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# On a Fuzzy Integral as the Product-Sum Calculation Between a Set Function and a Fuzzy Measure

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 610)

## Abstract

We propose the Choquet integral with respect set to a function defined as the product-sum calculation between a set function and a fuzzy measure. The fuzzy integral is an extension of the Choquet integral. The Choquet integral assumes that the interactions among input values are interact fully but the extension assumes the values partially interaction. In this paper, we define another integral expression and analyze its properties. For an input vector the optimal set function is calculated through linear programming. Lastly, we analyze coalitions among set functions that are a cooperative game using the proposed integral.

## Keywords

Set function Choquet integral Fuzzy measure Möbius transformation co-Möbius transformation Linear programming Supermodular Cooperative game

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## Copyright information

© Springer International Publishing Switzerland 2016

## Authors and Affiliations

1. 1.School of CommerceSenshu UniversityKawasakiJapan