Random-fuzzy variable: Difference between revisions

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==Definition==
[[File:Random-Fuzzy Variable.png|thumb|right|upright=2.0|<{{center>|Random-Fuzzy Variable</center>}}]]
A Random-fuzzy Variable (RFV) is defined as a type 2 fuzzy variable which satisfies the following conditions:<ref name = "saliconebook">{{Cite book|title=Measuring uncertainty within the theory of evidence|last=Salicone, Simona|others=Prioli, Marco|isbn=9783319741390|___location=Cham, Switzerland|oclc=1032810109}}</ref>
* Both the internal and the external functions of the RFV can be identified.
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Some common probability distributions and the corresponding possibility distributions can be seen in the figures.
[[File:Normal distribution in probability and possibility.png|thumb|left|upright=2.0|<{{center>|Normal distribution in probability and possibility.</center>}}]]
[[File:Uniform distribution in probability and possibility.png|thumb|right|upright=2.0|<{{center>|Uniform distribution in probability and possibility.</center>}}]]
[[File:Triangular distribution in probability and possibility.png|thumb|center|upright=2.0|<{{center>|Triangular distribution in probability and possibility.</center>}}]]
 
===The internal distribution(''r<sub>internal</sub>'')===
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An example for the construction of the corresponding external membership function(''r<sub>external</sub>'') and the RFV from a random PD and an internal PD can be seen in the following figure.
[[File:Construction of an RFV.png|thumb|center|upright=3.0|<{{center>|Construction of an external membership function and the RFV from internal and random possibility distributions.</center>}}]]
 
==See also==