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Journal articles on the topic 'Choquet integral'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Murofushi, Toshiaki, Katsushige Fujimoto, and Michio Sugeno. "Canonical Separated Hierarchical Decomposition of the Choquet Integral Over a Finite Set." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 06, no. 03 (1998): 257–72. http://dx.doi.org/10.1142/s0218488598000239.

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The paper shows the existence of a canonical separated hierarchical decomposition of the Choquet integral over a finite set. The decomposed system is a hierarchical combination of Choquet integrals with mutually disjoint domains, and equivalent to the original Choquet integral. The paper also gives canonical overlapped hierarchical decompositions of the Choquet integral over a semiatom.

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2

Gal, Sorin G. "On a Choquet-Stieltjes type integral on intervals." Mathematica Slovaca 69, no. 4 (2019): 801–14. http://dx.doi.org/10.1515/ms-2017-0269.

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Abstract In this paper we introduce a new concept of Choquet-Stieltjes integral of f with respect to g on intervals, as a limit of Choquet integrals with respect to a capacity μ. For g(t) = t, one reduces to the usual Choquet integral and unlike the old known concept of Choquet-Stieltjes integral, for μ the Lebesgue measure, one reduces to the usual Riemann-Stieltjes integral. In the case of distorted Lebesgue measures, several properties of this new integral are obtained. As an application, the concept of Choquet line integral of second kind is introduced and some of its properties are obtain

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3

Gong, Zengtai, Li Chen, and Gang Duan. "Choquet Integral of Fuzzy-Number-Valued Functions: The Differentiability of the Primitive with respect to Fuzzy Measures and Choquet Integral Equations." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/953893.

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This paper deals with the Choquet integral of fuzzy-number-valued functions based on the nonnegative real line. We firstly give the definitions and the characterizations of the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on the nonadditive measure. Furthermore, the operational schemes of above several classes of integrals on a discrete set are investigated which enable us to calculate Choquet integrals in some applications. Secondly, we give a representation of the Choquet integral of a nonnegative, continuous, and increasing fuzzy-number-valued funct

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4

Murofushi, Toshiaki, Michio Sugeno, and Katsushige Fujimoto. "Separated Hierarchical Decomposition of the Choquet Integral." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 05 (1997): 563–85. http://dx.doi.org/10.1142/s0218488597000439.

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The paper gives a necessary and sufficient condition for a Choquet integral to be decomposable into an equivalent separated hierarchical Choquet-integral system, which is a hierarchical combination of ordinary Choquet integrals with mutually disjoint domains.

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5

MUROFUSHI, Toshiaki. "Multilevel Choquet integral." Journal of Japan Society for Fuzzy Theory and Intelligent Informatics 16, no. 4 (2004): 319–27. http://dx.doi.org/10.3156/jsoft.16.319.

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6

Chen and Huang. "Forming a Hierarchical Choquet Integral with a GA-Based Heuristic Least Square Method." Mathematics 7, no. 12 (2019): 1155. http://dx.doi.org/10.3390/math7121155.

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: Identifying the fuzzy measures of the Choquet integral model is an important component in resolving complicated multi-criteria decision-making (MCDM) problems. Previous papers solved the above problem by using various mathematical programming models and regression-based methods. However, when considering complicated MCDM problems (e.g., 10 criteria), the presence of too many parameters might result in unavailable or inconsistent solutions. While k-additive or p-symmetric measures are provided to reduce the number of fuzzy measures, they cannot prevent the problem of identifying the fuzzy mea

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7

Anastassiou, George A. "Choquet integral analytic inequalities." Studia Universitatis Babes-Bolyai Matematica 65, no. 1 (2020): 17–28. http://dx.doi.org/10.24193/subbmath.2020.1.02.

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8

Gal, Sorin G. "Fredholm-Choquet integral equations." Journal of Integral Equations and Applications 31, no. 2 (2019): 183–94. http://dx.doi.org/10.1216/jie-2019-31-2-183.

