Random-fuzzy variable: Difference between revisions

Revision as of 18:48, 6 December 2021

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Using the above equations, the ''α''-cuts are calculated for every value of ''α'' which gives us the final plot of the RFV.

A Random-Fuzzy variable is capable of giving a complete picture of the random and systematic contributions to the total uncertainty from the ''α''-cuts for any confidence level as the confidence level is nothing but ''1-α''.<ref name="zadeh1">{{Citecite q journal|last Q57275767 |last1=Zadeh |firstfirst1=L. A. |date=1975-09 author-01|titlelink1 =Fuzzy logicLotfi andA. approximateZadeh reasoning|journal publisher =Synthese [[Springer Science+Business Media|language=en|volume=30|issue=3|pages=407–428|doi=10.1007/BF00485052|issn=1573-0964Springer]] }}</ref><ref name = "kaufman">{{Cite book|title=Introduction to fuzzy arithmetic : theory and applications|last=Kaufmann, A. (Arnold), 1911-|date=1991|publisher=Van Nostrand Reinhold Co|others=Gupta, Madan M.|isbn=0442008996|edition= [New ed.]|___location=New York, N.Y.|oclc=24309785}}</ref>

An example for the construction of the corresponding external membership function(''r_external'') and the RFV from a random PD and an internal PD can be seen in the following figure.