Modeling Uncertainty with Interval Valued Fuzzy Numbers

Abstract

This article describes how risk assessment is a significant aid in decision-making process. It is usually performed using models and a ‘model' is a function of some parameters which are usually affected by uncertainty due to lack of data, imprecision, vagueness, and a small sample size.. Fuzzy set is a well-established mathematical tool to handle this type of uncertainty. Normally, triangular fuzzy numbers (TFNs) or trapezoidal fuzzy numbers (TrFNs) are extensively deliberated to embody this type of uncertainty. However, in real world situations, bell-shaped fuzzy numbers may occur to characterize uncertainty. It is pragmatic that type-I fuzzy set may not always dispense single value from [0,1] and on the other hand, assigning a precise value to expert's judgment is excessively restrictive, therefore, the assignment of an interval value is more practical. Thus, interval valued fuzzy set (IVFS) comes into picture. It can be observed that representation of some model parameters of the risk assessment models are triangular interval valued fuzzy numbers (TIVFNs) while representation of some other parameters are bell-shaped IVFNs. In such circumstances, it is most important to devise a technique to combine TIVFNs and bell shaped IVFNs, as they are non-comparable. For this purpose, this article presents a technique to combine both types of incomparable IVFNs within the same framework and finally, a case study is carried out in risk assessment under this setting.