Fuzzy Probability for System Reliability

James P. Dunyak; Donald C. Wunsch

doi:10.1109/CDC.1998.757925

Fuzzy Probability for System Reliability

James P. Dunyak
, Donald C. Wunsch

Research output: Contribution to journal › Article › peer-review

Abstract

Fuzzy fault trees provide a powerful and computationally efficient technique for developing fuzzy probabilities based on independent inputs. The probability of any event that can be described in terms of a sequence of independent unions, intersections, and complements may be calculated by a fuzzy fault tree. Unfortunately, fuzzy fault trees do not provide a complete theory: many events of substantial practical interest cannot be described only by independent operations. In this paper, we introduce a new extension of crisp probability theory. Our model is based on n independent inputs, each with a fuzzy probability. The elements of our sample space describe exactly which of the n input events did and did not occur. Our extension is complete, since a fuzzy probability is assigned to every subset of the sample space. Our extension is also consistent with all calculations that can be arranged as a fault tree.

Original language	American English
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	3
DOIs	https://doi.org/10.1109/CDC.1998.757925
State	Published - Jan 1 1998

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Electrical and Computer Engineering

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https://doi.org/10.1109/CDC.1998.757925

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title = "Fuzzy Probability for System Reliability",

abstract = " Fuzzy fault trees provide a powerful and computationally efficient technique for developing fuzzy probabilities based on independent inputs. The probability of any event that can be described in terms of a sequence of independent unions, intersections, and complements may be calculated by a fuzzy fault tree. Unfortunately, fuzzy fault trees do not provide a complete theory: many events of substantial practical interest cannot be described only by independent operations. In this paper, we introduce a new extension of crisp probability theory. Our model is based on n independent inputs, each with a fuzzy probability. The elements of our sample space describe exactly which of the n input events did and did not occur. Our extension is complete, since a fuzzy probability is assigned to every subset of the sample space. Our extension is also consistent with all calculations that can be arranged as a fault tree.",

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AU - Dunyak, James P.

AU - Wunsch, Donald C.

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N2 - Fuzzy fault trees provide a powerful and computationally efficient technique for developing fuzzy probabilities based on independent inputs. The probability of any event that can be described in terms of a sequence of independent unions, intersections, and complements may be calculated by a fuzzy fault tree. Unfortunately, fuzzy fault trees do not provide a complete theory: many events of substantial practical interest cannot be described only by independent operations. In this paper, we introduce a new extension of crisp probability theory. Our model is based on n independent inputs, each with a fuzzy probability. The elements of our sample space describe exactly which of the n input events did and did not occur. Our extension is complete, since a fuzzy probability is assigned to every subset of the sample space. Our extension is also consistent with all calculations that can be arranged as a fault tree.

AB - Fuzzy fault trees provide a powerful and computationally efficient technique for developing fuzzy probabilities based on independent inputs. The probability of any event that can be described in terms of a sequence of independent unions, intersections, and complements may be calculated by a fuzzy fault tree. Unfortunately, fuzzy fault trees do not provide a complete theory: many events of substantial practical interest cannot be described only by independent operations. In this paper, we introduce a new extension of crisp probability theory. Our model is based on n independent inputs, each with a fuzzy probability. The elements of our sample space describe exactly which of the n input events did and did not occur. Our extension is complete, since a fuzzy probability is assigned to every subset of the sample space. Our extension is also consistent with all calculations that can be arranged as a fault tree.

UR - https://scholarsmine.mst.edu/ele_comeng_facwork/461

UR - https://doi.org/10.1109/CDC.1998.757925

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DO - 10.1109/CDC.1998.757925

M3 - Article

SN - 2576-2370

VL - 3

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

ER -

Fuzzy Probability for System Reliability

Abstract

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