Research On Consistency And Group Decision Making Method Of Interval Rough Number Reciprocal Judgment Matrix

The analytic hierarchy process has been widely used in risk management,performance evaluation and decision analysis.When measuring the importance of the scheme,the interval rough number judgment matrix has better rationality and flexibility than the interval number judgment matrix and fuzzy judgment matrix.The existing research rarely involve the content of interval rough number judgment matrix.This paper studies the consistency and group decision making problem of interval rough number reciprocal judgment matrix,which can help people solve practical problems effectively,facilitate decision makers to make decisions,and enrich the theory and method of interval rough number reciprocal judgment matrix,the main contents are as follows:1.Based on the two aspects of constructive thinking and set theory,this paper explores the consistency of the interval rough number reciprocal judgment matrix,and gives the new consistency,satisfactory consistency and complete consistency of the interval rough number reciprocal judgment matrix.The relationship between the two kinds of consistency is analyzed,and the correlation properties of the reciprocal judgment matrix of the consistency interval rough number are discussed,which lays a theoretical foundation for the ranking method based on the interval rough number judgment matrix.2.From the perspective of set theory,this paper proposes an adjustment method for the inconsistent interval rough number reciprocal judgment matrix,analyzes the possible occurrence of the inconsistent interval rough number judgment matrix,and adjusts the inconsistent reciprocal judgment matrix to satisfactory agreement.According to the original information provided by the inconsistent interval rough number reciprocal judgment matrix,the inner and outer center points and the central judgment matrix are defined to construct a consistent digital judgment matrix,on which the inner interval number offset and offset matrix are defined.The digital judgment matrix is used as a reference standard,and the interval rough number with the largest offset is found to be adjusted.Two sorting weight vector algorithm based on uniform approximatiorn and eigenvalue for interval rough number reciprocal judgment matrix is proposed.Combined with two sorting methods of interval rough numbers,the final ordering of the scheme is obtained.The effectiveness of the method is verified by an example.3.Based on the aggregation operator,compatibility and group judgment consistency,the consistency index,judgment method and adjustment method of group opinions are discussed.The group decision algorithm of three interval rough number reciprocal judgment matrices is given.And the feasibility and effectiveness of the algorithm are verified in the case--investment project selection.