Iterative Process of Group Decision Making using Fuzzy Influence Diagrams

Abstract

In this paper, the use of influence diagrams is extended to the group decision making using fuzzy logic, sequential approach and multi-criteria evaluation. Instead of classical Bayesian networks using conditional probability tables that are often difficult or impossible to obtain, a verbal expression of probabilistic uncertainty, represented by fuzzy sets is used in this approach. This inference engine is illustrated through the assessment of risk caused by improper drug storage in pharmaceutical cold chain by the group of experts in the iterative assessment process. Unlike standard group decision making procedure where the group consensus relies on the principle of majority, the risk assessment process outlines some behavioral characteristics that are opposite to this principle. Many papers have led to the conclusion that tendency for group decisions to be riskier than the average decision made by individuals exists and is referred to as risky shift. The predicted results were first noted in 1961 and similar results have been obtained since. This shift is an example of a broader result of group decision-making called group polarization. Findings that groups communicating via computer produce more polarized decisions than face-to-face groups are elaborated. This research is focused on influence diagrams and proposes their extension using fuzzy logic and multi-criteria evaluation. The fuzzy logic is introduced in a twofold manner: via fuzzy probability values expressed linguistically, and via fuzzy random variables. Instead of classical Bayesian networks, a verbal expression of probabilistic uncertainty, represented by fuzzy sets is used in this approach. Decision making brings the danger that some solutions will not be well accepted by some experts in the group. To overcome this problem, it is advisable that experts carry out a consensus process, where they discuss and negotiate in order to achieve a sufficient agreement before selecting the best alternative. The method of risk assessment is illustrated on an example taken from the supply chain management of pharmaceutical cold chain - pharmaceuticals that must be distributed at temperature between 2 and 8 °C. Results presented in case studies proved that this new form of description - fuzzy influence diagram, that is both a formal description of the problem that can be treated by computers and a simple, easily understood representation of the problem can be successfully implemented for various class of risk analysis problems in complex systems