FUZZY NUMBERS, GAME THEORY AND CLASSIFICATION ALGORITHMS AS AN AID TO SUSTAINABLE CARE FOR THE ELDERLY
Keywords:Sustainable care for the elderly, fuzzy numbers, game theory, fuzzy classification algorithms
AbstractOne of the biggest problems in the modern world, especially in the European Union, is the medical and social care of the elderly. Furthermore, by increasing the average age and the culture of individuals, an enhancement of the elderly as a resource is required. In this work, after a description of some of the rights and needs of the elderly, we try to understand if some mathematical tools can be useful to describe the various situations and to provide useful algorithms to make decisions. The role of fuzzy numbers and game theory to describe certain aspects is highlighted. The mathematical concepts of covering and fuzzy partition are used both for a classification of the elderly, and for a classification of the territory for a better organization of services.
Bezdek, J. (1981). Pattern recognition with fuzzy objective function algorithms, Plenum Press, New York.
Coletti, G., Scozzafava, R. (2002). Probabilistic Logic in a Coherent Setting. Kluwer Academic Publishers, Dordrecht.
Corsini, P. (1993). Prolegomena of Hypergroup Theory, Aviani Editore.
Corsini, P. (1994). Join spaces, power sets, fuzzy sets, Proc. of the Fifth Intern. Congress on Algebraic Hyperstructures and Applications, Iasi.
de Finetti, B. (1974). Theory of Probability. J. Wiley, New York.
Ferri, B, Maturo, A. (2001). Classifications and Hyperstructures in Problems of Architecture and Town-Planning. Journal of Interdisciplinary Mathematics, 1(4), 25-34.
Ferri, B., Maturo, A. (1999). Fuzzy Classification and Hyperstructures: An Application to Evaluation of Urban Project. In: Classification and Data Analysis, Springer-Verlag, Berlin, 55-62.
Klir, G.J., Yuan, B. (1995). Fuzzy sets and fuzzy logic, Prentice Hall, N. Jersey.
Lindley, D.V. (1985). Making Decisions. John Wiley & Sons, London.
March, J.G. (1994), A primer on Decision Making. How Decision Happen. The Free Press. New York.
Mares, M. (2001). Fuzzy Cooperative Games, Physica-Verlag, Heidelberg, New York.
Franchino, R., Maturo, A., Ventre, A., Violano, A. (2004). Strategie, processi e modelli decisionali per la gestione dell’ambiente, Edizioni Goliardiche.
Maturo A., Tofan I. (2001). Iperstrutture, strutture fuzzy ed applicazioni, dierre dizioni, San Salvo (Ch).
Maturo A., Ventre, A.G.S. (2011). Reaching Consensus in Multiagent Decision Making. International Journal of Intelligent Systems, 25, 266-273.
Maturo, A. (2012). Multi-objective decision making based on fuzzy events and their coherent (fuzzy) measures. Italian Journal of Pure and Applied Mathematics, 29, 309-324.
Maturo, A., Squillante, M., and Ventre, A.G.S. (2013). Dynamical Models for Representing and Building Consensus in Committees. In: Advanced Dynamic Modelling of Economic and Social Systems, Springer Verlag, Heidelberg Germany, 11-19.
Prenowitz, W., Jantosciak, J. (1979). Join geometries, Springer Verlag VTM.
Ross, T.J. (1997). Fuzzy Logic with engineering applications, MacGraw Hill.
Simon, H.A. (1982). Models for bounded rationality, vol 1-2. The Mit Press, Cambridge.
Von Neumann, J., Morgenstern, O., (1947). Theory of games and economic behaviour, Princeton.
Zadeh, L. (1965). Fuzzy sets. Information and Control, 8, 338-353.