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Abstrakty
This paper deals with the concept of mean. We make an overview of axioms used for the description of families of means and their consequences. We give examples of means fulfilling the respective sets of axioms, and moreover, some applications are indicated.
Czasopismo
Rocznik
Tom
Strony
25--39
Opis fizyczny
Bibliogr. 38 poz.
Twórcy
autor
- Institute of Mathematics University of Rzeszów 35-310 Rzeszów, ul. Rejtana 16a, Poland, jdziok@univ.rzeszow.pl
Bibliografia
- [1] J. Aczél, On mean values, Bull. Amer. Math. Soc. 54 (1948), 3512-400.
- [2] J, Aczé, Lectures on Functional Eguations and Their Applicalions, Acad. Press, New York, 1966.
- [3] J. Aczél, C. Alsina, Synthesizing judgments: a functional equations approach, Math. Modelling 9 (1987), 311-320.
- [4] J. Aczél, Z. Daróczy, Über verallgemeinerte quasilineare Mittelwerte, die mit Gewichtsfunktionen gebildetsind, Publ. Math. Debrecen 10 (1963), 171-190.
- [5] J. Aczél, J. Dhombres, Functional Equations in Several Variables with Applications to Mathematics, Information Theory and to the Natural and Social Sciences, Cambridge University Press, Cambridge, 1989.
- [6] M. Bajraktarevič, Sur une équation fonctionelle aux valeurs moyennes, Glasnik Mat. - Fiz. Astr. 13 (1958), 243-248.
- [7] P.S. Bullen, D.S, Mitrinović and P.M. Vasić, Means and Their Inegualities, Reidel, Dordrecbt, 1988.
- [8] T. Calvo. A. Pradera, Double aggregation operators, Fuzzy Sets Syst. 142 (2004), 15-33.
- [9] T. Calvo, A. Kolesárová. M. Komorniková and R. Mesiar, Aggregation operators: Properties, classes and construction methods, In: Aggregation Operators (T. Calvo et al., eds), Physica-Verlag, Heildelberg, 2002, 3-104.
- [10] T. Calvo, R. Mesiar, Stability of aggregation operators, Proc. EUSFLAT'2001, Leice-ster, 2001, 475-478.
- [11] A. L. Cauchy, Cours d'analyse de 1'Ecole Royale Polytechnique, vol. l, Analyse Algébraiąue, Debure, Paris, 1821.
- [12] O. Chisini, Sul concetto di media, Periodico di matematiche (4) 9 (1929), 106-116.
- [13] J. Drewniak, U. Dudziak, Aggregations preserving classes of fuzzy relations, Kybernetika 41 (2005), 265-284.
- [14] D. Dubois, H. Prade, Weighted minimum and maximum operations in fuzzy set theory, Inform. Sci. 39 (1986), 205-210.
- [15] D. Dubois, H. Prade, C. Testemale, Weighted fuzzy pattern matching, Fuzzy Sets Syst. 28 (1988), 313-331.
- [16] B. Finetti, Sul concetto di media, Giorn. Ital Attuari (3) 2 (1931), 369-396.
- [17] J. Fodor, J. Marichal, M. Roubens, Characterization of the ordered weighted averaging operators, IEEE Trans. Fuzzy Syst. (2) 3 (1995), 236-240.
- [18] J. Fodor, J. Marichal, On nonstrict means, Aeguationes Math. 54 (1997), 308-327.
- [19] J. Fodor, M. Roubens, Fuzzy Preference. Modelling and Multicriteria Decision Support, Kluwer Acad. Publ., Dordrecht, 1994,
- [20] J. Fodor, M. Roubens, Characterization of weighted maximum and some related operations, Inform. Sci. 84 (1995), 173-180.
- [21] J. Fodor, M. Roubens, On meaningfulness of means, J. Computational Appl Math. 64 (1995), 103-115.
- [22] M. Grabish, S. A. Orlovski, R. R. Yager, Fuzzy aggregation of numerical preferences, in: R. Słowiński (eds.), Fuzzy sets in decision analysis, operations research and statistics, vol. l, The Handbooks of Fuzzy Sets Series, Kluwer Acad. Publ., Dordrecht, 1998, 31-68,
- [23] G. H. Hardy, J. Littlewood, G. Pólya, Inequalities, Cambridge University Press, Cambridge, 1955.
- [24] T. Kitagawa, On some class of weighted means, Proc. Physico-Mathematical Society of Japan (3) 16 (1934), 117-126.
- [25] E.P. Klement, R. Mesiar, E. Pap, Triangular norms, Kluwer Acad. Publ., Dordrecht, 2000.
- [26] A. N. Kolmogorov, Sur la notion de la moyenne, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. (6) 12 (1930), 388-391.
- [27] J. L. Marichal, On an axiomatization of the quasi-arithmetic mean values without the symmetry axiom, Aeąuationes Math. 59 (2000), 74-83.
- [28] M. Nagumo, Über eine klasse der mittelwerte, Japan. J. Math. 7 (1930), 71-79.
- [29] S. Ostasiewicz, W, Ostasiewicz, Means and their applications, Ann. Oper, Res. 97 (2000), 337-355.
- [30] S. Ovchinnikov, Means on ordered sets, Math. Social Sci. 32 (1996), 39-56.
- [31] Zs. Páles, Characterization of quasideviation means, Acta Math, Acad. Sci. Hungar. (3-4) 40 (1982), 243-260.
- [32] V. Peneva, I. Popchev, Properties of the aggregation operators related with fuzzy relations, Fuzzy Sets Syst. 139 (2004), 615-633.
- [33] F. Qi, Generalized weighted mean values with two parameters, Proc. Roy. Soc. London Ser. A 454 (1998) no. 1978, 2723-2732.
- [34] F. Qi, Generalized abstracted mean values, J. Ineq;. Pure and Appl. Math. (1) 1 2000, Art. 4. Available online. at http://jipam.vu.edu.au/
- [35] U. Ricci, Confronti tra medie, Giorn. Economisti e Rivista di Statistica 26 (1935), 38-66.
- [36] P.K. Sahoo, T. Riedel, Mean value. theorems and functional equations, World Scientific Publ., Singapore, 1998.
- [37] R.. R. Yager, On ordered weighting averaging operators in multicriteria decision making, IEEE Trans. Syst. Man Cybernet. 18 (1988), 183-190.
- [38] H. J. Zimmermann. P. Zysno, Decisions and evaluations by hierarchical aggregation of Information, Fuzzy Seta Syst. 10 (1983), 243-260.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA7-0007-0003