Differentiation of nonnegative measurable function Choquet integral over real fuzzy measure space and its application to financial option trading model

2003 ◽  
Author(s):  
T. Kaino ◽  
K. Hirota
Keyword(s):  
Measurable Function ◽  
Measure Space ◽  
Choquet Integral ◽  
Fuzzy Measure ◽  
Option Trading ◽  
Trading Model ◽  
Nonnegative Measurable Function

Differentiation of the Choquet Integral and Its Application to Long-term Debt Ratings

2000 ◽  
Vol 4 (1) ◽  
pp. 66-75 ◽  
Author(s):  
Toshihiro Kaino ◽  
◽  
Kaoru Hirota
Keyword(s):  
Measurable Function ◽  
Quantitative Data ◽  
Capital Investment ◽  
Choquet Integral ◽  
Fuzzy Measure ◽  
Real Interval ◽  
Qualitative And Quantitative ◽  
Differential Coefficient ◽  
Nonnegative Measurable Function

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 coefficient, the lower differential coefficient, the differential coefficient, and the derived function of the Choquet integral along the range of an integrated function are defined by the limitation process of the interval limited Choquet integral. Two examples are given, where the measurable functions are either a simple function or a triangular function. Basic properties of differentiation about swn and multiple with constant, addition, subtraction, multiplication, and division are shown. Then, the Choquet integral is applied to long-term debt ratings model, where the input is qualitative and quantitative data of corporations, and the output is Moody’s long-term debt ratings. The fuzzy measure, which is given as the importance of each qualitative and quantitative data, is derived from a neural net method. Moreover, differentiation of the Choquet integral is applied to the long-term debt ratings, where this differentiation indicates how much evaluation of each specification influence to the rating of the corporation.

Forecasting stock market price by using fuzzified Choquet integral based fuzzy measures with genetic algorithm for parameter optimization

2020 ◽  
Vol 54 (2) ◽  
pp. 597-614
Author(s):  
Shanoli Samui Pal ◽  
Samarjit Kar
Keyword(s):  
Genetic Algorithm ◽  
Time Series ◽  
Linear Regression ◽  
Regression Model ◽  
Choquet Integral ◽  
Time Series Forecasting ◽  
Fuzzy Measure ◽  
Model Parameters ◽  
Forecasting Models ◽  
Non Linear

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 non classical measures. In the Choquet integral based regression model parameters are optimized by using a real coded genetic algorithm (GA). In these forecasting models, fuzzified integrands denote the participation of an individual attribute or a group of attributes to predict the current situation. Here, more generalized Choquet integral, i.e., fuzzified Choquet integral is used in case of non-linear time series forecasting models. Three different real stock exchange data are used to predict the time series forecasting model. It is observed that the accuracy of prediction models highly depends on the non-linearity of the time series.

CHOQUET INTEGRAL MODELS AND INDEPENDENCE CONCEPTS IN MULTIATTRIBUTE UTILITY THEORY

2000 ◽  
Vol 08 (04) ◽  
pp. 385-415 ◽  
Author(s):  
T. MUROFUSHI ◽  
M. SUGENO
Keyword(s):  
Utility Function ◽  
Utility Theory ◽  
Choquet Integral ◽  
Fuzzy Measure ◽  
Multiattribute Utility ◽  
Preference Relations ◽  
Multiattribute Utility Theory ◽  
A Value ◽  
Utility Independence

This paper discusses multiattribute preference relations compatible with a value/utility function represented by the Choquet integral with respect to a fuzzy measure, and shows that the additivity of the fuzzy measure is equivalent to each of mutual preferential independence, mutual weak difference independence, mutual difference independence, mutual utility independence, and additive independence.

On (L1)* for General Measure Spaces

1963 ◽  
Vol 6 (2) ◽  
pp. 211-229 ◽  
Author(s):  
H. W. Ellis ◽  
D. O. Snow
Keyword(s):  
Measurable Function ◽  
Measure Space ◽  
Finite Measure ◽  
Signed Measure ◽  
General Measure ◽  
Measure Spaces ◽  
Arbitrary Measure ◽  
Image Position ◽  
Nikodym Theorem

It is well known that certain results such as the Radon-Nikodym Theorem, which are valid in totally σ -finite measure spaces, do not extend to measure spaces in which μ is not totally σ -finite. (See §2 for notation.) Given an arbitrary measure space (X, S, μ) and a signed measure ν on (X, S), then if ν ≪ μ for X, ν ≪ μ when restricted to any e ∊ Sf and the classical finite Radon-Nikodym theorem produces a measurable function ge(x), vanishing outside e, with

A CHOQUET INTEGRAL REGRESSION MODEL BASED ON A NEW FUZZY MEASURE

2007 ◽  
pp. 1349-1355 ◽  
Author(s):  
HSIANG-CHUAN LIU ◽  
WEN-CHIH LIN ◽  
WEI-SHENG WENG
Keyword(s):  
Regression Model ◽  
Choquet Integral ◽  
Fuzzy Measure ◽  
Model Based

An Evaluation Model Based on Rough Sets

2014 ◽  
Vol 602-605 ◽  
pp. 3379-3383
Author(s):  
Yong Sheng Liu ◽  
Zan Zhang
Keyword(s):  
Decision Making ◽  
Information System ◽  
Knowledge Discovery ◽  
Rough Sets ◽  
Choquet Integral ◽  
Evaluation Model ◽  
Fuzzy Measure ◽  
Model Based

In multiattribute decision making, it is critical to indentify the importance degree of attributes before the overall assessment of the alternatives. In this paper, we give a measurement of importance degree of attributes based on knowledge discovery in the decision information system, which satisfies the conditions of fuzzy measure. Further, we construct an evaluation model combined Choquet integral with the importance degree measure. The case study illustrates the validity and the effectiveness of the method.

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