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9

Gal, Sorin G. "Volterra-Choquet integral equations." Journal of Integral Equations and Applications 31, no. 4 (2019): 495–504. http://dx.doi.org/10.1216/jie-2019-31-4-495.

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10

Mesiarová-Zemánková, A., R. Mesiar, and K. Ahmad. "The balancing Choquet integral." Fuzzy Sets and Systems 161, no. 17 (2010): 2243–55. http://dx.doi.org/10.1016/j.fss.2010.02.004.

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11

Mesiarová-Zemánková, Andrea, and Khurshid Ahmad. "Multi-polar Choquet integral." Fuzzy Sets and Systems 220 (June 2013): 1–20. http://dx.doi.org/10.1016/j.fss.2012.09.005.

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12

Gal. "Choquet Integral in Capacity." Real Analysis Exchange 43, no. 2 (2018): 263. http://dx.doi.org/10.14321/realanalexch.43.2.0263.

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13

Aggarwal, Manish. "Generalized attitudinal Choquet integral." International Journal of Intelligent Systems 34, no. 5 (2018): 733–53. http://dx.doi.org/10.1002/int.22074.

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14

Even, Yaarit, and Ehud Lehrer. "Decomposition-integral: unifying Choquet and the concave integrals." Economic Theory 56, no. 1 (2013): 33–58. http://dx.doi.org/10.1007/s00199-013-0780-0.

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15

Agahi, Hamzeh, and Radko Mesiar. "On Choquet-Pettis Expectation of Banach-Valued Functions: A Counter Example." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 26, no. 02 (2018): 255–59. http://dx.doi.org/10.1142/s0218488518500137.

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In probability theory, mathematical expectation of a random variable is very important. Choquet expectation (integral), as a generalization of mathematical expectation, is a powerful tool in various areas, mainly in generalized probability theory and decision theory. In vector spaces, combining Choquet expectation and Pettis integral has led to a challenging and an interesting subject for researchers. In this paper, we indicate and discuss a failure in the previous definition of Choquet-Pettis integral of Banach space-valued functions. To obtain a correct definition of Choquet-Pettis integral,

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16

Gong, Zengtai, Wenjing Lei, Kun Liu та Na Qin. "Weighted Moving Averages for a Series of Fuzzy Numbers Based on Nonadditive Measures with σ − λ Rules and Choquet Integral of Fuzzy-Number-Valued Function". Journal of Function Spaces 2020 (30 березня 2020): 1–11. http://dx.doi.org/10.1155/2020/3013648.

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The aim of this study is to generalize moving average by means of Choquet integral. First, by employing nonadditive measures with δ − λ rules, the calculation of the moving average for a series of fuzzy numbers can be transformed into Choquet integration of fuzzy-number-valued function under discrete case. Meanwhile, the Choquet integral of fuzzy number and Choquet integral of fuzzy number vector are defined. Finally, some properties are investigated by means of convolution formula of Choquet integral. It shows that the results obtained in this paper extend the previous conclusions.

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17

Kaino, Toshihiro, and Kaoru Hirota. "Differentiation of the Choquet Integral and Its Application to Long-term Debt Ratings." Journal of Advanced Computational Intelligence and Intelligent Informatics 4, no. 1 (2000): 66–75. http://dx.doi.org/10.20965/jaciii.2000.p0066.

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Differentiation of the Choquet integral of a nonnegative measurable function with respect to a fuzzy measure on fuzzy measure space is proposed and it is applied to the capital investment decision making problem by Kaino and Hirota. In this paper, differentiation of the Choquet integral of a nonnegative measurable function is extended to differentiation of the Sipos Choquet integral of a measurable function and its properties will be discussed. First, the real interval limited Schmeidler Choquet integral and Sipos Choquet integral are defined for preparation, then the upper differential coeffi

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18

Fujimoto, Katsushige, Toshiaki Murofushi, and Michio Sugeno. "Canonical Hierarchical Decomposition of Choquet Integral Over Finite Set with Respect to Null Additive Fuzzy Measure." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 06, no. 04 (1998): 345–63. http://dx.doi.org/10.1142/s021848859800029x.

