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On modeling possibilistic uncertainty in two-state reliability theory

Gert De Cooman (UGent)
(1996) FUZZY SETS AND SYSTEMS. 83(2). p.215-238
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Abstract
In this paper, we show how a possibilistic uncertainty model can be used to represent and manipulate uncertainty about the states of a system and of its components. At the same time, we present a thorough study of the incorporation of this possibilistic uncertainty model in classical, two-state reliability theory. The possibilistic reliability of a component or system is introduced and studied. Furthermore, we introduce the important notion of a possibilistic structure function, based upon the concept of a classical, two-valued structure function. Under certain conditions of possibilistic independence, it allows us to calculate the possibilistic reliability of a system in terms of the possibilistic reliabilities of its components. Finally, we give straightforward methods for determining a possibilistic structure function from its classical, two-valued counterpart. In this way, we intend to show that a possibilistic uncertainty model in two-state reliability theory is formally analogous to, and certainly not more complicated than, a probabilistic uncertainty model.
Keywords
measure theory, possibility theory, reliability theory, CONTINUUM STRUCTURE FUNCTIONS, STOCHASTIC PERFORMANCE, SYSTEMS

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Chicago
De Cooman, Gert. 1996. “On Modeling Possibilistic Uncertainty in Two-state Reliability Theory.” Fuzzy Sets and Systems 83 (2): 215–238.
APA
De Cooman, Gert. (1996). On modeling possibilistic uncertainty in two-state reliability theory. FUZZY SETS AND SYSTEMS, 83(2), 215–238.
Vancouver
1.
De Cooman G. On modeling possibilistic uncertainty in two-state reliability theory. FUZZY SETS AND SYSTEMS. 1996;83(2):215–38.
MLA
De Cooman, Gert. “On Modeling Possibilistic Uncertainty in Two-state Reliability Theory.” FUZZY SETS AND SYSTEMS 83.2 (1996): 215–238. Print.
@article{190508,
  abstract     = {In this paper, we show how a possibilistic uncertainty model can be used to represent and manipulate uncertainty about the states of a system and of its components. At the same time, we present a thorough study of the incorporation of this possibilistic uncertainty model in classical, two-state reliability theory. The possibilistic reliability of a component or system is introduced and studied. Furthermore, we introduce the important notion of a possibilistic structure function, based upon the concept of a classical, two-valued structure function. Under certain conditions of possibilistic independence, it allows us to calculate the possibilistic reliability of a system in terms of the possibilistic reliabilities of its components. Finally, we give straightforward methods for determining a possibilistic structure function from its classical, two-valued counterpart. In this way, we intend to show that a possibilistic uncertainty model in two-state reliability theory is formally analogous to, and certainly not more complicated than, a probabilistic uncertainty model.},
  author       = {De Cooman, Gert},
  issn         = {0165-0114},
  journal      = {FUZZY SETS AND SYSTEMS},
  keyword      = {measure theory,possibility theory,reliability theory,CONTINUUM STRUCTURE FUNCTIONS,STOCHASTIC PERFORMANCE,SYSTEMS},
  language     = {eng},
  number       = {2},
  pages        = {215--238},
  title        = {On modeling possibilistic uncertainty in two-state reliability theory},
  url          = {http://dx.doi.org/10.1016/0165-0114(95)00379-7},
  volume       = {83},
  year         = {1996},
}

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