Implications of estimating confidence intervals on group fuzzy decision making scores

Abstract

Group multi-criteria decision making methodologies are widely used tools in a democratic environment. Previous research work in this field has been done by aggregating results of Analytical Hierarchical Process (AHP) and Analytical Network Process (ANP). Further, elaboration of the group methodology has been done to include the fuzziness in the decision making environment in the AHP and ANP analysis. The current aggregation methods in group fuzzy AHP and group fuzzy ANP yield a certain rank-based best option among the available alternatives and criteria according to aggregated mean score method. This research introduces the concept of calculating standard deviation and 95% confidence interval on the aggregated mean score of group fuzzy AHP (GFAHP) and group fuzzy ANP (GFANP). The standard deviation suggests the deviance in the group decision making from the mean scores of the group, and the 95% confidence interval (CI) gives upper and lower CI of the mean score, thus providing the decision makers an interval where the ranks obtained may be valid instead of a single absolute rank. Tukey's HSD tests were done to show if the mean score of the alternatives were statistically significantly different from each other. The study uses Arrow's theorem as a guiding principle which helps in understanding and making decisions in a group fuzzy environment with multiple alternatives where ranking and choosing the alternatives may not always yield a single best choice of alternative. The concept of confidence interval on the group fuzzy decision making scores has been presented by comparing its implication on GFAHP and GFANP using a case study example of online purchase of cookware, perfume and a watches through shopping platforms, Amazon, Walmart and Macy's with male and female participants. An important implication of the study is presented by the results which show that in many instances the ranks of the alternatives are not statistically different from each other. This study acts as a foundation for future research where the methodology used can be combined with Delphi or other complex group argumentation methods to gain more meaningful outcomes in ranking alternatives.