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Verbally generated fuzzy quantities and their aggregation. (English) Zbl 1039.68128

Calvo, Tomasa (ed.) et al., Aggregation operators. New trends and applications. Heidelberg: Physica-Verlag (ISBN 3-7908-1468-7/hbk). Stud. Fuzziness Soft Comput. 97, 291-352 (2002).
The paper focuses on the model of fuzzy quantities (fuzzy numbers). A fuzzy number is a fuzzy set in the real line having nonzero kernel with the support being a closed interval. The main idea of the paper is to distinguish the kernel of the fuzzy quantity and its shape, being a function with special properties. Besides, they introduce the concept of verbal variable – any verbal expression with quantitative content. Unfortunately, in this place the authors ignore the already established and more general and precisely developed concept of evaluating linguistic expressions [see, e.g., V. Novák, I. Perfilieva and J. Močkoř, Mathematical principles of fuzzy logic. Kluwer, Boston/Dordrecht (1999; Zbl 0940.03028); V. Novák, Fuzzy Sets Syst. 124, No. 3, 335–351 (2001; Zbl 0994.03013)]. Part of a fuzzy quantity is also its context – the authors speak about scale. This means that various forms of accuracy are represented (e.g., accuracy of a fuzzy number within local distance in a room is different from the accuracy in the scale of continents). Several concepts for aggregation of both concepts are studied and accompanied by illustrative examples. Some of them are based on the theory of triangular norms.
For the entire collection see [Zbl 0983.00020].

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
03E72 Theory of fuzzy sets, etc.
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