Aoi Honda

Entropy of capacities on lattices and set systems

We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where the family of subsets is not necessarily the Boolean lattice of all subsets. Our definition encompasses the classical definition of Shannon for probability measures, as well as the entropy of Marichal defined for classical capacities. Some properties and examples are given.

Inclusion-Exclusion Integral and Its Application to Subjective Video Quality Estimation

A new integral for non-additive measure encompassing the Choquet integral is proposed. We construct a model using it for multi-criteria decision making problem and verify its feasibility applying to the subjective quality estimation of video delivery services.

Fuzzy fusion fairness relations for the evaluation of user preference

In this paper, formal representations for user preferences will be provided, which also take fairness in the achievement of probably conflicting goals into account. The analysis of the Bottleneck Flow Control (BFC) algorithm for congestion avoidance in traffic networks will serve as a base to specify extensions of relations among preference sets. In particular, these relations are the lexicographic minimum, the maxmin fairness, and the newly introduced ordered-ordered weighted averaging operator. All of them are shown to become, in a relational sense, maximized by the BFC algorithm. Their further expansion by introducing fuzzy fusion operators in their formal definitions than establishes a comprehensive sets of relations. The application of these relations to the Multiple Relation Analysis (MRA) of subjective video quality evaluation data is demonstrated and gives the conclusion that also fairness criterions are present in such evaluations, at least as a secondary preference criterion.

HDTV objective video quality assessment method applying fuzzy measure

High definition television (HDTV) video delivery services over IP networks have recently started. To make the delivered high-quality HDTV video comfortable to view, we need to design appropriate delivery systems and then monitor the quality of experience. Currently, subjective assessment is the main method used to quantify video quality. However, it is unsuitable for real time monitoring of video quality. Therefore, we need an objective video quality assessment method that can effectively estimate subjective video quality from the video characteristics. We propose a full-reference-type objective video quality measurement method that is applicable to the evaluation of coding distortions in HDTV. We analyzed the results from applying the conventional method (J.247 Annex A) to HDTV video and improved the conventional method on the basis of those results. We applied fuzzy measure to the conventional method so as to consider the interaction effects of each parameter because the conventional method tends to obtain different characteristics between high quality and low quality regions of video content.

Theory of inclusion-exclusion integral

A new class of integral that corresponds to a nonadditive measure.The new integral is defined using an interaction operator.Several mathematical properties of this integral are demonstrated.A mathematical model using this integral is proposed and constructed.The mathematical model is applied to a real dataset. We propose an integral with respect to a nonadditive monotone measure. This integral is a generalization of the Lebesgue integral and also the Choquet integral. It has appropriate properties, and can be extensively applied to real data analysis.

Inclusion-Exclusion Integral and t-norm Based Data Analysis Model Construction

A data analysis model using the inclusion-exclusion integral and a new construction method of a model utilizing t-norms are proposed. This model is based on the integral with respect to the nonadditive measure and is constructed in three steps of specifications of monotone functions, t-norm and of monotone measures. The model has good description ability and can be applied flexibly to real problems. Applying this model to the data set of a multiple criteria decision making problem, the efficiency of the model is verified by comparing it with the classical linear regression model and with the Choquet integral model.

Rescaling for Evaluations Using Inclusion-Exclusion Integral

On multivariate analyses generally distributions of explanatory variable have deviation depending on each unique quality, and eliminating deviation often beneficially effective. We propose two algorithms for rescaling of raw data and verify the validity of them using real reliable big data.

Canonical fuzzy measure on (0,1]

Abstract The fuzzy measure g on the unit interval (0,1] is called canonical if g is a distortion of the Lebesgue measure. The characterization of the canonical fuzzy measure is given by the invariance properties against translations.

Averaging aggregation functions based on inclusion-exclusion integrals

The inclusion-exclusion integral, defined with respect to a fuzzy measure and interaction operator, generalizes the Choquet integral. Here we look at some of its interesting properties and investigate the conditions on the interaction operator which ensure the integral is averaging. We present some illustrative examples.

Finding rules of attractive human poses using decision tree and generating novel attractive poses

In this paper, we propose a method to determine the rules for attractive poses and generate novel attractive poses based on the discovered rules. Given a set of attractive poses with a specific style and another set of unattractive poses, we can obtain the rules to separate those two sets of example poses by creating a decision tree based on the low-level pose features that are computed from the example poses. In this research, we implemented our approach for two kinds of attractive poses, Hero and JoJo standing poses, and successfully discovered the rules of these styles. We also developed a heuristic kinematics-based pose deformation method based on the discovered rules of attractive poses. The rules can be applied to any input pose with any specified scale. Using our system, a creator can interactively design novel poses.