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The Combination of the Possibility Distributions

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Measuring Uncertainty within the Theory of Evidence

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Abstract

In general, possibility distributions (PDs) can be combined in a quite simple way by means of Zadeh’s extension principle (ZEP) [60]:

$$\displaystyle r_Z(z)=\sup _{z=f(x,y)} r_{X,Y}(x,y) $$

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References

  1. C. Alsina, M.J. Frank, B. Schweizer, Associative Functions: Triangular Norms and Copulas (World Scientific, Singapore, 2006)

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  2. E.P. Klement, R. Mesiar, E. Pap, Triangular norms. Position paper I: basic analytical and algebraic properties. Fuzzy Sets Syst. 143(1), 5–26 (2004)

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  3. L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1(1), 3–28 (1978)

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Salicone, S., Prioli, M. (2018). The Combination of the Possibility Distributions. In: Measuring Uncertainty within the Theory of Evidence. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-74139-0_10

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