Probability and Fuzziness

Abstract

From the beginning of the theory of fuzzy sets, it has been a matter of concern for many researchers in the field to find an appropriate connection between probability and possibility. One such effort can be found in the randomness-fuzziness consistency principle where a fuzzy number of the type [α,β,γ] is expressed as a combination of two probability laws. The main intention of this work is to show that a fuzzy number of the type [α,β,β] or [β,β,γ] can be expressed by one probability law with the help of superimposition of uniformly fuzzy intervals.