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  • differentiation of choquet integral for nonnegative Measurable Function and its application to capital investment decision making
    IEEE International Conference on Fuzzy Systems, 2000
    Co-Authors: T Kaino, K Hirota
    Abstract:

    Differentiation of a Choquet integral for a nonnegative Measurable Function taken with respect to a fuzzy measure over a real fuzzy measure space is proposed. It is applied to the capital investment decision making problem. Kaino and Hirota (1999) proposed the X axis real interval limited Choquet integral for a preparation to define a fuzzy measure shift differentiation of the Choquet integral. Here, the upper differential coefficient, the lower differential coefficient, the differential coefficient, and the derived Function of the X axis real interval limited Choquet integral for a nonnegative Measurable Function over a real fuzzy measure space along the domain (a subset of real numbers) are defined by the limitation process of the X axis real interval limited Choquet integral. Two examples of differentiation are given, where the nonnegative Measurable Functions are either a simple Function or a triangular Function. Moreover, they are applied to the automobile factory capital investment decision making problem. Assume that an automobile company has a sales plan of a new car. The current factory line has a capacity to manufacture 3,200 new cars, additional to the current car lines. Then, it is easy to make a decision to invest or not using the differentiation of the X axis real interval limited Choquet integral over X, which give us the increase or decrease rate of the expected sales revenue (also profit) per new car.

  • differentiation of nonnegative Measurable Function choquet integral over real fuzzy measure space and its application to financial option trading model
    Systems Man and Cybernetics, 1999
    Co-Authors: T Kaino, K Hirota
    Abstract:

    Fuzzy measure shift differentiation of the Choquet integral for a nonnegative Measurable Function taken with respect to a fuzzy measure over a real fuzzy measure space is proposed. It is applied to financial engineering. First, a real interval limited Choquet integral for a nonnegative Measurable Function taken with respect to a fuzzy measure over a real fuzzy measure space is given, then a fuzzy measure left shift differential coefficient, a fuzzy measure right shift differential coefficient, a fuzzy measure shift differential coefficient, and a fuzzy measure shift derived Function of the real interval limited Choquet integral for a nonnegative Measurable Function over a real fuzzy measure space along the domain are defined by the limitation process of a fuzzy measure shift. Two examples of a fuzzy measure shift differentiation are given, where fuzzy measure distributions are either a continuous distribution or a discrete distribution, to understand the notion of the fuzzy measure shift differentiation. Moreover, they are applied to financial option trading. The pricing models of a European call option premium and a European put option premium are defined using the real interval limited Choquet integral for a nonnegative Measurable Function over a real fuzzy measure space. Then, the distribution of underlying securities of an option trading at the expiration date is given as a /spl lambda/-fuzzy measure, where the total fuzzy measure is equal to one. An important risk index, the delta, which is the rate of change of the premium with respect to underlying security price is defined using the fuzzy measure shift differentiation of the real interval limited Choquet integral for a nonnegative Measurable Function over a real fuzzy measure space. Finally, these option trading models based on the real interval limited Choquet integral over a real fuzzy measure space is tested with the real market data and is compared with the popular option trading model based on the probability measure and logarithmic normal distribution defined by Black and Sholes (1973).

  • differentiation of the choquet integral of a nonnegative Measurable Function
    IEEE International Conference on Fuzzy Systems, 1999
    Co-Authors: T Kaino, K Hirota
    Abstract:

    Differentiation of the Choquet integral of a nonnegative Measurable Function taken with respect to a fuzzy measure on fuzzy measure space is proposed. First, the real interval limited Choquet integral is defined for a 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 nonnegative Measurable Functions are either a simple Function or a triangular Function. Basic properties of differentiation about sum and multiple with constant, addition, subtraction, multiplication and division are shown. It should be noted that the derived Function of the Choquet integral of a composite Function with sum of nonnegative Measurable Functions is not always equal to the sum of each derived Functions of the Choquet integrals of these Functions. Moreover, they are applied to the capital investment decision making problem.

N Subramanian - One of the best experts on this subject based on the ideXlab platform.

T Kaino - One of the best experts on this subject based on the ideXlab platform.

