996). Refinements of the maximin approach to decision-making in a fuzzy environment. Fuzzy Sets Systems, 81(1), 103–122.CrossRef
Dubois, D., Fargier, H., Prade, H., Sabbadin, R. (2009). A survey of qualitative decision rules under uncertainty. In D. Bouyssou, D. Dubois, M. Pirlot, & Prade H. (Eds.) Decision-making process—Concepts and methods (Chap. 11, pp. 435–473). Wiley.
Dubois, D., & Fortemps, P. (1999). Computing improved optimal solutions to max-min flexible constraint satisfaction problems. European Journal of Operational Research, 118, 95–126.CrossRef
Dubois, D., Le Berre, D., Prade, H., & Sabbadin, R. (1999). Using possibilistic logic for modeling qualitative decision: ATMS-based algorithms. Fundamenta Informaticae, 37, 1–30.
Dubois, D., Marichal, J.-L., Prade, H., Roubens, M., & Sabbadin, R. (2001). The use of the discrete Sugeno integral in decision making: a survey. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9, 539–561.
Dubois, D., & Prade, H. (1980). Fuzzy Sets and Systems. Theory and Applications: Academic Press.
Dubois, D., & Prade, H. (1984). A theorem on implication functions defined from triangular norms. Stochastica, 8, 267–279.
Dubois, D., & Prade, H. (1985). Evidence measures based on fuzzy information. Automatica, 21, 547–562.
Dubois, D., & Prade, H. (1986). Weighted minimum and maximum operations. Information Sciences, 39, 205–210.CrossRef
Dubois, D., & Prade, H. (1988). Possibility Theory: An Approach to Computerized Processing of Uncertainty. New York: Plenum Press.CrossRef
Dubois, D., & Prade, H. (2004). Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems, 144(1), 3–23.CrossRef
Dubois, D., & Prade, H. (2008). An introduction to bipolar representations of information and preference. Int. J. Intelligent Systems., 23(8), 866–877.CrossRef
Dubois, D., Prade, H. (2015). Possibility theory and its applications: where do we stand? In J. Kacprzyk & W. Pedrycz (Eds.) Springer handbook of computational intelligence (pp. 31–60). Springer.
Dubois, D., Prade, H., & Rico, A. (2014). The logical encoding of Sugeno integrals. Fuzzy Sets and Systems, 241, 61–75.CrossRef
Dubois, D., Prade, H., & Rico, A. (2015). Representing qualitative capacities as families of possibility measures. International Journal Approximate Reasoning, 58, 3–24.CrossRef
Dubois, D., Prade, H., & Rico, A. (2016). Residuated variants of Sugeno integrals. Information Sciences, 329, 765–781.CrossRef
Dubois, D., Prade, H., Rico, A., & Teheux, B. (2017). Generalized qualitative Sugeno integrals. Information Sciences, 415, 429–445.
Dubois, D., Prade, H., & Sabbadin, R. (1998). Qualitative decision theory with Sugeno integrals. In Proceedings of 14th Conference on Uncertainty in AI (pp. 121–128)
Dubois, D., Prade, H., & Sabbadin, R. (2000). Qualitative decision theory with Sugeno integrals. In M. Grabisch, T. Murofushi, & M. Sugeno (Eds.) Fuzzy measures and integrals. Theory and applications, studies in fuzziness and soft computing (pp. 314–322). Physica-Verlag
Dubois, D., Prade, H., & Sabbadin, R. (2001). Decision theoretic foundations of qualitative possibility theory. European Journal of Operational Research, 128, 459–478.CrossRef
Dubois, D., & Rico, A. (2018). New axiomatisations of discrete quantitative and qualitative possibilistic integrals. Fuzzy Sets and Systems, 343, 3–19.CrossRef
Dvořák, A., & Holčapek, M. (2012). Fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices. Information Sciences, 185, 205–229.CrossRef
Fargier, H., Lang, J., Schiex, T. (1993). Selecting preferred solutions in fuzzy constraint satisfaction problems. In Proceedings 1st European Congress on Fuzzy and Intelligent Technologies (EUFIT ’93) (pp. 1128–1134). Aachen, Germany.
Fargier, H., & Sabbadin, R. (2005). Qualitative decision under uncertainty: Back to expected utility. Artificial Intelligence, 164, 245–280.CrossRef
Franklin, B., Letter to Priestley, J. B. 1772. (1887). In J. Bigelow (Ed.)The Complete Works. New York: Putnam.
Gérard, R., Kaci, S., Prade, H. (2007). Ranking alternatives on the basis of generic constraints and examples—A possibilistic approach. In M. M. Veloso (Ed.) Proceedings 20th International Joint Conference on Artificial Intelligence (IJCAI 2007) (pp. 393–398). Hyderabad.
Goodstein, R. L. (1965/1967). The solution of equations in a lattice. In Proceedings of Royal Society Edinburgh Sect. A, 67, 231–242.
Giang, P. H., & Shenoy, P. P. (2000). A qualitative utility theory for Spohn’s theory of epistemic beliefs. In Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence (pp. 220–227).
Giang, P. H., & Shenoy, P. P. (2005). Two axiomatic approaches to decision-making using possibility theory. European Journal of Operational Research, 162, 450–467.CrossRef
Gigerenzer, G., & Todd, P. M. (1999). The ABC group: Simple heuristics that make us smart. Oxford University Press.
Grabisch, M. (1996). The application of fuzzy integrals in multicriteria decision making. European Journal of Operational Research, 89(3), 445–456.CrossRef
Grabisch, M. (2003). The symmetric Sugeno integral. Fuzzy Sets and Systems, 139, 473–490.CrossRef
