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Mareš, M.; Mesiar, R.

Composition of shape generators. (English) Zbl 0870.04003

Acta Math. Inform. Univ. Ostrav. 4, No. 1, 37-45 (1996).
The authors study generating functions and shape generators of fuzzy quantities. The shape generators are functions which determine the transformation of the structure of vagueness into actual fuzzy quantities. Main attention is paid to compositions of shape generators, which are useful in algebraic processing of fuzzy data. Several examples of important compositions are presented and some results about repetitive compositions of shape generators are shown. Concluding remarks propose a model for fuzzy quantities processing.
Reviewer: A.Dvořák (Ostrava)

Cited in 7 Documents

MSC:

03E72 Theory of fuzzy sets, etc.

Keywords:

fuzzy quantity; generating function; shape generator
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\textit{M. Mareš} and \textit{R. Mesiar}, Acta Math. Inform. Univ. Ostrav. 4, No. 1, 37--45 (1996; Zbl 0870.04003)
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References:

[1] Jacas J., Mareš M., Recasens J.: Homogenous classes of fuzzy quantities. Mathware, to appear in 1997.
[2] Mareš M.: Computation Over Fuzzy Quantities. CRC-Press. Boca Raton, 1994. · Zbl 0859.94035
[3] Mareš M., Mesiar R.: Processing of sources of fuzzy quantitites. Transactions of the IPMU’96 Conference, Granada, July 1-5, 1996. University of Granada Vol. I (1996), 359-364.
[4] Mareš M.: Following fuzzy instructions. Fuzzy Economic Reviews)
[5] Mesiar R.: A note to the T-sum of L - R fuzzy numbers. Fuzzy Sets and Systems 79 (1996), 259-261. · Zbl 0871.04010 · doi:10.1016/0165-0114(95)00178-6
[6] Novák V.: Fuzzy Sets and Their Applications. A. Hilger, Bristol, 1989. · Zbl 0683.94018
[7] Yager R. R., Rybalov A.: Uniform aggregation operators. Technical report # MII-1407, Machine Intelligence Institute, New Rochelle, NY, 1994. · Zbl 0871.04007 · doi:10.1016/0165-0114(95)00133-6
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