Abstract
The paper presents a valued extension of the recently introduced concept of PQI interval order. The main idea is that, while comparing objects represented by interval of values there is a zone of hesitation between strict difference and strict similarity which could be modelled through valued relations. The paper presents suitable definitions of such valued relations fulfilling a number of interesting properties. The use of such a tool in data analysis and rough sets theory is discussed in the paper.
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References
Luce, R.D.: Semiorders and a theory of utility discrimination. Econometrica 24, 178–191 (1956)
Fishburn, P.C.: Interval Orders and Interval Graphs. J. Wiley, Chichester (1985)
Pirlot, M., Vincke, Ph.: Semi Orders. Kluwer Academic, Dordrecht (1997)
Tsoukiàs, A., Vincke, Ph.: A characterization of pqi interval orders. Discrete Applied Mathematics 127(2), 387–397 (2003)
Ngo The, A., Tsoukiàs, A., Vincke, Ph.: A polynomial time algorithm to detect PQI interval orders. International Transactions in Operational Research 7, 609–623 (2000)
Ngo The, A., Tsoukiàs, A.: Numerical representation of pqi interval orders. Discrete Applied Mathematics 147, 125–146 (2005)
Oztürk, M., Tsoukiàs, A.: Positive and negative reasons in interval comparisons: Valued pqi interval orders. In: Proceedings of IPMU 2004, pp. 983–989 (2004)
Roy, B., Vincke, P.: Relational systems of preference with one or more pseudo-criteria: Some new concepts and results. Management Science 30, 1323–1335 (1984)
Roy, B., Vincke, Ph.: Pseudo-orders: definition, properties and numerical representation. Mathematical Social Sciences 14, 263–274 (1987)
Perny, P., Roy, B.: The use of fuzzy outranking relations in preference modelling. Fuzzy Sets and Systems 49, 33–53 (1992)
Dubois, D., Prade, H.: Decision making under fuzziness. In: Advances in fuzzy set theory and applications, pp. 279–302. North Holland, Amsterdam (1979)
Dubois, D., Prade, H.: Fuzzy sets and systems - Theory and applications. Academic press, New York (1980)
Fodor, J., Roubens, M.: Fuzzy preference modelling and multicriteria decision support. Kluwer Academic Publishers, Dordrecht (1994)
Perny, P., Roubens, M.: Fuzzy preference modelling. In: Słowiński, R. (ed.) Fuzzy sets in decision analysis, operations research and statistics, pp. 3–30. Kluwer Academic, Dordrecht (1998)
Ovchinnikov, S.N.: Modelling valued preference relation. In: Kacprzyk, J., Fedrizzi, M. (eds.) Multiperson decion making usingfuzzy sets and possibility theory, pp. 64–70. Kluwer, Dordrecht (1990)
Van De Walle, B., De Baets, B., Kerre, E.: Charaterizable fuzzy preference structures. Annals of Operations Research 80, 105–136 (1998)
Ozturk, M.: Structures mathématiques et logiques pour la comparaison des intervalles. Thése de doctorat, Université Paris-Dauphine (2005)
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)
Slowinski, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: P., W., (eds) Advances in Machine Intelligence & Soft-computing, Bookwrights, Raleigh, pp. 17–33 (1997)
Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Transactions on Data and Knowledge Engineering 12, 331–336 (2000)
Greco, S., Matarazzo, B., Slowinski, R.: Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) New Directions in Rough Sets, Data Mining, and Granular-Soft Computing. LNCS (LNAI), vol. 1711, pp. 146–157. Springer, Heidelberg (1999)
Stefanowski, J., Tsoukiàs, A.: On the extension of rough sets under incomplete information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 73–81. Springer, Heidelberg (1999)
Stefanowski, J., Tsoukiàs, A.: Valued tolerance and decision rules. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 212–219. Springer, Heidelberg (2001)
Stefanowski, J., Tsoukiàs, A.: Incomplete information tables and rough classification. Computational Intelligence 17, 454–466 (2001)
Perny, P., Tsoukiàs, A.: On the continuous extension of a four valued logic for preference modelling. In: Proceedings of the IPMU 1998 conference, Paris, pp. 302–309 (1998)
Tsoukiàs, A., Perny, P., Vincke, Ph.: From concordance/discordance to the modelling of positive and negative reasons in decision aiding. In: Bouyssou, D., Jacquet-Lagrèze, E., Perny, P., Słowiński, R., Vanderpooten, D., Vincke, P. (eds.) Aiding Decisions with Multiple Criteria: Essays in Honour of Bernard Roy, pp. 147–174. Kluwer Academic, Dordrecht (2002)
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Öztürk, M., Tsoukiàs, A. (2007). Valued Hesitation in Intervals Comparison. In: Prade, H., Subrahmanian, V.S. (eds) Scalable Uncertainty Management. SUM 2007. Lecture Notes in Computer Science(), vol 4772. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75410-7_12
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DOI: https://doi.org/10.1007/978-3-540-75410-7_12
Publisher Name: Springer, Berlin, Heidelberg
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