Grabisch, M. (2004). The Moebius transform on symmetric ordered structures and its application to capacities on finite sets. Discrete Mathematics, 287, 17–34.CrossRef
Grabisch, M. (2016). Set functions, games and capacities in decision-making. Springer.
Grabisch, M., & Labreuche, C. (2010). A decade of application of the Choquet and Sugeno intégrals in multi-criteria décision aid. Annals of Operations Research, 175, 247–286.CrossRef
Grabisch, M. Marichal, J.-L., Mesiar, R., & Pap, E. (2009). Aggregation functions. Cambridge University Press.
Grabisch, M., Murofushi, T. Sugeno, & M., (1992). Fuzzy measure of fuzzy events defined by fuzzy integrals. Fuzzy sets and systems, 50(3), 293–313.
Greco, S., Matarazzo, B., & Slowinski, R. (2004). Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules. European Journal of Operational Research, 158, 271–292.CrossRef
Gutiérrez, P. A., Pérez-Ortiz, M., Sánchez-Monedero, J., Fernández-Navarro, F., & Hervás-Martínez, C. (2016). Ordinal regression methods: Survey and experimental study. IEEE Transactions on Knowledge and Data Engineering, 28(1), 127–146.
Kandel, A., & Byatt, W. J. (1978). Fuzzy sets, fuzzy algebra and fuzzy statistics. Proceedings of the IEEE, 68, 1619–1639.CrossRef
Kaufmann, A. (1978). Le calcul des admissibilités. Une idée nouvelle à partir de la théorie des sous-ensembles flous. In Proceedings Colloque International sur la Théorie et les Applications des Sous-Ensembles Flous (Vol. I, 14 p.). Marseilles.
Lewis, D. (1973). Counterfactuals and comparative possibility. Journal of Philosophical Logic, 2(4), 418–446.CrossRef
Marichal, J.-L. (2000). On Sugeno integral as an aggregation function. Fuzzy Sets and Systems, 114, 347–365.CrossRef
Marichal, J.-L. (2009). Weighted Lattice Polynomials. Discrete Mathematics, 309(4), 814–820.CrossRef
Mesiar, R. (1997). $k$-order pan-discrete fuzzy measures. In Proceedings 7th IFSA World Congress (Vol. 1, pp. 488–490). Prague.
Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63(2), 81–97.
Mitchell, T. (1982). Generalization as search. Artificial Intelligence, 18, 203–226.
Osgood, C. E., Suci, G. J., & Tannenbaum, P. H. (1957). The measurement of meaning. Chicago: University of Illinois Press.
Öztürk, M., & Tsoukiás, A. (2008). Bipolar preference modeling and aggregation in decision support. International Journal of Intelligent Systems, 23(9), 970–984.CrossRef
Prade, H., Rico, A., Serrurier, M. (2009a). Elicitation of Sugeno integrals: A version space learning perspective. In J. Rauch, Z. W. Ras, P. Berka, & T. Elomaa (Eds.) Proceedings 18th International Symposium on Foundations of Intelligent Systems (ISMIS ’09) (pp. 392–401). Prague, Czech Rep., Sept. 14–17, Springer LNCS 5722.
Prade, H., Rico, A., Serrurier, M., Raufaste, E. (2009b). Elicitating Sugeno integrals: Methodology and a case study. In C. Sossai & G. Chemello (eds.) Proceedings 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU ’09). Verona, Italy, July 1–3, LNCS 5590.
Ralescu, D., & Sugeno, M. (1996). Fuzzy integral representation. Fuzzy Sets and Systems, 84, 127–133.CrossRef
Rico, A. (2002). Modélisation des Préférences pour l’Aide à la Décision par l’Intégrale de Sugeno. Ph. D. Thesis, Université Paris I Sorbonne.
Rico, A., Grabisch, M., Labreuche, C., & Chateauneuf, A. (2005). Preference modeling on totally ordered sets by the Sugeno integral. Discrete Applied Mathematics, 147, 113–124.CrossRef
Roy, B. (1996). Multicriteria methodology for decision aiding. Nonconvex optimization and its applications (Vol. 12). Kluwer Academic Publishers: Dordrecht
Schmeidler, D. (1972). Cores of exact games. Journal of Mathematical Analysis and Applications, 40(1), 214–225.CrossRef
Shilkret, N. (1971). Maxitive measure and integration. Indagationes Mathematicae, 33, 109–116.CrossRef
Slovic, P., Finucane, M., Peters, E., & MacGregor, D. G. (2002). Rational actors or rational fools? implications of the affect heuristic for behavioral economics. The Journal of Socio-Economics, 31, 329–342.CrossRef
Snow, P. (1999). Diverse confidence levels in a probabilistic semantics for conditional logics. Artificial Intelligence, 113(1–2), 269–279.CrossRef
Sugeno, M. (1974). Theory of fuzzy integrals and its applications. Ph.D. Thesis, Tokyo Institute of Technology.
Sugeno, M. (1977). Fuzzy measures and fuzzy integrals: A survey. In: M. M. Gupta, et al. (Eds.)Fuzzy automata and decision processes (pp. 89–102). North-Holland.
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297–323.CrossRef
Weng, P. (2006). An axiomatic approach in qualitative decision theory with binary possibilistic utility. In Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006) (pp. 467–471). Riva del Garda, Italy, IOS Press.
Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.CrossRef
Metadata
Title
New Directions in Ordinal Evaluation: Sugeno Integrals and Beyond
Authors
Miguel Couceiro
Didier Dubois
Hélène Fargier
Michel Grabisch
Henri Prade
Agnès Rico
Copyright Year
2019
Book
New Perspectives in Multiple Criteria Decision Making

Print ISBN: 978-3-030-11481-7

Electronic ISBN: 978-3-030-11482-4

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-11482-4_7

Premium Partner

    Image Credits