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In this paper, we provide the necessary and sufficient condition for a Choquet integral model to be decomposable into a canonical hierarchical Choquet integral model constructed by hierarchical combinations of some ordinary Choquet integral models. This condition is characterized by the pre-Znclusion-Exclusion Covering (pre-IEC). Moreover, we show that the pre-IEC is the subdivision of an IEC and that the additive hierarchical structure is the most fundamental one on considering a hierarchical decomposition of the Choquet integral model.

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19

SUGENO, MICHIO, KATSUSHIGE FUJIMOTO, and TOSHIAKI MUROFUSHI. "A HIERARCHICAL DECOMPOSITION OF CHOQUET INTEGRAL MODEL." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 03, no. 01 (1995): 1–15. http://dx.doi.org/10.1142/s0218488595000025.

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In this paper we give a nesessary and sufficient condition for a Choquet integral model to be decomposable into an equivalent hierarchical Choquet integral model constructed by hierarchical combinations of some ordinary Choquet integral models. The condition is obtained by Inclution-Exclusion Covering (IEC). Moreover we show some properties on the set of IECs.

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20

Garg, Harish, Tehreem, Gia Nhu Nguyen, Tmader Alballa, and Hamiden Abd El-Wahed Khalifa. "Choquet Integral-Based Aczel–Alsina Aggregation Operators for Interval-Valued Intuitionistic Fuzzy Information and Their Application to Human Activity Recognition." Symmetry 15, no. 7 (2023): 1438. http://dx.doi.org/10.3390/sym15071438.

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Human activity recognition (HAR) is the process of interpreting human activities with the help of electronic devices such as computer and machine version technology. Humans can be explained or clarified as gestures, behavior, and activities that are recorded by sensors. In this manuscript, we concentrate on studying the problem of HAR; for this, we use the proposed theory of Aczel and Alsina, such as Aczel–Alsina (AA) norms, and the derived theory of Choquet, such as the Choquet integral in the presence of Atanassov interval-valued intuitionistic fuzzy (AIVIF) set theory for evaluating the nov

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21

Yang, Rong, and Ren Ouyang. "Classification based on Choquet integral." Journal of Intelligent & Fuzzy Systems 27, no. 4 (2014): 1693–702. http://dx.doi.org/10.3233/ifs-141136.

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22

OGURA, YUKIO, SHOUMEI LI, and DAN A. RALESCU. "SET DEFUZZIFICATION AND CHOQUET INTEGRAL." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 01 (2001): 1–12. http://dx.doi.org/10.1142/s0218488501000570.

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In this paper, we discuss the defuzzification problem. We first propose a set defuzzification method, (from a fuzzy set to a crisp set) by using the Aumann integral. From the obtained set to a point, we have two methods of defuzzification. One of these uses the mean value method and the other uses a fuzzy measure. In the first case, we compare our mean value method with the method of the center of gravity. In the second case, we compare fuzzy measure method with the Choquet integral method. We also give there a sufficient condition so that the results in the last two methods are equivalent.

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23

Auephanwiriyakul, Sansanee, James M. Keller, and Paul D. Gader. "Generalized Choquet fuzzy integral fusion." Information Fusion 3, no. 1 (2002): 69–85. http://dx.doi.org/10.1016/s1566-2535(01)00054-9.

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24

Greco, Salvatore, and Fabio Rindone. "The bipolar Choquet integral representation." Theory and Decision 77, no. 1 (2013): 1–29. http://dx.doi.org/10.1007/s11238-013-9390-3.

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25

Gal, Sorin G. "Approximation by Choquet integral operators." Annali di Matematica Pura ed Applicata (1923 -) 195, no. 3 (2015): 881–96. http://dx.doi.org/10.1007/s10231-015-0495-x.

