Aggregation Of Individual Priorities Research Articles

A Comparative Analysis of Homogenous Groups’ Preferences by Using AIP and AIJ Group AHP-PROMETHEE Model

Preference surveys often strive to reveal the perceptions of respondents with different demographic and habitual characteristics to reflect the features of a local community or city. However, the target group can be considered a priori homogenous in some cases, which requires an adjusted survey methodology. Apart from the smaller sample size, the aggregation technique of the individual preferences into a global common priority is also different in these types of problems according to the decision science principles. Interestingly, this feature is often ignored in group multi-criteria decision-making problems, especially in PROMETHEE model applications. This paper aims to apply the Aggregation of Individual Judgement technique in PROMETEHEE AIJ-PROMETHEE via the introduction of a hybrid Group AIJ-AHP-PROMETHEE model, specifically designed for homogenous group preference problems, to be compared with the conventional Aggregation of Individual Priorities (AIP). The new AIJ-AHP-PROMETHEE model, which is more suitable for homogenous groups, is less costly and less time-consuming than the general aggregations. The effectiveness of this new model is emphasized with real data, surveying university students’ perceptions of different transport modes in the city of Budapest. Results show considerable findings of the introduced model and its general applicability to the evaluation of the public transport service quality system.

Deriving 2-ranks from multiplicative preference relations in a group context: An investigation with axiomatic design

Multiplicative preference relations (MPRs) are broadly employed in the Analytic Hierarchy Process (AHP) to support group decision making (GDM). In AHP-GDM, aggregation of individual judgments (AIJ) and aggregation of individual priorities (AIP) are frequently used to acquire a full ranking of alternatives. However, in practical AHP-GDM, alternatives sometimes need to be assigned to two preference-ordered classes. In this paper, we call it the 2-rank GDM problem with MPRs and investigate it through axiomatic design. We start by proposing six axioms: Anonymity for alternatives (AA), Anonymity for individuals (AI), Positive responsiveness (PR), Non-dictatorship (ND), Independence of irrelevant alternatives (IIA), and Power invariance (PI) to identify a “perfect” 2-rank approach. Next, an impossibility theorem is presented stating that no 2-rank approach satisfies six axioms concurrently due to the inherent conflict among them. Based on AIJ and AIP, five 2-rank approaches M I, AIJ-M II, AIP-M II, AIP-M III, and AIP-M IV are developed. We then analyze and compare them based on the proposed axioms and prove that M I satisfies all axioms except for IIA, while other approaches only satisfy AA, AI, PR, and ND. Finally, simulation experiments are designed to further explore and compare the properties of these five 2-rank approaches. From the axiomatic and simulation analyses, it is found that M I is the best approach for the 2-rank GDM problem with MPRs.

A Practical Conflicting Role-Based Cloud Security Risk Evaluation Method

Background: Currently, Cloud Service Provider (CSP) or third party usually proposes principles and methods for cloud security risk evaluation, while cloud users have no choice but to accept them. However, since cloud users and cloud service providers have conflicts of interests, cloud users may not trust the results of security evaluation performed by the CSP. Different cloud users may have different security risk preferences, which makes it difficult for the third party to consider all users' needs during evaluation. In addition, current security evaluation indexes for the cloud are too impractical to test (e.g., indexes like interoperability, transparency, portability are not easy to be evaluated). Methods: To solve the above problems, this paper proposes a practical cloud security risk evaluation method of decision-making based on conflicting roles by using the Analytic Hierarchy Process (AHP) with Aggregation of Individual priorities (AIP). Results: Not only can our method bring forward a new index system based on risk source for cloud security and corresponding practical testing methods, but also can obtain the evaluation result with the risk preferences of conflicting roles, namely CSP and cloud users, which can lay a foundation for improving mutual trusts between the CSP and cloud users. The experiments show that the method can effectively assess the security risk of cloud platforms and in the case where the number of clouds increased by 100% and 200%, the evaluation time using our methodology increased by only by 12% and 30%. Conclusion: Our method can achieve consistent decision based on conflicting roles, high scalability and practicability for cloud security risk evaluation.

