A Mathematical Model for Subjective Evaluation of Alternatives in Fuzzy Multi-Criteria Group Decision Making Using COPRAS Method

Multi-criteria group decision-making approaches under fuzzy environment find their attention in the recent works in the area of decision science. In a real-life decision-making situation, decision makers express their opinions often linguistically. Such linguistic expressions are then captured by fuzzy set theory and represented in the present study by heptagonal fuzzy numbers for analytic purpose. Firstly, the concept, the arithmetic operations and a centroid-based ranking method of symmetric heptagonal fuzzy numbers (symHFN) are introduced, and then, some operators are proposed for aggregating the linguistic information. Secondly, the complex proportional assessment (COPRAS) method used for group decision making is extended within the context of the proposed symHFNs to develop an algorithm for fuzzy multi-criteria group decision-making (FMCGDM) method. The proposed method incorporates an efficient computational technique which handles the degree of satisfaction of the decision maker in their judgement. SymHFNs are used to handle the linguistic evaluation and assessment of alternatives by the decision makers. As it records the primary and secondary degree of satisfaction of decision makers' opinion, symHFN is more suitable and realistic in decision-making problems. Finally, by virtue of the proposed FMCGDM method, fire emergency alternative evaluation is carried out to illustrate the practicality and the effectiveness of the proposed method.