ABSTRACT
Due to the complexity of the alternatives and human thinking process, the linguistic label is usually adopted, which concerns the consistency of linguistic judgment, the transformation of different linguistic scales, and the decision-making method in group and in the incomplete information environment [108-111]. In recent years, many scholars have focused on the research of the linguistic comparison matrix, especially the integration method, the consistency measure, and the consistency improvement of linguistic comparison matrix. The internal consistency characteristics of the linguistic comparison matrix reflect the decision maker’s rationality in logical judgment, which plays a vital role in scientific decision making. Two aspects are studied in this chapter the satisfaction consistency of the linguistic comparison matrix and the ordinal consistency of the linguistic comparison matrix. With respect to satisfaction consistency in the linguistic comparison matrix, the definition of strength in complete consistency of the linguistic comparison matrix is given. But it is difficult to find the completely consistent comparison matrix in the process of decision making. So what are the conditions that the matrix should satisfy to meet the consistent linguistic preference relation? The matrix educed from the linguistic comparison matrix is used to research the consistency. But the scaling of the educed matrix is different from the traditional reciprocal comparison matrix, so it cannot determine whether the linguistic comparison matrix meets the consistent linguistic preference relation according to the consistency ratio of the educed matrix. The conclusions of the existing literature [100, 109] have the reference values to measure the satisfaction
consistency of the linguistic comparison matrix. With respect to transitive linguistic preference relation, the practicable method to check the ordinal consistency of linguistic comparison matrix is proposed in the literature. However, there is still no literature that provides a method to improve the linguistic comparison matrix, which does not meet ordinal consistency. The consistent problem of fuzzy comparison matrix is studied in the literature (the scale of elements in the comparison matrix is 0.1 to 0.9) [91, 100, 101, 108, 109]. There are some conclusions of comparison matrix in the literature [108-111] which give much enlightenment for the research in this chapter. Based on the existing research, the tasks of this chapter are to: (1) propose a new measure index for the satisfaction consistency of the linguistic comparison matrix and propose a method to improve matrix that does not meet the consistent linguistic preference relation; (2) propose a method to determine the ordinal consistency and propose heuristic modification rules for the matrix that does not meet the transitive linguistic preference relation.
