Consensus in group decision making under linguistic assessments

Abstract

Group decision-making is an essential activity is many domains such as financial, engineering, and medical fields. Group decision-making basically solicits opinions from experts and combines these judgments into a coherent group decision. Experts typically express their opinion in many different formats belonging to two categories: quantitative evaluations and qualitative ones. Many times experts cannot express judgment in accurate numerical terms and use linguistic labels or fuzzy preferences. The use of linguistic labels makes expert judgment more reliable and informative for decisionmaking. In this research, a new linguistic label fusion operator has been developed. The operator helps mapping one set of linguistic labels into another. This gives decision makers more freedom to choose their own linguistic preference labels with different granularities and/or associated membership functions. Three new consensus measure methods have been developed for group decision making problem in this research. One is a Markov chain based consensus measure method, the other is order based, and the last one is a similarity based consensus measure approach. Also, in this research, the author extended the concept of Ordered Weighted Average (OWA) into a fuzzy linguistic OWA (FLOWA). This aggregation operator is more detailed and includes more information about the aggregate than existing direct methods. After measuring the current consensus, we provide a method for experts to modify their evaluations to improve the consensus level. A cost based analysis gives the least cost suggestion for this modification, and generates a least cost of group consensus. In addition, in this research I developed an optimization method to maximize two types of consensus under a budget constraint. Finally considering utilization of the consensus provides a practical recommendation to the desired level of consensus, considering its cost benefits.