An Agreement Index with Respect to a Consensus Preorder

In this paper, we propose an index to measure the agreement level of an individual preorder with respect to a collective preorder (or reference preorder). The originality of the proposed index consists in the two following facts: (i) it quantifies the agreement level between two preorders which are not necessarily complete (i.e. they may include the incomparability relation), a preference system rarely tackled in the literature and (ii) it takes into account the positions of the alternatives in the individual preorder. The proposed index is then used to compute, within the framework of a consensus preorder research, the agreement level of all group’s members with respect to a collective preorder.     

A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights

In this paper we propose a preference aggregation procedure for those cases in which the decision-makers express their preferences by means of a ranking of alternatives. Among the most applied methods for this purpose are those inspired by the Borda–Kendall rule, which attach to each alternative an aggregated value of the votes received in the different rank positions, and those based on distance measures between individual and collective preferences, which look for the solution that maximizes the consensus. The main idea here is to integrate these two approaches. Taking into account that the information about the values of weights or utilities assigned to each rank position is imprecise, we propose an evaluation of the alternatives using that vector of weights that minimizes the disagreement between DMs. In order to solve the problem, mixed-integer linear programming models are constructed. Two numerical examples are examined to illustrate the applicability of the proposed procedure.     

A Distance-Based Collective Weak Ordering

A group decision-making approach can be seen as a two stage process. The first stage allows for multi-cirteria evaluation of the alternatives and the second aims at deriving a collective weak ordering from the partial orderings supplied by the members after the first stage. The problem of combining the weak orderings to form a collective ranking is investigated. An axiomatic structure relating to the concept of distance between binary relations is developed. An algorithm for deriving the collective weak ordering is proposed, based on the idea of ranking first the least dominated alternatives.     

Ordered Weighted Disagreement Functions

In this paper a preference aggregation procedure is proposed for those cases in which decision-makers express their preferences by means of a ranking of alternatives. Among the most commonly applied methods for this purpose are those based on distance measures between individual and collective preferences, which look for the solution that minimizes the disagreement across decision-makers. Some models based on the minimization of the distance between rankings include weights to adjust the relative importance of the agents in the final decision, although in those cases, the weights are related with an a priori evaluation of the individuals and not with the behaviour of the agents in the group decision making process. In the model proposed here, a weighted disagreement function whose emphasis is on the ordered position of the individuals’ disagreement values is developed. In order to solve the problem, a mixed-integer linear programming model is constructed.     

A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making

The aim of this article is to investigate the approach to multiple attribute group decision making (MAGDM) with intuitionistic fuzzy information. We first introduce a deviation measure between two intuitionistic fuzzy numbers, and then utilize the intuitionistic fuzzy hybrid aggregation operator to aggregate all individual intuitionistic fuzzy decision matrices into a collective intuitionistic fuzzy decision matrix. Based on the deviation measure, we develop an optimization model by which a straightforward formula for deriving attribute weights can be obtained. Furthermore, based on the intuitionistic fuzzy weighted averaging operator and information theory, we utilize the score function and accuracy function to give an approach to ranking the given alternatives and then selecting the most desirable one(s). In addition, we extend the above results to MAGDM with interval-valued intuitionistic fuzzy information.     

The Role of the DS/AHP in Identifying Inter-Group Alliances and Majority Rule Within Group Decision Making

DS/AHP is a nascent method of multi-criteria decision-making, based on the Dempster-Shafer theory of evidence and indirectly the Analytic Hierarchy Process. It is concerned with the identification of the levels of preference that decision makers have towards certain decision alternatives (DAs), through preference judgements made over a number of different criteria. The working result from a DS/AHP analysis is the body of evidence (BOE), which includes a series of mass values that represent the exact beliefs in the best DA(s) existing within certain subsets of DAs. This paper considers the role of DS/AHP as an aid to group decision-making, through the utilisation of a distance measure (between BOEs). Here, the distance measure enables the identification of the members of the decision-making group who are in most agreement, with respect to the judgements they have individually made. The utilisation of a single linkage dendrite approach to clustering elucidates an appropriate order to the aggregation of the judgements of the group members. This develops the DS/AHP method as a tool to identify inter-group alliances, as well as introduce a ‘majority rule’ approach to decision-making through consensus building.     

