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Keywords:
fuzzy quantity; extension principle; fuzzy data
Summary:
The development of effective methods of data processing belongs to important challenges of modern applied mathematics and theoretical information science. If the natural uncertainty of the data means their vagueness, then the theory of fuzzy quantities offers relatively strong tools for their treatment. These tools differ from the statistical methods and this difference is not only justifiable but also admissible. This relatively brief paper aims to summarize the main fuzzy approaches to vague data processing, to discuss their main advantages and also their essential limitations, and to specify their place in the wide scale of information and knowledge processing methods effective for vague data.
References:
[1] Dubois D., Prade H.: Fuzzy numbers: An overview. In: Analysis of Fuzzy Information (J. C. Bezdek, ed.), Vol. 2, CRC-Press, Boca Raton 1988, pp. 3–39 MR 0910312
[2] Dubois D., Kerre E. E., Mesiar, R., Prade H.: Fuzzy interval analysis. In: Fundamental of Fuzzy Sets, Vol. 1, Kluwer Academic Publishers Kluwer Acad. Publ, Dodrecht 2000, pp. 483–581 DOI 10.1007/978-1-4615-4429-6_11 | MR 1890240 | Zbl 0988.26020
[3] Kacprzyk J., (eds.) M. Fedrizi: Fuzzy Regression Analysis. Omnitech Press, Physica–Verlag, Warsaw 1992 MR 1212587
[4] Kerre E. E., Wang X.: Reasonable properties for the ordering of fuzzy quantities. Part I, Part II. Fuzzy Sets and Systems 118 (2001), 375–385, 387–405 Zbl 0971.03055
[5] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000 MR 1790096 | Zbl 1087.20041
[6] Calvo T., Mayor, G., (eds.) R. Mesiar: Aggregation Operators. Physica–Verlag, Heidelberg 2002 MR 1936383 | Zbl 0983.00020
[7] Mareš M.: Computation Over Fuzzy quantities. CRC–Press, Boca Raton 1994 MR 1327525 | Zbl 0859.94035
[8] Mareš M.: Weak arithmetics of fuzzy numbers. Fuzzy Sets and Systems 91 (1997), 2, 143–154 DOI 10.1016/S0165-0114(97)00136-X | MR 1480041
[9] Mareš M., Mesiar R.: Verbally generated fuzzy quantities and their aggregation. In: Analysis of Fuzzy Information (J. C. Bezdek, ed.), Vol. 2, CRC-Press, Boca Raton 1988, pp. 291–3352 MR 1936394
[10] Mareš M., Mesiar R.: Dual meaning of verbal quantities. Kybernetika 38 (2002), 6, 709–716 MR 1954392
[11] Chien, Tran Quoc: Medium distances of probability fuzzy-points and an application to linear programming. Kybernetika 25 (1989), 6, 494–504 MR 1035154 | Zbl 0715.90074
[12] Zadeh L. A.: Fuzzy sets. Inform. and Control 8 (1965), 3, 338–353 DOI 10.1016/S0019-9958(65)90241-X | MR 0219427 | Zbl 0139.24606
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