Measure Identification for the Choquet Integral: A Python Module

Fuzzy integrals are common concepts which are used to aggregate input values in practical applications. Aggregation of inputs using fuzzy integrals opens up numerous possibilities for modeling interaction, redundancy, and synergy of inputs. However, fuzzy integrals need a fuzzy measure to start this...

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Bibliographic Details
Published in:International journal of computational intelligence systems Vol. 15; no. 1; pp. 1 - 10
Main Authors: Türkarslan, Ezgi, Torra, Vicenç
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 21.10.2022
Springer Nature B.V
Springer
Subjects:
Artificial Intelligence
Belief functions
Computational Intelligence
Control
Engineering
Fuzzy measure identification
Integrals
k-additive fuzzy measure
Learning
Mathematical Logic and Foundations
Mechatronics
Modules
Monotony
Möbius transform
Python
Redundancy
Research Article
Robotics
Belief functions
additive fuzzy measure
Möbius transform
Fuzzy measure identification
Python
ISSN:1875-6883, 1875-6891, 1875-6883
Online Access:Get full text
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Summary:Fuzzy integrals are common concepts which are used to aggregate input values in practical applications. Aggregation of inputs using fuzzy integrals opens up numerous possibilities for modeling interaction, redundancy, and synergy of inputs. However, fuzzy integrals need a fuzzy measure to start this aggregation process. This situation pushes us into the fuzzy measure identification process. This process becomes difficult due to the monotony condition of the fuzzy measure and the exponential increase on the number of measure parameters. There are in the literature many ways to determine fuzzy measures. One of them is learning from data. In this paper, our aim is to introduce a new fuzzy measure identification tool to learn measures from empirical data. It is a Python module which finds the measure that minimizes the difference between the computed and expected outputs of the Choquet integral. In addition, we study some properties of the learning process. In particular, we consider k -additive fuzzy measures and belief functions as well as arbitrary fuzzy measures. Using these variety of measures we examine the effect of k and noisy data on the learning process.
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ISSN:1875-6883
1875-6891
1875-6883
DOI:10.1007/s44196-022-00146-w