On optimal completions of incomplete pairwise comparison matrices

An important variant of a key problem for multi-attribute decision making is considered. We study the extension of the pairwise comparison matrix to the case when only partial information is available: for some pairs no comparison is given. It is natural to define the inconsistency of a partially filled matrix as the inconsistency of its best, completely filled completion. We study here the uniqueness problem of the best completion for two weighting methods, the Eigen-vector Method and the Logarithmic Least Squares Method. In both settings we obtain the same simple graph theoretic characterization of the uniqueness. The optimal completion will be unique if and only if the graph associated with the partially defined matrix is connected. Some numerical experiences are discussed at the end of the paper

Managing Incomplete Preference Relations in Decision Making: A Review and Future Trends

In decision making, situations where all experts are able to efficiently express their preferences over all the available options are the exception rather than the rule. Indeed, the above scenario requires all experts to possess a precise or sufficient level of knowledge of the whole problem to tackle, including the ability to discriminate the degree up to which some options are better than others. These assumptions can be seen unrealistic in many decision making situations, especially those involving a large number of alternatives to choose from and/or conflicting and dynamic sources of information. Some methodologies widely adopted in these situations are to discard or to rate more negatively those experts that provide preferences with missing values. However, incomplete information is not equivalent to low quality information, and consequently these methodologies could lead to biased or even bad solutions since useful information might not being taken properly into account in the decision process. Therefore, alternative approaches to manage incomplete preference relations that estimates the missing information in decision making are desirable and possible. This paper presents and analyses methods and processes developed on this area towards the estimation of missing preferences in decision making, and highlights some areas for future research

Pairwise comparison matrix in multiple criteria decision making

The measurement scales, consistency index, inconsistency issues, missing judgment estimation and priority derivation methods have been extensively studied in the pairwise comparison matrix (PCM). Various approaches have been proposed to handle these problems, and made great contributions to the decision making. This paper reviews the literature of the main developments of the PCM. There are plenty of literature related to these issues, thus we mainly focus on the literature published in 37 peer reviewed international journals from 2010 to 2015 (searched via ISI Web of science). We attempt to analyze and classify these literatures so as to find the current hot research topics and research techniques in the PCM, and point out the future directions on the PCM. It is hoped that this paper will provide a comprehensive literature review on PCM, and act as informative summary of the main developments of the PCM for the researchers for their future research. First published online: 02 Sep 201

The analytic hierarchy process as a support for decision making

The first part of this text deals with a convention site selection as one of the most lucrative areas in the tourism industry. The second part gives a further description of a method for decision making - the analytic hierarchy process. The basic characteristics: hierarchy constructions and pair wise comparison on the given level of the hierarchy are allured. The third part offers an example of application. This example is solved using the Super - Decision software, which is developed as a computer support for the analytic hierarchy process. This indicates that the AHP approach is a useful tool to help support a decision of convention site selection.

A study of regret and rejoicing and a new MCDM method based on them

Multi-criteria decision-making (MCDM) is one of the most widely used decision methodologies in the sciences, business, and engineering worlds. MCDM methods aim at improving the quality of decisions by making the process more explicit, rational, and efficient. One controversial problem is that some well-known MCDM methods, like the additive AHP methods and the ELECTRE II and III methods, may cause some types of rank reversal problems. Rank reversal means that the ranking between two alternatives might be reversed after some variation occurs to the decision problem, like adding a new alternative, dropping an old alternative or replacing a non-optimal alternative by a worse one etc. Usually such a rank reversal is undesirable for decision-making problems. If a method does allow it to happen, the validity of the method could be questioned. However, some recent studies indicate that rank reversals could also happen because of people’s rational preference reversal which may be caused by their emotional feelings, like regret and rejoicing. Since regret and rejoicing may play a pivotal role in evaluating alternatives in MCDM problems, sometimes the decision maker (DM) may want to anticipate these emotional feelings and consider them in the decision-making process. Most of the regret models in the literature use continuous functions to measure this emotional factor. This dissertation proposes to use an approach based on a linguistic scale and pairwise comparisons to measure a DM’s anticipated regret and rejoicing feelings. The approach is shown to exhibit some key advantages over existing approaches. Next a multiplicative MCDM model is adopted to aggregate the alternatives’ associated regret and rejoicing values with their performance values to get their final priorities and then rank them. A simulated numerical example is used to illustrate the process of the proposed method. Some sensitivity analyses which aim at examining how changes of regret and rejoicing values might affect the ranking results of the decision problems are also developed. Then a fuzzy version of the new method is introduced and illustrated by a numerical example. Finally, some concluding remarks are made. Ranking intransitivity and some other issues about the proposed method are analyzed too

NORTH- HOIJ-AND Development and Evaluation of Five Fuzzy Multiattribute Decision-Making Methods

We present the development of five fuzzy multiattribute decision-making methods. These methods are based on the analytic hierarchy process (original and ideal mode), the weighted-sum model, the weighted-product model, and the TOPSlS method. Moreover, these methods are examined in terms of two evaluative criteria. Computational results on test problems suggest that although all the methods are inaccurate, some of them seem to be more accurate than the others. The proposed evaluation methodology can easily be used in evaluating more fuzzy multiattribute decision making methods

Multiplicative Consistency Ascertaining, Inconsistency Repairing, and Weights Derivation of Hesitant Multiplicative Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This article investigates multiplicative consistency ascertaining, inconsistency repairing, and weights derivation for hesitant multiplicative preference relations (HMPRs). First, the completely multiplicative consistency and weakly multiplicative consistency of HMPRs are defined. Based on them, 0-1 mixed programming models and simple algebraic operations are proposed to ascertain the multiplicative consistency of HMPRs. Then, some goal programming models are developed to generate the weights from consistent HMPRs and to revise inconsistent HMPRs. An integrated procedure to manage the multiplicative consistencies of HMPRs is designed. The proposed methods are also extended to accommodate incomplete HMPRs, and to estimate missing values. Finally, some numerical examples, a comparative analysis with existent approaches, and a simulation analysis are included to illustrate the practicality and effectiveness of the developed models

Weighting methods for multi-criteria decision making technique

Determining criteria weights is a problem that arises frequently in many multi-criteria decision-making (MCDM) techniques. Taking into account the fact that the weights of criteria can significantly influence the outcome of the decision-making process, it is important to pay particular attention to the objectivity factors of criteria weights. This paper provides an overview of different weighting methods applicable to multi-criteria optimization techniques. There are a lot of concept been reported from the literature that are very useful in solving multicriteria problems. The present work emphasized on the use of these weighting methods in determining the criteria preference of each criterion to bring about desirable properties and in order to establish and satisfy a multiple measure of performance across all the criteria selected by identifying the best options possible. And from the results, it shows that subjective weighting methods are easy and straight forward in terms of their computations than the objective weighting methods which derived their information from each criterion by adopting a mathematical function to determine the weights without the decision-maker’s input,. This can be seen from the pairwise comparison which gives an internal storage and random access memory of a smart phone a weight value of 0.33 and 0.22 respectively as they have the highest criteria weights.Keywords: Multi-criteria, Decision-making, Relative importance, Alternative, Criteri