Expertise-based decision makers’ importance weights for solving group decision making problems under fuzzy preference relations

The quality of a decision is influenced by the level of expertise of the Decision Makers (DMs). In Group Decision Making, alternatives’ scores are obtained by integrating the DMs opinions and the importance weights of the DMs greatly affect the resulted value. Expertise level is defined as the ability to differentiate consistently and expressed as the CWS-Index, a ratio between the Discrimination and Inconsistency. The DMs give their evaluations in pairwise comparison of Fuzzy Preference Relations (FPR) and the additivity property of FPR generates the estimators needed to get the CWS-Indexes and the expertise-based ranking of DMs. The weights of the DMs are obtained by using Induced Ordered Weighted Averaging (IOWA) operator and Basic Unit Monotonic Increasing functions and the resulted weights are used to evaluate the available alternatives to get the best one based on Fuzzy Majority and IOWA operators. This paper proposed an expertise-based weight allocation method for DMs and a numerical example is discussed to illustrate this expertise-based model to get the best alternative and it concluded that the higher the DMs’ expertise level, the higher his/her weight, and these weights affect the alternatives’ score and the rank of the alternatives

Modelling Heterogeneity among Experts in Multi-criteria Group Decision Making Problems

Heterogeneity in group decision making problems has been recently studied in the literature. Some instances of these studies include the use of heterogeneous preference representation structures, heterogeneous preference representation domains and heterogeneous importance degrees. On this last heterogeneity level, the importance degrees are associated to the experts regardless of what is being assessed by them, and these degrees are fixed through the problem. However, there are some situations in which the experts’ importance degrees do not depend only on the expert. Sometimes we can find sets of heterogeneously specialized experts, that is, experts whose knowledge level is higher on some alternatives and criteria than it is on any others. Consequently, their importance degree should be established in accordance with what is being assessed. Thus, there is still a gap on heterogeneous group decision making frameworks to be studied. We propose a new fuzzy linguistic multi-criteria group decision making model which considers different importance degrees for each expert depending not only on the alternatives but also on the criterion which is taken into account to evaluate them.FUZZYLINGProject TIN200761079FUZZYLING-II Project TIN201017876PETRI Project PET20070460Andalusian Excellence Project TIC-05299project of Ministry of Public Works 90/0

Algorithms to Detect and Rectify Multiplicative and Ordinal Inconsistencies of Fuzzy 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.Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised (1) to find the multiplicative inconsistent elements, and (2) to detect the ordinal inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods

Expertise-based ranking of experts: An assessment level approach

The quality of a formal decision is influenced by the level of expertise of the decision makers (DMs). The composition of a team of DMs can change when new members join or old members leave, based on their ranking. In order to improve the quality of decisions, this ranking should be based on their demonstrated expertise. This paper proposes using the experts’ expertise levels, in terms of ‘the ability to differentiate consistently’, to determine their ranking, according to the level at which they assess alternatives. The expertise level is expressed using the CWS-Index (Cochran-Weiss-Shanteau), a ratio between Discrimination and Inconsistency. The experts give their evaluations using pairwise comparisons of Fuzzy Preference Relations with an Additive Consistency property. This property can be used to generate estimators, and replaces the repetition needed to obtain the CWS-Index. Finally, a numerical example is discussed to illustrate the model for producing expertise-based ranking of experts

EXPERTISE-BASED EXPERTS IMPORTANCE WEIGHTS IN ADVERSE JUDGMENT

The objective of this research was to propose the use of expertise levels of experts to determine the experts’ importance weights since there has been no research that determines the 'importance weight' using the expertise level as a whole. The significance of this research was the integration of three concepts, namely: the expert’s expertise level, FPR’s Additive Consistency and the Induced-OWA operator to obtain the expert’s importance weight in adverse judgment situation. The Expertise level of an expert in adverse judgment situation is determined by his/her own assessment on a set of alternatives and defined as ‘the ability to differentiate consistently’ and expressed as the ratio between Discrimination and Inconsistency. The experts provided their preferences using FPR (Fuzzy Preference Relations) since FPR has Additive Consistency property to replicate each element of FPR matrix. Experts were sorted according to their expertise level and the experts’ importance weights followed the OWA (Ordered Weighted Averaging) operator’s weights which were determined by parameterization using Basic Unit-Interval Increasing Monotonic functions. The experts’ importance weights model illustrated by a numerical example, and it concluded that the higher the expert’s expertise level, the higher his/her importance weight

A chi-square method for priority derivation in group decision making with incomplete reciprocal preference relations

This paper proposes a chi-square method (CSM) to obtain a priority vector for group decision making (GDM) problems where decision-makers’ (DMs’) assessment on alternatives is furnished as incomplete reciprocal preference relations with missing values. Relevant theorems and an iterative algorithm about CSM are proposed. Saaty’s consistency ratio concept is adapted to judge whether an incomplete reciprocal preference relation provided by a DM is of acceptable consistency. If its consistency is unacceptable, an algorithm is proposed to repair it until its consistency ratio reaches a satisfactory threshold. The repairing algorithm aims to rectify an inconsistent incomplete reciprocal preference relation to one with acceptable consistency in addition to preserving the initial preference information as much as possible. Finally, four examples are examined to illustrate the applicability and validity of the proposed method, and comparative analyses are provided to show its advantages over existing approaches

