Fuzzy memberships as likelihood functions in a possibilistic framework

https://doi.org/10.1016/j.ijar.2016.11.017Get rights and content
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Highlights

  • Coherent T-conditional possibility envelopes and their extension.

  • Likelihood functions in probabilistic and possibilistic settings.

  • Interpretation of a fuzzy membership as a coherent T-conditional possibility.

  • Possibility of fuzzy events and imprecise possibilistic fuzzy IF–THEN rules.

Abstract

Likelihood functions are studied in a probabilistic and possibilistic setting: inferential conclusions are drawn from a set of likelihood functions and prior information relying on the notion of disintegrability. The present study allows for a new interpretation of fuzzy membership functions as coherent conditional possibilities. The concept of possibility of a fuzzy event is then introduced and a comparison with the probability of a fuzzy event is provided.

Keywords

Conditional possibility
Conditional probability
Likelihood function
Inference
Fuzzy set

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