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The generation of fuzzy sets and the~construction of~characterizing\ functions of~fuzzy data | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 2، دوره 12، شماره 6، اسفند 2015، صفحه 1-16 اصل مقاله (1.77 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2015.2175 | ||
| نویسندگان | ||
| L. Kovarova* 1؛ R. Viertl2 | ||
| 1Faculty of Mathematics and Physics, Charles Univer- sity in Prague, Czech Republic | ||
| 2Faculty of Mathematics and Geoinformation, Vienna University of Tech- nology, Austria | ||
| چکیده | ||
| Measurement results contain different kinds of uncertainty. Besides systematic errors and random errors individual measurement results are also subject to another type of uncertainty, so-called emph{fuzziness}. It turns out that special fuzzy subsets of the set of real numbers $RR$ are useful to model fuzziness of measurement results. These fuzzy subsets $x^*$ are called emph{fuzzy numbers}. The membership functions of fuzzy numbers have to be determined. In the paper first a characterization of membership function is given, and after that methods to obtain special membership functions of fuzzy numbers, so-called emph{characterizing functions} describing measurement results are treated. | ||
| کلیدواژه‌ها | ||
| Characterizing function؛ fuzzy data؛ Generating families؛ Measurement results؛ Vector-characterizing function | ||
| مراجع | ||
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[1] A. Ferrero, M. Prioli and S. Salicone, Conditional random-fuzzy variables representing mea- surement results, IEEE Transactions on Instrumentation and Measurement, 64(5) (2015), 1170-1178. [2] S. Jain and M. Khare, Construction of fuzzy membership functions for urban vehicular ex- haust emissions modeling, Environmental monitoring and assessment, 167(1-4) (2010), 691- 699. [3] G. Klir and B. Yuan, Fuzzy sets and fuzzy logic { theory and applications, Prentice Hall, Upper Saddle River, 1995. [4] A. Sancho-Royo, and J. L. Verdegay, Methods for the construction of membership functions, International Journal of Intelligent Systems, 14(12) (1999), 1213-1230. [5] R. Viertl, Fuzzy models for precision measurements, Mathematics and Computers in Simu- lation, 79(4) (2008), 847-878. [6] R. Viertl, Statistical methods for fuzzy data, John Wiley & Sons, Chichester, 2011. [7] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338-353. [8] A-X. Zhu, L. Yang, B. Li, C. Qin, T. Pei and B. Liu, Construction of membership functions for predictive soil mapping under fuzzy logic, Geoderma, 155(3) (2010), 164-174. | ||
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