Modelling Bipolar Multicriteria Decision Making.

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Google Scholar
Research Projects
Organizational Units
Journal Issue
In this paper we revisit some classical multicriteria decision making aid models in order to stress the presence of dual concepts, which will be consistent with Bipolar Fuzzy Sets (sometimes called Atanassov's Intuitionistic Fuzzy Sets). In addition, we point out how such a dual approach is a non necessary binary heritage, so we can conclude how relevant in practice are decision aid models based in linguistic terms.
MAR 30-APR 02, 2009
K.T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems vol. 20, 87-96, 1986. K.T. Atanassov, Intuitionistic Fuzzy sets, Physica-Verlag., Heidelberg,New York, 1999. K.T. Atanassov, “A personal view on intuitionistic fuzzy sets,” in: H.Bustince, F. Herrera and J. Montero (Eds.), Fuzzy Sets and Their Extensions:Representation, Aggregation and Models, pp. 23-43, Springer Verlag, Berlin, 2008. A. Bechara, D. Tranel and H. Damasio, “Characterization of the decision-making deficit of patients with ventromedial prefrontal cortex lesions,” Brain vol. 123, 2189-2202, 2000. S. Benferhat, D. Dubois, S. Kaci and H. Prade, “Bipolar possibility theory in preference modelling: representation, fusion and optimal solutions,” Information Fusion vol. 7, 135-150, 2006. H. Bustince, F. Herrera and J. Montero (Eds.), Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, Springer Verlag,Berlin, 2008. H. Bustince, J. Montero, M. Pagola, E. Barrenechea and D. Gomez,“A survey on interval-valued fuzzy sets,” in: W. Pedrycz, A. Skowron and V. Kreinovichedrycz (Eds.),Handbook of Granular Computing, pp. 491-515, John Wiley and Sons,2008. Cutello and J. Montero, “A characterization of rational amalgamation operations,” International Journal of Approximate Reasoning, vol. 8,325-344, 1993. V. Cutello and J. Montero, “Fuzzy rationality measures,”, Fuzzy Sets and Systems, vol. 62, 39-44, 1994. V. Cutello and J. Montero, “Recursive connective rules,” Int. J. Intelligent Systems, vol. 14, pp. 3-20,1999. A. Del Amo, J. Montero, G. Biging and V. Cutello, “Fuzzy classification systems,” European Journal of Operational Research, vol. 156,pp. 459-507, 2004. A. Del Amo, J. Montero and E. Molina, “Representation of consistent recursive rules,” European Journal of Operational Research, vol. 130,pp. 29-53, 2001. D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade, “Terminological difficulties in fuzzy set theory - the case of intuitionistic fuzzy sets,” Fuzzy Sets and Systems vol. 156, 485-491, 2005. J. Fodor and M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer Academic Publishers, Dordrecht, 1994. D. G´omez and J. Montero, “A discussion on aggregation operators,” Kybernetika, vol. 40, pp. 107-120, 2004. D. G´omez, J. Montero and J. Y´a nez, “An algorithmic approach to preference representation,” International Journal of Uncertainty, Fuzzyness and Knowledge-Based Systems vol. 16, 1-18, 2008. J. Gonz´alez-Pach´on, D. G´omez, J.Montero and J.Yañez, “Searching for the dimension of binary valued preference relations,” International Journal of Approximate Reasoning vol. 33, 133-157, 2003. J. Gonzalez-Pachon, D. Gomez, J. Montero and J.Yañez, “Soft dimension theory,” Fuzzy Sets and Systems vol. 137, 137–149 (2003). M. Grabish, S. Greco and M. Pirlot, “Bipolar and bivariate models in multicriteria decision analysis,” International Journal of Intelligent Systems vol. 23, 930-969, 2008. J. Montero, “Arrow’s theorem under fuzzy rationality,” Behavioral Science, vol. 32, pp. 267-273, 1987. J. Montero, “The impact of fuzziness in social choice paradoxes,” Soft Computing, vol. 12, 177-182, 2008. J. Montero, “Fuzzy logic and science,” Studies in Fuzziness and Soft Computing, vol. 243, pp. 67-78, 2009. J. Montero, D. G´omez and H. Bustince, “On the relevance of some families of fuzzy sets, ” Fuzzy Sets and Systems vol. 158, 2429-2442,2007. J. Montero, V. Lopez and D. Gomez, “The role of fuzziness in decision making,” in: D. Ruan et al., Fuzzy Logic: an spectrum of applied and theoretical issues, pp. 337-349, Springer, Berlin, 2007. J. Montero and J. Tejada, “A necessary and sufficient condition for the existence of Orlovsky‘s choice set,” Fuzzy Sets and Systems, vol. 26,121-125, 1988. J. Montero, J. Tejada and V. Cutello, “A general model for deriving preference structures from data,” Europearn Journal of Operational Research vol. 98, 98-110, 1997. S.A. Orlovsky, “Decision-making with a fuzzy preference relation,” Fuzzy Sets and Systems, vol. 1, 155-167, 1978. A.D. Pearman, J. Montero and J. Tejada, “Fuzzy multicriteria techniques:an application to transport planning,” Lecture Notes in Computer Science vol. 521, pp. 510-519, 1991. B. Roy, “Decision sciences or decision aid sciences,” European Journal of Operational Research vol. 66, pp. 184-203, 1993. [30] E.H. Ruspini, “A new approach to clustering,” Information and Control,vol. 15, pp. 22-32, 1969. T.L. Saaty, “Fundamentals of Decision Making with the Analytic Hierarchy Process,” RWS Publications, Pittsburgh, 1994 (Revised in 2000). G. Shafer, “Savage revisited,” Statistical Science vol. 1, 463–501,1986. Y. Siskos and A. Spyridakos, “Intelligent multicriteria decision support:overview and perspectives,” European Journal of Operational Research, vol. 113, 236-246, 1999. J. Y´a˜nez and J. Montero, “A poset dimension algorithm,” Journal of Algorithms vol. 30, 185-208, 1999. W. Zhang, “Bipolar fuzzy sets,” in: Proceedigns of the IEEE World Congress on Computational Science (FuzzIEEE),Anchorage, Alaska,pp. 835-840, 1998