On Incomplete Fuzzy and Multiplicative Preference Relations In Multi-Person Decision Making

This research work has been developed with the financing of FEDER funds in FUZZYLING-II Project TIN2010- 17876, the Andalusian Excellence Projects TIC-05299 and TIC-5991 and the mobility grant program awarded by the University of Granada ’s International Office.2nd International Conference on Information Technology and Quantitative Management, ITQM 2014Rapid changes in the business environment such us the globalization as well as the increasing necessity to make crucial decisions involving a huge range of alternatives in short period of time or even in real time have made that computerized group decision support systems become very useful tools. However in the majority of the cases the panel of experts cannot provide all the information about their preferences due to different reasons such as lack of knowledge, time etc. Therefore different approaches have been presented to deal with the missing preferences in group decision making contexts. In this paper we review and analyse the state-of-the-art research efforts carried out on this topic for incomplete fuzzy preference relations and multiplicative preference relations.FEDER funds in FUZZYLING-II Project TIN2010- 17876Andalusian Excellence Projects TIC-05299 and TIC-5991Mobility grant program awarded by the University of Granada ’s International Offic

Subgroup Preference Neural Network.

Subgroup label ranking aims to rank groups of labels using a single ranking model, is a new problem faced in preference learning. This paper introduces the Subgroup Preference Neural Network (SGPNN) that combines multiple networks have different activation function, learning rate, and output layer into one artificial neural network (ANN) to discover the hidden relation between the subgroups' multi-labels. The SGPNN is a feedforward (FF), partially connected network that has a single middle layer and uses stairstep (SS) multi-valued activation function to enhance the prediction's probability and accelerate the ranking convergence. The novel structure of the proposed SGPNN consists of a multi-activation function neuron (MAFN) in the middle layer to rank each subgroup independently. The SGPNN uses gradient ascent to maximize the Spearman ranking correlation between the groups of labels. Each label is represented by an output neuron that has a single SS function. The proposed SGPNN using conjoint dataset outperforms the other label ranking methods which uses each dataset individually. The proposed SGPNN achieves an average accuracy of 91.4% using the conjoint dataset compared to supervised clustering, decision tree, multilayer perceptron label ranking and label ranking forests that achieve an average accuracy of 60%, 84.8%, 69.2% and 73%, respectively, using the individual dataset

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

Are incomplete and self-confident preference relations better in multicriteria decision making? A simulation-based investigation

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.Incomplete preference relations and self-confident preference relations have been widely used in multicriteria decision-making problems. However, there is no strong evidence, in the current literature, to validate their use in decision-making. This paper reports on the design of two bounded rationality principle based simulation methods, and detailed experimental results, that aim at providing evidence to answer the following two questions: (1) what are the conditions under which incomplete preference relations are better than complete preference relations?; and (2) can self-confident preference relations improve the quality of decisions? The experimental results show that when the decision-maker is of medium rational degree, incomplete preference relations with a degree of incompleteness between 20% and 40% outperform complete preference relations; otherwise, the opposite happens. Furthermore, in most cases the quality of the decision making improves when using self-confident preference relations instead of incomplete preference relations. The paper ends with the presentation of a sensitivity analysis that contributes to the robustness of the experimental conclusions

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)

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

Incomplete interval fuzzy preference relations and their applications

This paper investigates incomplete interval fuzzy preference relations. A characterization, which is proposed by Herrera-Viedma et al. (2004), of the additive consistency property of the fuzzy preference relations is extended to a more general case. This property is further generalized to interval fuzzy preference relations (IFPRs) based on additive transitivity. Subsequently, we examine how to characterize IFPR. Using these new characterizations, we propose a method to construct an additive consistent IFPR from a set of n − 1 preference data and an estimation algorithm for acceptable incomplete IFPRs with more known elements. Numerical examples are provided to illustrate the effectiveness and practicality of the solution process

A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices

This article presents a goal programming framework to solve group decision making problems where decision-makers’ judgments are provided as incomplete interval additive reciprocal comparison matrices (IARCMs). New properties of multiplicative consistent IARCMs are put forward and used to define consistent incomplete IARCMs. A two-step goal programming method is developed to estimate missing values for an incomplete IARCM. The first step minimizes the inconsistency of the completed IARCMs and controls uncertainty ratios of the estimated judgments within an acceptable threshold, and the second step finds the most appropriate estimated missing values among the optimal solutions obtained from the previous step. A weighted geometric mean approach is proposed to aggregate individual IARCMs into a group IARCM by employing the lower bounds of the interval additive reciprocal judgments. A two-step procedure consisting of two goal programming models is established to derive interval weights from the group IARCM. The first model is devised to minimize the absolute difference between the logarithm of the group preference and that of the constructed multiplicative consistent judgment. The second model is developed to generate an interval-valued priority vector by maximizing the uncertainty ratio of the constructed consistent IARCM and incorporating the optimal objective value of the first model as a constraint. Two numerical examples are furnished to demonstrate validity and applicability of the proposed approach

Investigating Rank Reversal in Reciprocal Fuzzy Preference Relation Based on Additive Consistency: Causes and Solutions

Rank reversal is a common phenomenon in decision making. Rank reversal occurs when a new alternative is added to (or removed from) a set of alternatives, which causes change in the ranking order of the alternatives. This paper studies the possible causes of rank reversal in reciprocal preference relation based on additive consistency. Our investigation reveals that inconsistency of information is the main cause of this phenomena in preference relations followed by ranking score aggregation. We propose score aggregation methods to address the phenomenon of rank reversal. The proposed methods are illustrated using numerical examples. The results are better than other tested methods