Homogeneous Groups of Actors in an AHP-Local Decision Making Context: A Bayesian Analysis

The two procedures traditionally followed for group decision making with the Analytical Hierarchical Process (AHP) are the Aggregation of Individual Judgments (AIJ) and the Aggregation of Individual Priorities (AIP). In both cases, the geometric mean is used to synthesise judgments and individual priorities into a collective position. Unfortunately, positional measures (means) are only representative if dispersion is reduced. It is therefore necessary to develop decision tools that allow: (i) the identification of groups of actors that present homogeneous and differentiated behaviours; and, (ii) the aggregation of the priorities of the near groups to reach collective positions with the greatest possible consensus. Following a Bayesian approach to AHP in a local context (a single criterion), this work proposes a methodology to solve these problems when the number of actors is not high. The method is based on Bayesian comparison and selection of model tools which identify the number and composition of the groups as well as their priorities. This information can be very useful to identify agreement paths among the decision makers that can culminate in a more representative decision-making process. The proposal is illustrated by a real-life case study.

A consensus facilitation model based on experts’ weights for investment strategy selection

In this paper, we investigate group decision-making in a multi-criteria complex environment using an analytical hierarchy process (AHP) seeking to solve the problem of how to effectively aggregate individual preferences to reach a group consensus. Currently, the two methods considered most useful for aggregating individual preferences are the aggregation of individual judgments (AIJ) and the aggregation of individual priorities (AIP). These two aggregation methods involve two independent stages, which disconnect the processes from each other, and the relationship between the two has not yet been researched. Besides, the authorities of different experts can vary, as they are restricted by the individuals’ expertise and experiences as well as the complexity of real-world applications. In this article, a new consensus facilitation model for AHP group decision-making that takes into account experts’ weights, called EWAHP-GDM, is established to address these aspects. In this model, two aggregation methods are unified and integrated in group decision-making with AHP. We present the quantification steps for the experts’ weights and conduct an empirical analysis to verify our model by comparing it with four classic models/methods. The numerical results demonstrate that our model can provide effective investment strategy selection in investment decision-making.

A Comparison of Multi-Criteria Decision Making Approaches for Maintenance Strategy Selection (A Case Study)

The growth of world-class manufacturing companies and global competition caused significant changes in the manufacturing companies operations. These changes have affected maintenance and made its role even more crucial to stay ahead of the competition. Maintenance strategy selection is one of the strategic decision-making issues that manufacturing companies in the current competitive world are facing. In this paper, a comparison between different Multiple Criteria Decision Making (MCDM) approaches is conducted in a dairy manufacturing factory to rank the maintenance strategies. The aim is to suggest an appropriate approach for the best selection of the maintenance strategy. The decision-making elements including evaluation criteria/sub-criteria and problem alternatives, i.e., maintenance strategies are determined and a group of experts from the case-study factory are asked to make their pair-wise comparisons. The pair-wise comparison matrix is constructed by using the crisp and triangular fuzzy numbers, while the aggregation of individual priorities (AIP) approach is utilized to aggregate the decision-makers' judgments. The priority vectors of decision elements are calculated by Mikhailov's fuzzy preference programming (FPP) methods and the final weights of the decision elements are found. Results show that when the effectiveness of one element on the other elements is higher, it will have greater weights; and therefore, the results from the analytic network process (ANP) method is completely different from those of the analytic hierarchy process (AHP). The reason for the differences between the AHP and Fuzzy AHP (FAHP) with the ANP and Fuzzy ANP (FANP) is that both AHP and FAHP evaluate the criteria only based on the level of importance and do not consider the interdependencies and interactions among the evaluation elements. In this research, a predictive maintenance is selected as the most appropriate strategy in the case company and the preventive strategies outperformed the corrective strategies. The results of this research are consistent with the results of previous studies found in the literature.

