Multi-Criteria Decision-Making Method Based on Vague Number Similarity with Incomplete Certain Information

Trapezoidal vague numbers and similarity between two trapezoidal vague numbers are defined. And their properties are studied. A fuzzy multi-criteria decision making method with incomplete certain information on weights is proposed. This method extends TOPSIS to fuzzy multi-criteria decision-making. Based on the principle that the best alternative should have the largest similarity to the ideal and the least similarity to the anti-ideal, the weights of the alternatives can be obtained and the ranking can be determined. An example shows the proposed method is reasonable and effective.