Modeling Group Preferences Using a Decompositional Preference Approach

This article examines an extension of the decompositional, conjoint, or stated-preference approach to model group decisions. In the conventional approach, only one member is chosen to be the group's representative and provide answers for the group as a whole. In this study, all group members are brought together and asked to jointly complete a conjoint preference experiment. The hypothesis is tested that this joint group approach predicts group behavior better than the conventional approach with representatives. The paper presents the estimated part-worth utilities of the group model and compares preference structures of individual group members and groups. Finally, group preference models are tested to determine whether they outperform representative-based preference models in terms of the ability to correctly predict the group preferences for new alternatives. These analyses are performed in the context of residential preferences of co-ops, which are groups of young people, usually not partners, who live together in owner-occupied houses.     

A Study on Aggregation of TOPSIS Ideal Solutions for Group Decision-Making

The technique for order preference by similarity to ideal solution (TOPSIS) has become a popular multi-criteria decision making (MCDM) technique, since it has a comprehensible theoretical structure and is able to provide an exact model for decision making. For the use of TOPSIS in group decisions, the common approaches in aggregating individual decision makers’ judgments are the geometric and the arithmetic mean methods, although these are too intuitive and do not consider either preference levels or preference priorities among alternatives for individual decision makers. In this paper, a TOPSIS group decision aggregation model is proposed in which the construction consists of three stages: (1) The weight differences are calculated first as the degrees of preferences among different alternatives for each decision maker; (2) The alternative priorities are then derived, and the highest one can be denoted as the degree to which a decision maker wants his most favorite alternative to be chosen; (3) The group ideal solutions approach in TOPSIS is used for the aggregation of similarities obtained from different decision makers. A comparative analysis is performed, and the proposed aggregation model seems to be more satisfactory than the traditional aggregation model for solving compromise-oriented decision problems.     

A linguistic decision process in group decision making

Assuming a set of linguistic preferences representing the preferences of the individuals, a linguistic choice process is presented. This is developed using the concept of fuzzy majority for deriving a collective linguistic preference, and the concept of nondominated alternatives for deriving the selected alternatives in the linguistic choice process. The fuzzy majorities are equated with fuzzy linguistic quantifiers. The collective linguistic preference is derived by means of a linguistic ordered weighted averaging operator whose weights are defined using a fuzzy linguistic quantifier. In order to obtain the nondominated alternatives, we present a novel reformulation of Orlovski's nondominance degree under linguistic information.     

Entrepreneurship through a qualitative lens: Insights on the construction and/or discovery of entrepreneurial opportunity

This article applies inductive analytic techniques to identify and elaborate on two recurring themes that underpin the core puzzle of entrepreneurship research — where entrepreneurial opportunities come from. The first theme is the unique role of imprinting, or the profound influence of social and historical context in constraining the perceptual apparatus of entrepreneurs and delimiting the range of opportunities for innovation available to them. Second, our analysis offers insight into the counterbalancing role of reflexivity, operating at both individual and collective levels of analysis, in generating the ability of entrepreneurs to overcome the constraints of imprinting. These insights are based on a thematic review of the nine studies that comprise this special issue on qualitative research. The nine studies, individually and each in their own way, offer key insights into how we might better understand the emergence of entrepreneurial opportunity.     

Compatibility Analysis of Intuitionistic Fuzzy Preference Relations in Group Decision Making

Compatibility analysis is an efficient and important tool used to measure the consensus of opinions within a given group of individuals. In this paper, we give a compatibility measure between intuitionistic preference values and a compatibility measure between intuitionistic preference relations, respectively, and study their properties. It is shown that each individual intuitionistic preference relation and the collective intuitionistic preference relation is perfectly compatible if and only if all the individual intuitionistic preference relations are perfectly compatible. Based on the compatibility measures, a consensus reaching procedure in group decision making with intuitionistic preference relations is developed, and a method for comparing intuitionistic fuzzy values is pointed out, by which the considered objects are ranked and selected. In addition, we extend the developed measures, procedure and method to accommodate group decision making situations with interval-valued intuitionistic preference relations. Numerical analysis on our results through an illustrative example is also carried out.     

An Integrated Group Decision-Making Method Dealing with Fuzzy Preferences for Alternatives and Individual Judgments for Selection Criteria

Organizations often require decisions to be made by a group, and decision makers often have fuzzy preferences for alternatives and individual judgments when attempting to reach an optimal solution. In order to deal with the fuzziness of preference of decision makers, this paper proposes an integrated fuzzy group decision-making method. This method allows group members to express fuzzy preferences for alternatives and individual judgments for solution selection criteria. It also allowed for the weighting of group members. The method then aggregates these elements into a compromise group decision which is the most acceptable for the group as a whole. This method has been implemented and tested. An example is presented to illustrate the method.     