Group Aggregation Techniques for Analytic Hierarchy Process and Analytic Network Process: A Comparative Analysis

The analytic hierarchy process (AHP) and the analytic network process are important multiple criteria decision making methods for supporting complex, discrete strategic management decision problems. In order to exploit a broader information basis as well as to achieve a sufficient degree of objectivity strategic decision settings are mostly embedded into a multi-personal decision context to which different individuals with expert status contribute. Owing to the fact that there is a vast number of different methods and further internal possibilities (derivation of means) to aggregate the individual expert preferences to a group consensus, the first aim of this paper is to present a comprehensive literature review on various aggregation possibilities. The second aim is the conduction of a transparent comparative analysis of selected approaches and methods (geometric/arithmetic aggregation of individual judgments, geometric/arithmetic aggregation of individual priorities, geometric/arithmetic loss function approach and Group AHP model). Therefore, we use four different evaluation scenarios and point out under which assumptions which solution is suitable. Starting from these results, the aggregation techniques adequate to a specific decision context are provided.

Research on the IAMM and IGMM Operators in Group Decision Making with Intuitionistic Preference Relations

Preference relations are the most common techniques to express decision makers preference information over alternatives or criteria. This paper focus on investigating effective operators for multiple attribute group decision making with intuitionistic fuzzy preference relations. Firstly, we extend arithmetic mean method operator and geometric mean method operator for accommodating intuitionistic fuzzy information to present the intuitionistic arithmetic mean method (IAMM) operator and the intuitionistic geometric mean method (IGMM) operator. Then the compatibility properties of intuitionistic preference relations obtained by IAMM and IGMM are analyzed, we found that aggregation of individual judgments and aggregation of individual priorities provide the same priorities of alternatives, and that if all the individual decision makers have acceptable consensus degree, then the collective preference relations obtained also are of acceptable consensus degree. Finally, the results are verified by an illustrative example carried out in the background of parts supplier selection.

An agent-oriented decision support system combining fuzzy clustering and the AHP

Decision making is a complex process, particularly when it is carried out by multidisciplinary team. Methods based on the analytical hierarchy process have been widely employed because they provide solid mathematical background. Nevertheless, solutions such as the Aggregation of Individual Judgements (AIJ) and the Aggregation of Individual Priorities (AIP) do not offer sufficient explanatory data in regards with the final decision. We developed an agent-based decision support system (DSS) that employs fuzzy clustering to group individual evaluations and the AHP to reach a final decision. Fuzzy clustering is adequate to determine important pieces of data such as the largest group of evaluations that exist around a centroid value. On the other hand, the MAS paradigm offers capabilities for achieving distributed and asynchronous processing of data. The AHP is used after the individual evaluations are clustered, as if the group were a single evaluator. Altogether, the proposed solution enhances the quality of multi-criteria group decision making.

An ILOWG operator based group decision making method and its application to evaluate the supplier criteria

The aim of this work is to present some cases of the induced linguistic ordered weighted geometry (ILOWG) operators and study their desired properties, which are very suitable to deal with group decision making (GDM) problems involving multiplicative linguistic preference relations. First, the concepts of compatibility index (CI) for two multiplicative linguistic preference relations are defined. Then, we provide some ILOWG operators to aggregate multiplicative linguistic preference relations in GDM problems. In particular, we present the compatibility index ILOWG (CI-ILOWG) operator, which induces the order of argument values by utilizing the compatibility index of experts; and the importance ILOWG (I-ILOWG) operator, which induces the order of argument values based on the importance index of the experts. Next, the reciprocity, consistency and compatibility properties of the collective multiplicative linguistic preference relations obtained by these cases of ILOWG operators are verified. Finally, the aggregation of individual judgements (AIJ) and the aggregation of individual priorities (AIP) provide the same priorities of alternatives by utilizing the row geometric mean method (RGMM) as a prioritization procedure and the ILOWG operators as an aggregation procedure. Our results show that if all the individual decision makers have an acceptable consensus degree, then the collective preference relation is also of an acceptable consensus degree. Moreover, the compatibility index induced linguistic ordered weighted geometric mean complex judgement matrix (CI-ILOWGCJM) guarantees that the group compatibility degree is at least as good as the arithmetic mean of all the individual compatibility degrees. Accordingly, a theoretic basis has been developed for the application of these cases of ILOWG operators in linguistic group decision making. Finally, a numerical example for evaluating criteria of supply selection is given to illustrate the application of the results.

