The Determination Method of Satisfactory Consistency of the Interval Number Pairwise Comparisons Matrix Based on Submatrix

Abstract

The decision-maker obtains the pairwise comparisons matrix by comparing two entities. In the process of comparing the two entities, the relationship between the two entities and other entities is not considered. In this way, the judgment may be illogical. This paper mainly studies the satisfactory consistency of the interval number pairwise comparisons matrix based on cyclic matrix. Firstly, the illogical judgment entity in the process of the decision-maker’s judgment is expressed by the cyclic matrix. There are three entities and four entities to form the cyclic matrix. The relationship and various forms of the cyclic cycle formed by the four entities and the three entities are discussed; then, the satisfactory consistency of the interval number pairwise comparisons matrix is determined by judging whether there is a cyclic matrix in the submatrix of the interval number pairwise comparisons matrix. Finally, two examples are given to verify the rationality and effectiveness of the method.

Keywords

• interval number pairwise comparisons matrix
• satisfying consistency
• permutation matrix
• cyclic matrix