Modeling Uncertainty with Interval Valued Fuzzy Numbers: Case Study in Risk Assessment

Modeling Uncertainty with Interval Valued Fuzzy Numbers: Case Study in Risk Assessment

Palash Dutta (Deptartment of Mathematics, Dibrugarh University, Didrugarh, India)
DOI: 10.4018/IJITSA.2018070101

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.
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1. Introduction

Risk assessment is an important tool in decision-making process and it is highly important to accrue knowledge on the features of each and every existing data, information and model parameters involved in risk assessment process. It is observed that most frequently existing data/ information are construed in probabilistic conceptualization because it is an extremely well-built and well instituted Mathematical apparatus to treat uncertainty (aleatory) that arises due to inherent variability, natural stochasticity, environmental or structural variation across space or time, due to heterogeneity or the random character of natural processes. However, it is comprehensible that not each and every existing data, information and model parameters are influenced by this type of uncertainty and so it cannot be handled by conventional probability theory. However, model parameters may be fouled with uncertainty (epistemic) that arises due to lack of precision, deficiency in data, diminutive sample sizes or data acquisition from specialist opinion or subjective construal of existing data or information. In such situations, conventional probability theory is improper to characterize (epistemic) uncertainty. To overcome the drawback of probabilistic method, L.A Zadeh in 1965 commenced a new notion called fuzzy set theory.

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