A Note on Fuzzy Random Vectors as Models for Vague but Synthetic Descriptions of Complex Random Phenomena

Fukuda, Tokuo

doi:10.5687/sss.2006.119

Cited by 3 publications

(4 citation statements)

References 6 publications

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“…Although there are no consideration on the capricious vague perception of crisp phenomena, we have developed a similar discussion in [5].…”

Section: Fuzzy Random Sets As Models Of Capricious Vague Perceptions mentioning

confidence: 99%

“…According to the framework mentioned in the above example, the elementary discrete fuzzy random set is defined as follows: Definition 1. Let (Ω, A, P u o ) be an elementary probability space given by (3), (4) and (5). Then, an elementary fuzzy random set as a vague perception of the original point u o ∈ R n is defined as follows:…”

Section: Fuzzy Random Sets As Models Of Capricious Vague Perceptions mentioning

confidence: 99%

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On Statistical Moments for Capricious Vague Perceptions

Fukuda

2013

Stochastic Systems Theory and its Applications (SSS)

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In this paper, the author investigates the statistical moments such as expectations and variances for a class of fuzzy random sets, where the fuzzy random set is considered as a model of the capricious vague perception of a crisp phenomenon or a crisp random phenomenon. First, the class of fuzzy random sets, which has been proposed by author[1, 2], where the vague perception of a crisp phenomenon fluctuates slightly but randomly by the state of a capricious person's mind, is refined and its expectation and variance are introduced. Secondly, the refined class of fuzzy random sets is extended to the models for the capricious vague perceptions of crisp random phenomena, and their expectations and variances are investigated from the viewpoint of the multivalued logic.

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“…Although there are no consideration on the capricious vague perception of crisp phenomena, we have developed a similar discussion in [5].…”

Section: Fuzzy Random Sets As Models Of Capricious Vague Perceptions mentioning

confidence: 99%

Section: Fuzzy Random Sets As Models Of Capricious Vague Perceptions mentioning

confidence: 99%

On Statistical Moments for Capricious Vague Perceptions

Fukuda

2013

Stochastic Systems Theory and its Applications (SSS)

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“…Therefore, applying the fuzzy logic(see e.g., [4,5,12]), the truth value of s Vm,u o U (x) is given by…”

Section: Variance Of U (U O ω)mentioning

confidence: 99%

“…and 1 Although there are no consideration on the capricious vague perception of crisp phenomena, we have developed a similar discussion in [12].…”

Section: Fuzz Capr Crispmentioning

confidence: 99%

On Second Statistical Moments for Capricious Vague Perceptions

Fukuda

2013

Transactions of ISCIE

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In this paper, the author investigates the statistical moments such as expectations and variances for a class of fuzzy random sets, where the fuzzy random set is considered as a model of the capricious vague perception of a crisp phenomenon or a crisp random phenomenon.First, the class of fuzzy random sets, which has been proposed by author [1][2][3], where the vague perception of a crisp phenomenon fluctuates slightly but randomly by the state of a capricious person's mind, is refined and its expectation and variance are introduced.Secondly, the refined class of fuzzy random sets is extended to the models for the capricious vague perceptions of crisp random phenomena, and their expectations and variances are investigated from the viewpoint of the multi-valued logic.

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On Fuzzy Random Vectors with Stepwise Membership Levels and Their Application to Questionnaire Survey

Egawa

Fukuda

2007

Stochastic Systems Theory and its Applications (SSS)

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A Note on Fuzzy Random Vectors as Models for Vague but Synthetic Descriptions of Complex Random Phenomena

Cited by 3 publications

References 6 publications

On Statistical Moments for Capricious Vague Perceptions

On Statistical Moments for Capricious Vague Perceptions

On Second Statistical Moments for Capricious Vague Perceptions

On Fuzzy Random Vectors with Stepwise Membership Levels and Their Application to Questionnaire Survey

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