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

2016 ◽  
pp. 91-100 ◽  
Author(s):  
Eiichiro Takahagi
Keyword(s):  
Fuzzy Measure ◽  
Fuzzy Integral ◽  
Set Function

A (⋆, ∗)-Based Minkowski’s Inequality for Sugeno Fractional Integral of Order α > 0

2015 ◽  
Vol 18 (4) ◽  
Author(s):  
Azizollah Babakhani ◽  
Hamzeh Agahi ◽  
Radko Mesiar
Keyword(s):  
Fractional Integral ◽  
Fuzzy Measure ◽  
Minkowski’S Inequality ◽  
Fuzzy Integral ◽  
Binary Operations

AbstractWe first introduce the concept of Sugeno fractional integral based on the concept of g-seminorm. Then Minkowski’s inequality for Sugeno fractional integral of the order α > 0 based on two binary operations ⋆, ∗ is given. Our results significantly generalize the previous results in this field of fuzzy measure and fuzzy integral. Some examples are given to illustrate the results.

Multi-Attribution Classification Based on Lower Integral with Genetic Algorithm

2014 ◽  
Vol 668-669 ◽  
pp. 1090-1093
Author(s):  
Ai Xia Chen ◽  
Jun Hua Li
Keyword(s):  
Genetic Algorithm ◽  
Linear Programming ◽  
Linear Programming Problem ◽  
Fuzzy Integral ◽  
Data Sets ◽  
Fuzzy Measures ◽  
Benchmark Data ◽  
Minimum Potential ◽  
And Performance ◽  
Set Function

Fuzzy integral has been widely used in multi-attribution classification when the interactions exist between the attributions. Because the fuzzy measure defined on the attributions represents the weights of all the attributions and the interactions between them. The lower integral is a type of fuzzy integral with respect to fuzzy measures, which represents the minimum potential of efficiency for a group of attributions with interaction. The value of lower integrals can be evaluated through solving a linear programming problem. Considering the lower integral as a classifier, this paper investigates its implementation and performance. The difficult step in the implementation is how to learn the non-additive set function used in lower integrals. And Genetic algorithm is used to solve the problem. Finally, numerical simulations on some benchmark data sets are given.

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