Some issues on properties of the extended IOWA operators in fuzzy group decision making

Chiclana et al. [Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S. (2007). European Journal of Operational Research 182, 383–399] provided some IOWA operators for aggregating the individual fuzzy preference elations. The aim of this work is further to study their desired properties under group decision making problem with fuzzy preference relations. First, it is proved that the collective preference relations obtained by these cases of IOWA operators verified the reciprocity and the consistency properties. Next, the aggregation of individual judgements (AIJ) and the aggregation of individual priorities (AIP) provide the same priorities of alternatives by utilizing the IOWA operators as aggregation procedure and the row arithmetic mean method (RAMM) as prioritization procedure. Additionally, the Consistency IOWA (C-IOWA) operator guarantees that the group consistency degree is no less than the arithmetic mean of all the individual consistency degree. Finally, two illustrative numerical examples are used to verify the developed approaches.

A multicriteria group decision model aggregating the preferences of decision-makers based on electre methods

Often decisions taken in organizations are made by a group of people, and in order to build a collective decision, the preferences of individuals must be considered. The two most useful approaches to aggregating individual preferences are the aggregation of individual judgments and the aggregation of individual priorities. This paper focuses on the latter approach and proposes a multicriteria group decision model in situations where there is no information with regard to the relative importance of the decision-makers. This model includes three stages. In the first, the ELECTRE II method is applied so as to obtain the individual rankings. In the second stage, a global matrix of alternatives versus decision-makers is built up using the results from the previous stage. Finally, the third stage aggregates the individual preferences by applying the ELECTRE IV method and the final collective evaluation is undertaken. A numerical application is presented to illustrate the model.

A Bayesian priorization procedure for AHP-group decision making

This paper proposes a new priorization procedure for Analytic Hierarchy Process Group Decision Making (AHP-GDM). Unlike the methods normally employed in AHP-GDM, this process does not require intermediate filters for the actors’ initial judgements. The procedure is based on a Bayesian analysis of the problem and in general, it provides more efficient estimates than the techniques conventionally applied in the literature for AHP-GDM: aggregation of individual judgements (AIJ) and aggregation of individual priorities (AIP). The proposed procedure naturally extends to the analysis of incomplete and/or imprecise pairwise comparison matrices, enhancing realism, practicality and scope. The methodology has been illustrated by the analysis of a case study.

Aggregation of Individual Preference Structures in Ahp-Group Decision Making

This paper presents a new procedure, to which we have given the name Aggregation of Individual Preference Structures (AIPS), whose objective is to deal with multiactor decision making when using Analytic Hierarchy Process (AHP) as the methodological support. This procedure incorporates ideas similar to Borda count methods and transfers to the case of preference structures the principle of aggregation employed in the two approaches traditionally followed in AHP-group decision making (aggregation of individual judgments and aggregation of individual priorities). The new aggregation method allows us to capture: (i) the richness of uncertainty inherent to human beings; (ii) the vision of each decision maker within the context of the problem; (iii) the interdependencies between the alternatives being compared and (iv) the intensities of the preferences that each decision maker gives to these interdependencies. From the preference structure distribution associated to each decision maker, this new approach (AIPS) provides the holistic importance of each alternative and ranking, as well as the most representative preference structure distribution for the group. The knowledge derived from these could be employed as an initial step in the search for consensus, which characterises the negotiation processes followed by the actors involved in the resolution of decisional problems.

Aggregating individual judgments and priorities with the analytic hierarchy process

The Analytic Hierarchy Process (AHP) is often used in group settings where group members either engage in discussion to achieve a consensus or express their own preferences. Individual judgments can be aggregated in different ways. Two of the methods that have been found to be most useful are the aggregation of individual judgments (AIJ) and the aggregation of individual priorities (AIP). We propose that the choice of method depends on whether the group is assumed to act together as a unit or as separate individuals and explain why AIJ is appropriate for the former while AIP is appropriate for the latter. We also address the relationships between the choice of method, the applicability of the Pareto principle, and the use of arithmetic or geometric means in aggregation. Finally, we discuss Ramanathan and Ganesh's method to derive priorities for individual decision-makers that can be used when aggregate group preferences of individuals whose judgments are not all equally weighted. We conclude that while this method can be useful, it is applicable only in special circumstances.