  • differentiation of choquet integral for nonnegative Measurable Function and its application to capital investment decision making
    IEEE International Conference on Fuzzy Systems, 2000
    Co-Authors: T Kaino, K Hirota
    Abstract:

    Differentiation of a Choquet integral for a nonnegative Measurable Function taken with respect to a fuzzy measure over a real fuzzy measure space is proposed. It is applied to the capital investment decision making problem. Kaino and Hirota (1999) proposed the X axis real interval limited Choquet integral for a preparation to define a fuzzy measure shift differentiation of the Choquet integral. Here, the upper differential coefficient, the lower differential coefficient, the differential coefficient, and the derived Function of the X axis real interval limited Choquet integral for a nonnegative Measurable Function over a real fuzzy measure space along the domain (a subset of real numbers) are defined by the limitation process of the X axis real interval limited Choquet integral. Two examples of differentiation are given, where the nonnegative Measurable Functions are either a simple Function or a triangular Function. Moreover, they are applied to the automobile factory capital investment decision making problem. Assume that an automobile company has a sales plan of a new car. The current factory line has a capacity to manufacture 3,200 new cars, additional to the current car lines. Then, it is easy to make a decision to invest or not using the differentiation of the X axis real interval limited Choquet integral over X, which give us the increase or decrease rate of the expected sales revenue (also profit) per new car.

  • differentiation of nonnegative Measurable Function choquet integral over real fuzzy measure space and its application to financial option trading model
    Systems Man and Cybernetics, 1999
    Co-Authors: T Kaino, K Hirota
    Abstract:

    Fuzzy measure shift differentiation of the Choquet integral for a nonnegative Measurable Function taken with respect to a fuzzy measure over a real fuzzy measure space is proposed. It is applied to financial engineering. First, a real interval limited Choquet integral for a nonnegative Measurable Function taken with respect to a fuzzy measure over a real fuzzy measure space is given, then a fuzzy measure left shift differential coefficient, a fuzzy measure right shift differential coefficient, a fuzzy measure shift differential coefficient, and a fuzzy measure shift derived Function of the real interval limited Choquet integral for a nonnegative Measurable Function over a real fuzzy measure space along the domain are defined by the limitation process of a fuzzy measure shift. Two examples of a fuzzy measure shift differentiation are given, where fuzzy measure distributions are either a continuous distribution or a discrete distribution, to understand the notion of the fuzzy measure shift differentiation. Moreover, they are applied to financial option trading. The pricing models of a European call option premium and a European put option premium are defined using the real interval limited Choquet integral for a nonnegative Measurable Function over a real fuzzy measure space. Then, the distribution of underlying securities of an option trading at the expiration date is given as a /spl lambda/-fuzzy measure, where the total fuzzy measure is equal to one. An important risk index, the delta, which is the rate of change of the premium with respect to underlying security price is defined using the fuzzy measure shift differentiation of the real interval limited Choquet integral for a nonnegative Measurable Function over a real fuzzy measure space. Finally, these option trading models based on the real interval limited Choquet integral over a real fuzzy measure space is tested with the real market data and is compared with the popular option trading model based on the probability measure and logarithmic normal distribution defined by Black and Sholes (1973).

  • differentiation of the choquet integral of a nonnegative Measurable Function
    IEEE International Conference on Fuzzy Systems, 1999
    Co-Authors: T Kaino, K Hirota
    Abstract:

    Differentiation of the Choquet integral of a nonnegative Measurable Function taken with respect to a fuzzy measure on fuzzy measure space is proposed. First, the real interval limited Choquet integral is defined for a 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 nonnegative Measurable Functions are either a simple Function or a triangular Function. Basic properties of differentiation about sum and multiple with constant, addition, subtraction, multiplication and division are shown. It should be noted that the derived Function of the Choquet integral of a composite Function with sum of nonnegative Measurable Functions is not always equal to the sum of each derived Functions of the Choquet integrals of these Functions. Moreover, they are applied to the capital investment decision making problem.

Deepmala Rai - One of the best experts on this subject based on the ideXlab platform.

José Manuel Benítez - One of the best experts on this subject based on the ideXlab platform.

  • neural networks with a continuous squashing Function in the output are universal approximators
    Neural Networks, 2000
    Co-Authors: Juan Castro, Carlos Javier Mantas, José Manuel Benítez
    Abstract:

    Abstract In 1989 Hornik as well as Funahashi established that multilayer feedforward networks without the squashing Function in the output layer are universal approximators. This result has been often used improperly because it has been applied to multilayer feedforward networks with the squashing Function in the output layer. In this paper, we will prove that also this kind of neural networks are universal approximators, i.e. they are capable of approximating any Borel Measurable Function from one finite dimensional space into (0,1) n to any desired degree of accuracy, provided sufficiently many hidden units are available.