The likelihood interpretation as the foundation of fuzzy set theory

In order to use fuzzy sets in real-world applications, an interpretation for the values of membership functions is needed. The history of fuzzy set theory shows that the interpretation in terms of statistical likelihood is very natural, although the connection between likelihood and probability can be misleading. In this paper, the likelihood interpretation of fuzzy sets is reviewed: it makes fuzzy data and fuzzy inferences perfectly compatible with standard statistical analyses, and sheds some light on the central role played by extension principle and α-cuts in fuzzy set theory. Furthermore, the likelihood interpretation justifies some of the combination rules of fuzzy set theory, including the product and minimum rules for the conjunction of fuzzy sets, as well as the probabilistic-sum and bounded-sum rules for the disjunction of fuzzy sets

A fuzzy-QFD approach for the enhancement of work equipment safety: a case study in the agriculture sector

The paper proposes a design for safety methodology based on the use of the Quality Function Deployment (QFD) method, focusing on the need to identify and analyse risks related to a working task in an effective manner, i.e. considering the specific work activities related to such a task. To reduce the drawbacks of subjectivity while augmenting the consistency of judgements, the QFD was augmented by both the Delphi method and the fuzzy logic approach. To verify such an approach, it was implemented through a case study in the agricultural sector. While the proposed approach needs to be validated through further studies in different contexts, its positive results in performing hazard analysis and risk assessment in a comprehensive and thorough manner can contribute practically to the scientific knowledge on the application of QFD in design for safety activities

The likelihood interpretation of fuzzy data

© Springer International Publishing Switzerland 2017. The interpretation of degrees of membership as statistical likelihood is probably the oldest interpretation of fuzzy sets. It allows in particular to easily incorporate fuzzy data and fuzzy inferences in statistical methods, and sheds some light on the central role played by extension principle and α-cuts in fuzzy set theory