The phrase "a possibility distribution" is correct and usable in written English.
It can be used in contexts related to probability, statistics, or decision theory to describe a function that represents the likelihood of various outcomes.
Example: "In our analysis, we will utilize a possibility distribution to model the uncertainty in the data."
Alternatives: "a probability distribution" or "a likelihood distribution".
The most commonly used clustering method, k-means, is introduced to identify the subgroups and a possibility distribution based hesitant fuzzy element (PDHFE) is employed to represent each cluster preference.
The "overall map unit composition percentage" available in the soil survey tabular data can be treated as a possibility distribution of the prevalence of different soil series within all occurrences of the map unit in the survey area.
A possibility distribution is defined as a mapping (pi : varOmega rightarrow [0,1]).
Possibility theory does so only indirectly, although possibility measures on a field of propositions A can also be defined without recourse to a possibility distribution on the underlying set W of possibilities.
A possibility distribution is associated with two measures, namely, the possibility ((varPi )) and necessity (N) measures, which are represented by Eq. (1): begin{aligned} varPi (A) = mathrm{sup}_{xin A} pi (x), quad N(A) = mathrm{inf}_{x notin A} (1-pi (x)).
Conversely, a collection of nested sets (A_i) with (lower) confidence levels (lambda _i) can be modeled as a possibility distribution, since the (alpha ) cut of a (continuous) possibility distribution can be understood as the probabilistic constraint (P(X in [underline{x}_alpha, overline{x}_alpha ]) ge 1-alpha ).
In our approach, the measurement uncertainty is translated into an a-priori possibility distribution for e m from sensor characteristics.
Hence, we have for each measurement, i.e. measurements uncertainty is represented as a quadratic possibility distribution.
Then, a consistent possibility distribution may be defined on Δ via: (3) and the possibility of an event A is given by replacing the possibility definition (3) in (1), resulting in: (4) In the next sections, abusing the notation, an event A will be usually described by a set of constraints on the decision variables δ.
The basic building block of possibility theory is a user-defined possibility distribution π : Δ → [0, 1].
The plant is considered as possibility distribution on a plant space and the closed loop specifications are given in terms of the peak of sensitivity function described by fuzzy numbers.