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26

Heilpern, Stanislaw. "Using Choquet integral in economics." Statistical Papers 43, no. 1 (2002): 53–73. http://dx.doi.org/10.1007/s00362-001-0086-3.

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27

Abril, Daniel, Guillermo Navarro-Arribas, and Vicenç Torra. "Choquet integral for record linkage." Annals of Operations Research 195, no. 1 (2011): 97–110. http://dx.doi.org/10.1007/s10479-011-0989-x.

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28

Yan, Leifan, Tong Kang, and Huai Zhang. "Decomposition Integrals of Set-Valued Functions Based on Fuzzy Measures." Mathematics 11, no. 13 (2023): 3013. http://dx.doi.org/10.3390/math11133013.

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The decomposition integrals of set-valued functions with regards to fuzzy measures are introduced in a natural way. These integrals are an extension of the decomposition integral for real-valued functions and include several types of set-valued integrals, such as the Aumann integral based on the classical Lebesgue integral, the set-valued Choquet, pan-, concave and Shilkret integrals of set-valued functions with regard to capacity, etc. Some basic properties are presented and the monotonicity of the integrals in the sense of different types of the preorder relations are shown. By means of the

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29

Fujimoto, Katsushige, and Michio Sugeno. "Obtaining Admissible Preference Orders Using Hierarchical Bipolar Sugeno and Choquet Integrals." Journal of Advanced Computational Intelligence and Intelligent Informatics 17, no. 4 (2013): 493–503. http://dx.doi.org/10.20965/jaciii.2013.p0493.

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In this paper, we demonstrate the modeling capabilities of certain types of fuzzy integrals such as hierarchical bipolar/cumulative-prospect-theory-type Sugeno and Choquet integrals. The notion ofadmissible preference structures, introduced by Nakama and Sugeno, is one of the weakest restrictions in rational preference structures. Nakama and Sugeno also proved that, under a certain condition, any admissible preference can be modeled by a hierarchical bipolar Sugeno integral. Here, we extend this result and show that if we use an extra dummy attribute, we can use the hierarchical Choquet integr

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30

Zhang, Xiaohong, Haojie Jiang, and Jingqian Wang. "New Classifier Ensemble and Fuzzy Community Detection Methods Using POP Choquet-like Integrals." Fractal and Fractional 7, no. 8 (2023): 588. http://dx.doi.org/10.3390/fractalfract7080588.

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Among various data analysis methods, classifier ensemble (data classification) and community network detection (data clustering) have aroused the interest of many scholars. The maximum operator, as the fusion function, was always used to fuse the results of the base algorithms in the classifier ensemble and the membership degree of nodes to classes in the fuzzy community. It is vital to use generalized fusion functions in ensemble and community applications. Since the Pseudo overlap function and the Choquet-like integrals are two new fusion functions, they can be combined as a more generalized

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31

Wang, Ruodu, Yunran Wei, and Gordon E. Willmot. "Characterization, Robustness, and Aggregation of Signed Choquet Integrals." Mathematics of Operations Research 45, no. 3 (2020): 993–1015. http://dx.doi.org/10.1287/moor.2019.1020.

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This article contains various results on a class of nonmonotone, law-invariant risk functionals called the signed Choquet integrals. A functional characterization via comonotonic additivity is established along with some theoretical properties, including six equivalent conditions for a signed Choquet integral to be convex. We proceed to address two practical issues currently popular in risk management, namely robustness (continuity) issues and risk aggregation with dependence uncertainty, for signed Choquet integrals. Our results generalize in several directions those in the literature of risk

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32

YAGER, RONALD R. "CHOQUET AGGREGATION USING ORDER INDUCING VARIABLES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, no. 01 (2004): 69–88. http://dx.doi.org/10.1142/s0218488504002667.