Consistency test and weight generation for additive interval fuzzy preference relations

Some simple yet pragmatic methods of consistency test are developed to check whether an interval fuzzy preference relation is consistent. Based on the definition of additive consistent fuzzy preference relations proposed by Tanino (Fuzzy Sets Syst 12:117–131, 1984), a study is carried out to examine the correspondence between the element and weight vector of a fuzzy preference relation. Then, a revised approach is proposed to obtain priority weights from a fuzzy preference relation. A revised definition is put forward for additive consistent interval fuzzy preference relations. Subsequently, linear programming models are established to generate interval priority weights for additive interval fuzzy preference relations. A practical procedure is proposed to solve group decision problems with additive interval fuzzy preference relations. Theoretic analysis and numerical examples demonstrate that the proposed methods are more accurate than those in Xu and Chen (Eur J Oper Res 184:266–280, 2008b)

PRIORIZAÇÃO DE ACORDOS MULTILATERAIS DE CONTROLE DE EXPORTAÇÃO DE PRODUTOS DE DEFESA E TECNOLOGIAS SENSÍVEIS POR PROCESSO DE ANÁLISE HIERÁRQUICA

This paper proposes a model to support the decision to choose which multilateral export control regime of defense products and sensitive technologies in which Brazil does not yet participate, namely, Wassenaar Arrangement, Australia Group and Zangger Committee, should be prioritized for adhesion. For the development of this model, the Analytic Hierarchy Process (AHP) method was used, considered adequate for solving problems where criteria are qualitative and decisions tend to be based on personal experiences. The hierarchical structure of the problem used seven criteria (Country Legislation, Regulatory System, Licensing Structure, Enforcement Capacity, International Cooperation, Costs of Adhesion and Benefits for the Defense Industrial Base) to compare the three mentioned agreements. A questionnaire was set up and specialists related to National Defense were selected to answer them, after which their answers were collected, standardized, processed and analyzed. At the end, the agreements were ordered by preference to support decision making, illustrating the application of the proposed model.O artigo propõe um modelo de apoio à decisão para a priorização de acordos multilaterais de controle de exportação de produtos de defesa e tecnologias sensíveis de que o Brasil ainda não participa, quais sejam, Acordo de Wassenaar, Grupo da Austrália e Comitê Zangger. Para o desenvolvimento do modelo foi utilizado o Processo de Análise Hierárquica (AHP), considerado adequado para a resolução de problemas onde os critérios qualitativos e as decisões tendem a ser baseadas em experiências pessoais. A estrutura hierárquica do problema utilizou sete critérios (Legislação do País, Sistema Regulatório, Estrutura de Licenciamento, Capacidade de Imposição, Cooperação Internacional, Custos da Adesão e Benefícios para a Base Industrial de Defesa) para comparar os três acordos mencionados. Foi elaborado um questionário e selecionados especialistas em Defesa para respondê-los. Os dados coletados padronizados, processados e analisados. Ao final, os acordos foram ordenados por preferência para apoiar a tomada de decisão, ilustrando a aplicação do modelo propost

Fuzzy Rankings for Preferences Modeling in Group Decision Making

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.Although fuzzy preference relations (FPRs) are among the most commonly used preference models in group decision making (GDM), they are not free from drawbacks. First of all, especially when dealing with many alternatives, the definition of FPRs becomes complex and time consuming. Moreover, they allow to focus on only two options at a time. This facilitates the expression of preferences but let experts lose the global perception of the problem with the risk of introducing inconsistencies that impact negatively on the whole decision process. For these reasons, different preference models are often adopted in real GDM settings and, if necessary, transformation functions are applied to obtain equivalent FPRs. In this paper, we propose fuzzy rankings, a new approximate preference model that offers a higher level of user‐friendliness with respect to FPRs while trying to maintain an adequate level of expressiveness. Fuzzy rankings allow experts to focus on two alternatives at a time without losing the global picture so reducing inconsistencies. Conversion algorithms from fuzzy rankings to FPRs and backward are defined as well as similarity measures, useful when evaluating the concordance between experts’ opinion. A comparison of the proposed model with related works is reported as well as several explicative examples

The multi-attribute group decision making method based on the interval grey linguistic variables weighted harmonic aggregation operators

With respect to the characteristics of fuzziness, complexity and uncertainty for many group-decision making problems in real world, the paper proposes a novel method based on the interval grey linguistic variables hybrid weighted harmonic aggregation operators to solve the multiple attribute group decision making problems in which the attribute values and the weights take the form of the interval grey linguistic variables. In the approach, the relative concepts and the operation rules of interval grey linguistic variables are defined, and some operators (such as interval grey linguistic weighted harmonic aggregation (IGLWHA) operator, interval grey linguistic ordered weighted harmonic aggregation (IGLOWHA) operator, and interval grey linguistic hybrid weighted harmonic aggregation (IGLHWHA) operator) are proposed to solve the group decision making problems. The computational results from an illustrative example have shown that the proposed approach is feasible and effective for the group-decision making problems