Chofugaoka, Japan

Toho Gakuen School of Music

www.tohomusic.ac.jp
Chofugaoka, Japan

Toho Gakuen School of Music , Tōhō Gakuen Daigaku ) is a private conservatoire in Chōfu, Tokyo, Japan. Wikipedia.

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Narukawa Y.,Toho Gakuen School of Music | Narukawa Y.,Tokyo Institute of Technology | Torra V.,IIIA CSIC
Communications in Computer and Information Science | Year: 2014

Fuzzy measures on multisets are studied in this paper. We show that a class of multisets on a finite space can be represented as a subset of positive integers. Comonotonicity for multisets are defined. We show that a fuzzy measure on multisets with some comonotonicity condition can be represented by a generalized fuzzy integral. © Springer International Publishing Switzerland 2014.


Narukawa Y.,Toho Gakuen School of Music | Narukawa Y.,Tokyo Institute of Technology | Torra V.,Institute dInvestigacio en Intelligncia Artificial
International Journal of Approximate Reasoning | Year: 2011

Fuzzy measures are used in conjunction with fuzzy integrals for aggregation. Their role in the aggregation is to permit the user to express the importance of the information sources (either criteria or experts). Due to the fact that fuzzy measures are set functions, the definition of such measures requires the definition of 2n parameters, where n is the number of information sources. To make the definition easier, several families of fuzzy measures have been defined in the literature. In this paper m-separable fuzzy measures are introduced. We present some results on this type of measures and we relate them to some of the previous existing ones. We study generating functions for m-separable fuzzy measures and some properties related to these generating functions. © 2011 Elsevier Ltd. All rights reserved.


Narukawa Y.,Toho Gakuen School of Music | Narukawa Y.,Tokyo Institute of Technology | Stokes K.,Rovira i Virgili University | Torra V.,Institute dInvestigacio en Intelligencia Artificial
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2011

Fuzzy measures on multisets are studied. We show that a class of multisets can be represented as a subset of positive integers. Comonotonicity for multisets are defined. We show that a fuzzy measure on multisets with some comonotonicity condition can be represented by generalized fuzzy integral. © 2011 Springer-Verlag Berlin Heidelberg.


Torra V.,Autonomous University of Barcelona | Stokes K.,Rovira i Virgili University | Narukawa Y.,Toho Gakuen School of Music | Narukawa Y.,Tokyo Institute of Technology
IEEE Transactions on Fuzzy Systems | Year: 2012

Fuzzy measures are monotonic set functions on a reference set; they generalize probabilities replacing the additivity condition by monotonicity. The typical application of these measures is with fuzzy integrals. Fuzzy integrals integrate a function with respect to a fuzzy measure, and they can be used to aggregate information from a set of sources (opinions from experts or criteria in a multicriteria decision-making problem). In this context, background knowledge on the sources is represented by means of the fuzzy measures. For example, interactions between criteria are represented by means of nonadditive measures. In this paper, we introduce fuzzy measures on multisets. We propose a general definition, and we then introduce a family of fuzzy measures for multisets which we show to be equivalent to distorted probabilities when the multisets are restricted to proper sets. © 2012 IEEE.


Torra V.,Institute dInvestigacio en Intelligencia Artificial CSIC | Narukawa Y.,Toho Gakuen School of Music
Information Sciences | Year: 2012

Mahalanobis distance can be used in problems where variables are not independent. The presence of the covariance matrix in this expression permits us to represent the dependence between the variables. Fuzzy measures and Choquet integrals have a similar purpose. In this paper we compare these two expressions. To do so in the proper setting, we introduce a Choquet integral based distance. Then, we consider probability-density functions based on these two distances. In particular, we review the Gaussian distribution, which is based on the Mahalanobis distance and introduce another distribution based on the Choquet distance. Then, we introduce an operator that generalizes the Choquet integral and the Mahalanobis distance. It is the Choquet-Mahalanobis integral. Some propositions are also proven establishing equivalences and links between the Choquet-Mahalanobis integral, the Choquet integral, and the Mahalanobis distance. © 2011 Elsevier Inc. All rights reserved.


Torra V.,IIIA CSIC Institute dInvestigacio en Intelligencia Artificial | Narukawa Y.,Toho Gakuen School of Music
Soft Computing | Year: 2010

The number of aggregation operators existing nowadays is rather large. In this paper, we study some of these operators and establish some relationships between them. In particular, we focus on neat operators. We link some of these operators with the Losonczi's mean. The results permit us to define a Losonczi's OWA and a Losonczi's WOWA. © 2009 Springer-Verlag.


Torra V.,University of Skövde | Narukawa Y.,Toho Gakuen School of Music
Information Fusion | Year: 2016

Choquet integrals with respect to non-additive (or fuzzy measures) have been used in a large number of applications because they permit us to integrate information from different sources when there are interactions. Successful applications use a discrete reference set. In the case of measures on a continuous reference set, as e.g. the real line, few results have been obtained that permit us to have an analytical expression of the integral. However, in most of the cases there is no such analytical expression. In this paper we describe how to perform the numerical integration of a Choquet integral with respect to a non-additive measure. © 2016 Elsevier B.V. All rights reserved.


Torra V.,University of Skövde | Narukawa Y.,Toho Gakuen School of Music | Sugeno M.,ECSC
Fuzzy Sets and Systems | Year: 2015

The f-divergence evaluates the dissimilarity between two probability distributions defined in terms of the Radon-Nikodym derivative of these two probabilities. The f-divergence generalizes the Hellinger distance and the Kullback-Leibler divergence among other divergence functions. In this paper we define an analogous function for non-additive measures. We discuss them for distorted Lebesgue measures and give examples. Examples focus on the Hellinger distance. © 2015 Elsevier B.V.


Torra V.,Institute dInvestigacio en Intelligencia Artificial | Narukawa Y.,Toho Gakuen School of Music
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

Non-additive (fuzzy) measures also known as cooperative games or capacities are set functions that can be used to evaluate subsets of a reference set. In order to evaluate their similarities and differences, we can consider distances between pairs of measures. Games have been extended to communication situations in which besides of the game there is a graph that establishes which sets are feasible (which coalitions are possible, which individuals can cooperate). In this paper we consider the problem of defining a distance for pairs of measures when not all sets are feasible. © 2014 Springer International Publishing.


Narukawa Y.,Toho Gakuen School of Music | Narukawa Y.,Tokyo Institute of Technology
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2012

The Choquet integral is one of the operators that can be used for aggregation and synthesis of information. It integrates a function with respect to a fuzzy measure. In this paper we study the Choquet integral with respect to a symmetric fuzzy measure, which is a generalization of the OWA operator. We present some results about the approximation of Choquet integral for the calculation. We also present the inequalities for Choquet integral with respect to a symmetric fuzzy measure. © 2012 Springer-Verlag.

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