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Axiomatic Definition

The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform

Barbara Vantaggi – 1st expert on this subject based on the ideXlab platform

  • Conditional submodular Choquet expected values and conditional coherent risk measures
    International Journal of Approximate Reasoning, 2019
    Co-Authors: Davide Petturiti, Barbara Vantaggi

    Abstract:

    Abstract We provide an Axiomatic Definition of conditional submodular capacity that allows conditioning on “null” events and is the basis for the notions of consistency and of consistent extension of a partial assessment. The same Definition gives rise to an Axiomatic Definition of conditional submodular Choquet expected value, which is a conditional functional defined on conditional gambles, that can be expressed as the Choquet integral with respect to its restriction on conditional indicators. Finally, the notion of conditional submodular Choquet expected value is used to provide a Definition of conditional submodular coherent risk measure that, locally on every conditioning event, has an upper expected loss interpretation.

  • independence and conditional possibility for strictly monotone triangular norms research articles
    International Journal of Intelligent Systems, 2006
    Co-Authors: Laura Ferracuti, Barbara Vantaggi

    Abstract:

    In the literature there are different Definitions of conditional possibility. Starting from a general Axiomatic Definition, we propose a Definition of independence for o-conditional possibility, in the case that o is a strictly monotone triangular norm. We study its main properties to compare it to other Definitions introduced in possibility theory. Then, we show that the controversial aspects related to logical dependencies (structural zeros) can be circumvented. Moreover, a set of properties (the well-known graphoid properties) has been considered to be tested, allowing us to compare the proposed Definition to the independence notions given in the context of other uncertainty formalisms. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 299–323, 2006.

  • independence and conditional possibility for strictly monotone triangular norms
    International Journal of Intelligent Systems, 2006
    Co-Authors: Laura Ferracuti, Barbara Vantaggi

    Abstract:

    In the literature there are different Definitions of conditional possibility. Starting from a general Axiomatic Definition, we propose a Definition of independence for ⊙-conditional possibility, in the case that 0 is a strictly monotone triangular norm. We study its main properties to compare it to other Definitions introduced in possibility theory. Then, we show that the controversial aspects related to logical dependencies (structural zeros) can be circumvented. Moreover, a set of properties (the well-known graphoid properties) has been considered to be tested, allowing us to compare the proposed Definition to the independence notions given in the context of other uncertainty formalisms.

Laura Ferracuti – 2nd expert on this subject based on the ideXlab platform

  • independence and conditional possibility for strictly monotone triangular norms research articles
    International Journal of Intelligent Systems, 2006
    Co-Authors: Laura Ferracuti, Barbara Vantaggi

    Abstract:

    In the literature there are different Definitions of conditional possibility. Starting from a general Axiomatic Definition, we propose a Definition of independence for o-conditional possibility, in the case that o is a strictly monotone triangular norm. We study its main properties to compare it to other Definitions introduced in possibility theory. Then, we show that the controversial aspects related to logical dependencies (structural zeros) can be circumvented. Moreover, a set of properties (the well-known graphoid properties) has been considered to be tested, allowing us to compare the proposed Definition to the independence notions given in the context of other uncertainty formalisms. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 299–323, 2006.

  • independence and conditional possibility for strictly monotone triangular norms
    International Journal of Intelligent Systems, 2006
    Co-Authors: Laura Ferracuti, Barbara Vantaggi

    Abstract:

    In the literature there are different Definitions of conditional possibility. Starting from a general Axiomatic Definition, we propose a Definition of independence for ⊙-conditional possibility, in the case that 0 is a strictly monotone triangular norm. We study its main properties to compare it to other Definitions introduced in possibility theory. Then, we show that the controversial aspects related to logical dependencies (structural zeros) can be circumvented. Moreover, a set of properties (the well-known graphoid properties) has been considered to be tested, allowing us to compare the proposed Definition to the independence notions given in the context of other uncertainty formalisms.

Gao Zheng – 3rd expert on this subject based on the ideXlab platform

  • A Similarity Measure between Fuzzy Sets
    Applied Mechanics and Materials, 2012
    Co-Authors: Gao Zheng

    Abstract:

    The similarity measure is one of the most useful fuzzy measures in fuzzy logic theory. In this paper, we propose a new similarity measure between fuzzy sets. As a preparation, we first choose an Axiomatic Definition for the similarity measure. Then, according to the chosen Axiomatic Definition, we propose a new computation formula. Finally, we give two examples to validate its performance. The results show that the new similarity measure is rational for fuzzy sets.

  • FSKD – An inclusion measure between general type-2 fuzzy sets
    2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery, 2010
    Co-Authors: Gao Zheng, Jian Xiao, Yong Zhang

    Abstract:

    The inclusion measure indicates the degree that a fuzzy set is contained in another fuzzy set and can be used in many fields. However, the inclusion measure between type-2 fuzzy sets has received little attention. Hence in this paper, we propose an inclusion measure for general type-2 fuzzy sets. Firstly, we select an Axiomatic Definition for the new inclusion measure. Then, according to the selected Axiomatic Definition, we propose a computation formula by considering the FOU and the secondary membership function of the general type-2 fuzzy set. Finally, we present two examples to explain its calculation and validate its performance. The results show that the proposed inclusion measure is reasonable and reliable for general type-2 fuzzy sets.

  • An inclusion measure between general type-2 fuzzy sets
    2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery, 2010
    Co-Authors: Gao Zheng, Jian Xiao, Yong Zhang

    Abstract:

    The inclusion measure indicates the degree that a fuzzy set is contained in another fuzzy set and can be used in many fields. However, the inclusion measure between type-2 fuzzy sets has received little attention. Hence in this paper, we propose an inclusion measure for general type-2 fuzzy sets. Firstly, we select an Axiomatic Definition for the new inclusion measure. Then, according to the selected Axiomatic Definition, we propose a computation formula by considering the FOU and the secondary membership function of the general type-2 fuzzy set. Finally, we present two examples to explain its calculation and validate its performance. The results show that the proposed inclusion measure is reasonable and reliable for general type-2 fuzzy sets.