Fuzzy vectors as a tool for modeling uncertain multidimensional quantities. (English) Zbl 1186.90144

Summary: The paper deals with modeling uncertain multidimensional quantities by means of fuzzy vectors. In connection with possible interactions among variables, the separability of fuzzy vectors is discussed in detail. For the case when interconnections among variables are given by a crisp relation, a more general form of separability of fuzzy vectors-the separability on a given relation (e.g. on a probability simplex) is introduced. Properties of fuzzy vectors separable on a given relation are studied, and ways of convenient setting of such fuzzy vectors are proposed. Finally, fuzzy extensions of real-valued functions and real-vector-valued functions to general input fuzzy vectors are investigated.


90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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[1] Dubois, D.; Ostasiewicz, W.; Prade, H., Fuzzy sets: history and basic notions, (), 21-124 · Zbl 0967.03047
[2] Dubois, D.; Prade, H., Additions of interactive fuzzy numbers, IEEE trans. automat. control, AC-26, 4, 926-936, (1981)
[3] Fullér, R.; Majlender, P., On interactive fuzzy numbers, Fuzzy sets and systems, 143, 355-369, (2004) · Zbl 1056.94023
[4] Inuiguchi, M., Necessity measure optimization in linear programming problems with fuzzy polytopes, Fuzzy sets and systems, 158, 17, 1882-1891, (2007) · Zbl 1137.90757
[5] Inuiguchi, M.; Ramík, J.; Tanino, T., Oblique fuzzy vectors and their use in possibilistic linear programming, Fuzzy sets and systems, 135, 123-150, (2003) · Zbl 1026.90104
[6] Inuiguchi, M.; Tanino, T., Fuzzy linear programming with interactive uncertain parameters, Reliable comput., 10, 5, 357-367, (2004) · Zbl 1048.65062
[7] Inuiguchi, M.; Tanino, T., Possibilistic linear programming with fuzzy if – then rule coefficients, Fuzzy optim. decision making, 1, 1, 65-91, (2002) · Zbl 1056.90142
[8] Klir, G.J.; Pan, Y., Constrained fuzzy arithmetic: basic questions and some answers, Soft comput., 2, 100-108, (1998)
[9] Negoita, C.V.; Ralescu, D.A., Representation theorems for fuzzy concepts, Kybernetes, 4, 169-174, (1975) · Zbl 0352.02044
[10] O. Pavlačka, Fuzzy methods of decision making, Dissertation Thesis, Palacký University Olomouc, 2007 (in Czech.).
[11] O. Pavlačka, J. Talašová, Application of the fuzzy weighted average of fuzzy numbers in decision making models, in: U. Bodenhofer, V. Novák, M. Štěpnička, (Eds.), New Dimensions in Fuzzy Logic and Related Technologies, Vol II, Proc. 5th EUSFLAT Conf., Ostrava, Czech Republic, Ostravská univerzita, Ostrava, September 11-14, 2007, pp. 455-462.
[12] Pavlačka, O.; Talašová, J., Fuzzy vectors of normalized weights and their application in decision making models, APLIMAT—J. appl. math., 1, 1, 451-462, (2008)
[13] Talašová, J.; Pavlačka, O., Fuzzy probability spaces and their applications in decision making, Austrian J. statist., 35, 2&3, 347-356, (2006)
[14] Viertl, R., Statistical methods for non-precise data, (1996), CRC Press Boca Raton, FL
[15] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 338-353, (1965) · Zbl 0139.24606
[16] Zadeh, L.A.; Zadeh, L.A., Concept of a linguistic variable and its application to approximate reasoning III, Inform. sci., Inform. sci., 9, 43-80, (1975), 301-357 · Zbl 0404.68075
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