An extended TOPSIS method based on ordered fuzzy numbers for group decision making

Multiple criteria decision making methods have become very popular in recent years and are frequently applied in many real-life situations. One of the most commonly used is the Technique for Order Preference by Similarity to Ideal Solution. Its original version is based on the information provided by the decision maker as exact numerical values. However, in some real-life situations, the decision maker may not be able to precisely express the value of the ratings of alternatives with respect to criteria or else he/she uses linguistic expressions. In such situations he/she may use other data formats, such as: interval numbers, fuzzy numbers, ordered fuzzy numbers, hesitant fuzzy sets, intuitionistic fuzzy sets and other. On the other hand, the increasing complexity of the decision problems analysed makes it less feasible to consider all the relevant aspects of the problems by a single decision maker. As a result, many real-life problems are discussed by a group of decision makers. The aim of this paper and its main contribution is to present a new approach for ranking of alternatives for group decision making using the Technique for Order Preference by Similarity to Ideal Solution method based on ordered fuzzy numbers. This is an alternative to methods that use different forms of averages for the aggregation of the individual matrices into a collective matrix. In the proposed approach aggregation is not needed and all individual decision information of decision makers is taken into account in determining the ranking of alternatives and the selecting the best one. The key stage of this method is the transformation of the decision matrices provided by the decision makers into matrices of alternatives. A matrix corresponding to an alternative is composed of its assessments with respect to all criteria, performed by all the decision makers. A numerical example illustrates the proposed approach.