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We discuss the OWA and Choquet integral aggregation operators and point out the central role the ordering operation plays in these operators. We extend the capabilities of the Choquet integral aggregation by allowing the ordering to be induced by some values other then those being aggregated. This allows us to consider an induced Choquet Choquet integral aggregation operator. We look at the properties of this operator. We then look at its applications. Among the applications considered are aggregations guided by linguistic and other ordinal structures. We look at the use of induced aggregation

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33

CARDIN, MARTA, MIGUEL COUCEIRO, SILVIO GIOVE, and JEAN-LUC MARICHAL. "AXIOMATIZATIONS OF SIGNED DISCRETE CHOQUET INTEGRALS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 19, no. 02 (2011): 193–99. http://dx.doi.org/10.1142/s0218488511006964.

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We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovász extension of a pseudo-Boolean function which vanishes at the origin. We present axiomatizations of this generalized Choquet integral, given in terms of certain functional equations, as well as by necessary and sufficient conditions which reveal desirable properties in aggregation theory.

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34

Pal, Shanoli Samui, and Samarjit Kar. "Forecasting stock market price by using fuzzified Choquet integral based fuzzy measures with genetic algorithm for parameter optimization." RAIRO - Operations Research 54, no. 2 (2020): 597–614. http://dx.doi.org/10.1051/ro/2019117.

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In this paper, fuzzified Choquet integral and fuzzy-valued integrand with respect to separate measures like fuzzy measure, signed fuzzy measure and intuitionistic fuzzy measure are used to develop regression model for forecasting. Fuzzified Choquet integral is used to build a regression model for forecasting time series with multiple attributes as predictor attributes. Linear regression based forecasting models are suffering from low accuracy and unable to approximate the non-linearity in time series. Whereas Choquet integral can be used as a general non-linear regression model with respect to

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35

Gal, Sorin, and Ionut Iancu. "Quantitative approximation by nonlinear Angheluta-Choquet singular integrals." Journal of Numerical Analysis and Approximation Theory 49, no. 1 (2020): 54–65. http://dx.doi.org/10.33993/jnaat491-1217.

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By using the concept of nonlinear Choquet integral with respect to a capacity and as a generalization of the Poisson-Cauchy-Choquet operators, we introduce the nonlinear Angheluta-Choquet singular integrals with respect to a family of submodular set functions. Quantitative approximation results in terms of the modulus of continuity are obtained with respect to some particular possibility measures and with respect to the Choquet measure \(\mu(A)=\sqrt{M(A)}\), where \(M\) represents the Lebesgue measure. For some subclasses of functions we prove that these Choquet type operators can have essent

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36

Sofian-Boca, Floarea-Nicoleta. "A Multi-Valued Choquet Integral with Respect to a Multisubmeasure." Annals of the Alexandru Ioan Cuza University - Mathematics 61, no. 1 (2015): 129–52. http://dx.doi.org/10.2478/aicu-2014-0003.

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Abstract Jang, Kim and Kwon introduced a multi-valued Choquet integral for multifunctions with respect to real fuzzy measures and Zhang, Guo and Liu established for this kind of integral some convergence theorems. The aim of this paper is to present another type of set-valued Choquet integral, called by us the Aumann-Choquet integral, for non-negative measurable functions with respect to multisubmeasures taking values in the class of all non-empty,compact and convex sets of ℝ+ on which we use the order relation considered by Guo and Zhang. For this kind of integral, we study some important pro

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37

NARUKAWA, YASUO, and VICENÇ TORRA. "GRAPHICAL INTERPRETATION OF THE TWOFOLD INTEGRAL AND ITS GENERALIZATION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 13, no. 04 (2005): 415–24. http://dx.doi.org/10.1142/s0218488505003540.

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In this work we define a generalization of the twofold integral (generalization of the Choquet and Sugeno integrals) that operates in an arbitrary universal set. A graphical representation of this integral is also introduced.

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38

Gal, Sorin. "Shape preserving properties and monotonicity properties of the sequences of Choquet type integral operators." Journal of Numerical Analysis and Approximation Theory 47, no. 2 (2018): 135–49. http://dx.doi.org/10.33993/jnaat472-1154.

