Application of Z-Numbers Based Approach to Project Risks Assessment

Abstract

At every phase of the project management process various risks originate owing to occurrence of uncertain events. In this research, we are analyzing potentialities of the Z-numbers in improving the quality of risk assessment. Risk assessment uses probability theory, theory of possibilities, fuzzy approach, Z-number based approach etc. Combined risk measure based on probability and consequence is calculated by applying the disjoint events probability formula or as a product of events. Reliability of relevant information unaccounted in this approach and this circumstance limits the descriptive power of the approach. Suggested by L. Zade a bi-component Z-number Z = (A, B) represents in a unified way a restriction on the values of the uncertain variable (A) and its certainty (B) and allows to take into account the reliability of information. Prediction identical to (High, Very Sure) can be formalized as a Z- evaluation “X is Z (A,B)”, where X is random variable of Risk Likelihood, A and B are fuzzy sets, describing soft constraints on a risk likelihood and a partial reliability, respectively. Usually, A and B are sense-based and in effect are imprecise.Z-number describes a probability of threat as: Likelihood =Z1(High,Very Sure),where A is expressed by linguistic terms High, Medium, Low, and B is expressed by terms Very Sure, Sure and so on. Similarly, Сonsequence measure is described as Сonsequence measure = Z2 (Low, Sure).Risk levels (Z12) is calculated as the product of the likelihood (Z1) and consequence measures (Z2).Effectiveness of the approach illustrated by examples. A general and computationally effective approach suggested to computation with Z-numbers allows using Z-information for the solving decision-making problem which can be utilized for risk factors estimation.. Application of the Z-number based approach for a project risks assessment increases adequacy of the risks representation due to better approximation of the combined effects