期刊
IEEE TRANSACTIONS ON FUZZY SYSTEMS
卷 28, 期 10, 页码 2313-2319出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2019.2933803
关键词
Aggregation function; Choquet integral; fuzzy measure; Mobius transform
资金
- Slovak Research and Development Agency [APVV-17-0066, VEGA 1/0682/16, VEGA 1/0614/18]
- Grant Agency of the Czech Republic [18-06915S, TIN2016-77356-P]
In this article, we propose a generalization of the Choquet integral, starting fromits definition in terms of the Mobius transform. We modify the product on R considered in the Lovasz extension form of the Choquet integral into a function F, and we discuss the properties of this new functional. For a fixed n, a complete description of all F yielding an n-ary aggregation function with a fixed diagonal section, independent of the considered fuzzy measure, is given, and several particular examples are presented. Finally, all functionsF yielding an aggregation function, independent of the number n of inputs and of the considered fuzzy measure, are characterized, and related aggregation functions are shown to be just the Choquet integrals over the distorted inputs.
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