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In this paper, for the univariate Bernstein-Kantorovich-Choquet, Szasz-Kantorovich-Choquet, Baskakov-Kantorovich-Choquet and Bernstein-Durrmeyer-Choquet operators written in terms of the Choquet integrals with respect to monotone and submodular set functions, we study the preservation of the monotonicity and convexity of the approximated functions and the monotonicity of some approximation sequences.

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39

Броневич, Андрей Георгиевич, and Игорь Наумович Розенберг. "Algebraic properties of the Choquet integral." Fuzzy Systems and Soft Computing, no. 1 (August 12, 2022): 28–58. http://dx.doi.org/10.26456/fssc86.

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В данной работе рассматриваются свойства интеграла Шоке в зависимости от монотонной меры, относительно которой производится интегрирование, а именно, от ее принадлежности к семействам монотонных мер, рассматриваемых в теории неточных вероятностей. В частности, рассматривается порождение монотонных мер с помощью интеграла Шоке, а также порождение монотонных мер на алгебре нечетких множеств. Приводится также новый подход аксиоматизации интеграла Шоке, основанного на каноническом представлении простых функций. In the paper, we analyze how the properties of the Choquet integral depend on a monoton

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40

MUROFUSHI, Toshiaki, and Michio SUGENO. "Hierarchical decomposition of Choquet integral systems." Journal of Japan Society for Fuzzy Theory and Systems 4, no. 4 (1992): 749–52. http://dx.doi.org/10.3156/jfuzzy.4.4_749.

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41

Adams, David R. "Weighted capacity and the Choquet integral." Proceedings of the American Mathematical Society 102, no. 4 (1988): 879. http://dx.doi.org/10.1090/s0002-9939-1988-0934860-7.

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42

Karczmarek, Paweł, Adam Kiersztyn, and Witold Pedrycz. "Generalized Choquet Integral for Face Recognition." International Journal of Fuzzy Systems 20, no. 3 (2017): 1047–55. http://dx.doi.org/10.1007/s40815-017-0355-5.

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43

Grabisch, Michel, and Christophe Labreuche. "Bi-capacities—II: the Choquet integral." Fuzzy Sets and Systems 151, no. 2 (2005): 237–59. http://dx.doi.org/10.1016/j.fss.2004.08.013.

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44

Kawabe, Jun. "The Choquet integral in Riesz space." Fuzzy Sets and Systems 159, no. 6 (2008): 629–45. http://dx.doi.org/10.1016/j.fss.2007.09.013.

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45

Timonin, Mikhail. "Robust optimization of the Choquet integral." Fuzzy Sets and Systems 213 (February 2013): 27–46. http://dx.doi.org/10.1016/j.fss.2012.04.014.

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46

Pap, Endre. "Three types of generalized Choquet integral." Bollettino dell'Unione Matematica Italiana 13, no. 4 (2020): 545–53. http://dx.doi.org/10.1007/s40574-020-00244-7.

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47

Yang, Xiuli, Xiaoqiu Song, and Leilei Huang. "Some General Inequalities for Choquet Integral." Applied Mathematics 06, no. 14 (2015): 2292–99. http://dx.doi.org/10.4236/am.2015.614201.

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48

Sheng, Changtao, Jiuliang Shi, and Yao Ouyang. "Chebyshev’s inequality for Choquet-like integral." Applied Mathematics and Computation 217, no. 22 (2011): 8936–42. http://dx.doi.org/10.1016/j.amc.2011.03.099.

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49

Torra, Vicenç, and Yasuo Narukawa. "Numerical integration for the Choquet integral." Information Fusion 31 (September 2016): 137–45. http://dx.doi.org/10.1016/j.inffus.2016.02.007.

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50

Groes, Ebbe, Hans Jørgen Jacobsen, Birgitte Sloth, and Torben Tranæs. "Axiomatic characterizations of the Choquet integral." Economic Theory 12, no. 2 (1998): 441–48. http://dx.doi.org/10.1007/s001990050230.

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