Advances in Fuzzy Sets — An Overview

Kaufmann, Arnold

doi:10.1007/978-1-4613-3754-6_2

Cited by 5 publications

(7 citation statements)

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“…We believe that the focus should be on the specific practical surroundings a certain method is available to, rather than which is better than the other. After all, each concept is useful in its own domain and blending is normal in several situations, as Kaufmann (1983) said.…”

Section: Disadvantages Of Evidence Theorymentioning

confidence: 99%

“…Although each measure or concept of the different theories is useful in its own domain and has its own definition and application, consideration and blending is normal in several situations (Kaufmann, 1983). Comparisons are necessary in order to evaluate and characterize those measures.…”

Section: Comparison Of Possibility Theory and Probability Theorymentioning

confidence: 99%

“…Klir and Folger (1988); and Klir and Yuan (1995) concluded that possibility theory emerged as a natural tool for modeling and handling uncertainty involving knowledge expressed in natural language and represented by fuzzy propositions. Kaufmann (1983) thought that the role possibility theory plays for fuzzy sets is analogous to that mathematical expectancy plays in probability theory and that such valuation agrees with information available subjectively.…”

Section: Possibility Theorymentioning

confidence: 99%

“…The first adoption of fuzzy methodology in reliability and failure analysis, i.e., the proposed notion of component possibility as a reliability index, may be dated back to Kaufman's study (Kaufmann, 1983), although the motivation and exact meaning of component possibility were not explained at that time and now fuzzy-based approaches are appearing in various areas of reliability evaluation (Bai and Asgarpoor, 2004) and modeling (Delmotte and Borne, 1998).…”

Section: Reliabilitymentioning

confidence: 99%

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Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

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Engineering design under uncertainty has gained considerable attention in recent years. A great multitude of new design optimization methodologies and reliability analysis approaches are put forth with the aim of accommodating various uncertainties. Uncertainties in practical engineering applications are commonly classified into two categories, i.e., aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty arises because of unpredictable variation in the performance and processes of systems, it is irreducible even adding more data or knowledge. On the other hand, epistemic uncertainty stems from lack of knowledge of the system due to limited data, measurement limitations, or simplified approximations in modeling system behavior and it can be reduced by obtaining more data or knowledge. More specifically, aleatory uncertainty is naturally represented by a statistical distribution and its associated parameters can be characterized by sufficient data. If, however, the data is limited and can be quantified in a statistical sense, epistemic uncertainty can be considered as an alternative tool in such a situation. Of the several optional treatments for epistemic uncertainty, possibility theory and evidence theory have proved to be the most computationally efficient and stable for reliability analysis and engineering design optimization. This study first attempts to provide a better understanding of uncertainty in engineering design by giving a comprehensive overview of its classifications, theories and design considerations. Then a review is conducted of general topics such as the foundations and applications of possibility theory and evidence theory. This overview includes the most recent results from theoretical research, computational developments and performance improvement of possibility theory and evidence theory with an emphasis on revealing the capability and characteristics of quantifying uncertainty from different perspectives. Possibility and evidence theory-based reliability methods have many advantages for practical engineering when compared with traditional probability-based reliability methods. They can work well under limited data while the latter need large amounts of information, more than possible in engineering practice due to aleatory and epistemic uncertainties. The possible directions for future work are summarized.

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Section: Disadvantages Of Evidence Theorymentioning

confidence: 99%

Section: Comparison Of Possibility Theory and Probability Theorymentioning

confidence: 99%

Section: Possibility Theorymentioning

confidence: 99%

Section: Reliabilitymentioning

confidence: 99%

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Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

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“…The term 'event' applied in probability theory requires a certain level of distinctiveness in defining what is occurring and what is not. 'The term 'sensation' has therefore been proposed in possibility theory, and it is something weaker than an event' (Kaufmann 1983). The idea behind 'sensation' is important in corporate settings because the degree of distinctness that the definition of 'event' requires is not always obtainable.…”

Section: Fig 2 Two Non-mutually Exclusive Outcomes In Outcome Space Smentioning

confidence: 99%