József Temesi

Pairwise comparison matrices and the error-free property of the decision maker

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal.

An application of incomplete pairwise comparison matrices for ranking top tennis players

Pairwise comparison is an important tool in multi-attribute decision making. Pairwise comparison matrices (PCM) have been applied for ranking criteria and for scoring alternatives according to a given criterion. Our paper presents a special application of incomplete PCMs: ranking of professional tennis players based on their results against each other. The selected 25 players have been on the top of the ATP rankings for a shorter or longer period in the last 40 years. Some of them have never met on the court. One of the aims of the paper is to provide ranking of the selected players, however, the analysis of incomplete pairwise comparison matrices is also in the focus. The eigenvector method and the logarithmic least squares method were used to calculate weights from incomplete PCMs. In our results the top three players of four decades were Nadal, Federer and Sampras. Some questions have been raised on the properties of incomplete PCMs and remains open for further investigation.

Analysis of pairwise comparison matrices: an empirical research

Pairwise comparison (PC) matrices are used in multi-attribute decision problems (MADM) in order to express the preferences of the decision maker. Our research focused on testing various characteristics of PC matrices. In a controlled experiment with university students (N=227) we have obtained 454 PC matrices. The cases have been divided into 18 subgroups according to the key factors to be analyzed. Our team conducted experiments with matrices of different size given from different types of MADM problems. Additionally, the matrix elements have been obtained by different questioning procedures differing in the order of the questions. Results are organized to answer five research questions. Three of them are directly connected to the inconsistency of a PC matrix. Various types of inconsistency indices have been applied. We have found that the type of the problem and the size of the matrix had impact on the inconsistency of the PC matrix. However, we have not found any impact of the questioning order. Incomplete PC matrices played an important role in our research. The decision makers behavioral consistency was as well analyzed in case of incomplete matrices using indicators measuring the deviation from the final order of alternatives and from the final score vector.

Decision support system for production control: Multiple criteria decision making in practice

This paper presents a development of decision support systems for solving scheduling problems. It consists of two parts — the first describing the production processes which can be handled by the system and the second describing how the system works.

An interactive approach to determine the elements of a pairwise comparison matrix

The elicitation process, which provides initial data for further analysis in various decision making problems, can influence the final result (preference scores, weights). The elicitation process is crucial for getting consistent, near-consistent or inconsistent PCM. Decision support systems apply different approaches in practice. This paper aims at investigating two questions. Correction methods are interpreted and analyzed from the viewpoints of their philosophy and techniques to decrease the degree of inconsistency. On the other hand improving consistency in real-world decision problems is not possible without additional information from the decision maker. The proposed interactive method can be applied for individual decision making problems with verbal scale. The involvement of the decision maker and a heuristic rule can ensure that the process either provides a near-consistent and error-free PCM or demonstrates the inability of the decision maker to reach that goal.

Computer aided licence selection

A model of multiple criteria decision making is presented for selecting the “best” of a finite number of alternatives. Techniques of scoring the alternatives and weighting the criteria are combined with different evaluating procedures and amalgamated in an interactive algorithm. Application of this method for choosing the best tender in a competitive bidding is discussed and a case is presented in some detail.