Robust risk aggregation with neural networks

We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g., the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice, the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: First, we derive a dual representation of the considered problem and prove that strong duality holds. Second, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real‐world instance.     

Influence Allocation Methods in Group Decision Support Systems

Influence allocation processes are voting and opinion aggregating methods that allow members to distribute some or all of their decision making influence to others in the group in order to exploit not only the group's knowledge of the alternatives, but its knowledge of itself. Only with the common use of group decision support systems (GDSS) has their use become practical. In this paper we reconsider SPAN, an influence allocation process introduced by MacKinnon (1966a). Experimental comparison shows SPAN to be significantly better at selecting a correct option from a set of options than two common voting methods. An alternative influence allocation process that we call RCON (Rational Consensus), is based on a weighting method proposed by DeGroot (1974) and has been explicated as a normative standard for combining opinion by Lehrer and Wagner (1981). The judgmental inputs to SPAN would appear to be logically related to those for RCON. Submitting the SPAN inputs from the experiment, transformed in this logical way, to the RCON process results in somewhat better performance than with SPAN. However, evidence indicated that the two methods are conceptually and psychologically sufficiently different that an experimental comparison is needed between them.     

Multi-criteria Remote Asynchronous Group Decision Screening: An Experimental Study

A new visualization-based multi-criteria procedure for group decision screening is presented. The procedure supports a group in selecting a small number of alternatives from an initial list described by a collection of attributes which are used as screening criteria. We propose and experimentally study the Group Remote Asynchronous Screening Support (GRASS) procedure that can be used by a large number of participants who are not able to meet face to face. GRASS does not use any interaction between the participants and the group screening is based on the individual preferences expressed by them independently from each other. GRASS uses the concepts of Borda count, by applying the visualization of information to simplify the analysis of large lists of multi-criteria alternatives. Visualization is used to support the individual analysis of the variety of alternatives and the individual selecting of a small number of alternatives from the list for the subsequent scoring through Borda count. Visualization is carried via the Interactive Decision Maps / Reasonable Goals Method (IDM/RGM) technique. We first check a speculative supposition that participants are able to find a single best alternative by using the GRASS procedure. As it is not the case, we re-formulate our hypothesis and check whether the most preferred alternative is part of a short list of alternatives returned through GRASS. The experiment was carried out with senior applied mathematics students who managed to apply GRASS without any problem.     

Information,individual errors,and collective performance: Empirical evidence on the Condorcet Jury Theorem

The Condorcet Jury Theorem implies that the collective performance of a group, in arriving at a “correct” judgment on the basis of majority or plurality rule, will be superior to the average performance of individual members of the group, if certain apparently plausible conditions hold. Variants of the Jury Theorem are reviewed, particularly including the politically relevant variant that allows for conflicting interests within the group. We then examine two kinds of empirical data. First, we compare individual and collective performance in a large number of multiple-choice tests, and we find that collective performance invariably and substantially exceeds average individual performance. Second, we analyze American National Election Study data to create dichotomous-choice tests concerning positions of candidates on a variety of political issues; Condorcet-like effects are again evident. Finally, continuing to use NES data, we construct, on each political issue, a simulated referendum (direct voting on the issue) and election (indirect voting on the issue by voting for candidates on the basis of their perceived positions on the issue), and we compare the two results. Despite high rates of individual error, electoral error is quite small, and collective performance is fairly high, providing evidence of Condorcet-like effects in situations of conflicting preferences.     

A Model of Elitist Qualification

This paper deals with the collective qualification of members of society as belonging to a certain category or group based on a fixed attribute. Our model contains three main features: the existence of individual gradual opinions, the notion of elitism (only the opinions of certain individuals are taken into account to delineate the reference group), and the idea of sequentiality (elites are successively created by using the previous elites’ opinions on a social decision scheme). The main results of the paper characterize when this sequential procedure converges for some intuitive ways of aggregating individual opinions. Finally, we analyze the role of convergence for two extra basic properties (symmetry and contractiveness) that elitist rules should possess.     

Aggregation and Disaggregation of Preferences for Collective Decision-Making

Group decisions are of longstanding interest to researchers from a wide spectrum of disciplines. Group Decision Support Systems (GDSS) can play a vital role in situations where multiple persons are involved, each having their own private perceptions of the context and the decision problem to be tackled. In such an environment the conflict between the members of the planning group is not an unusual situation. Multiple criteria decision aid (MCDA) methods may be a useful tool in coping with such interpersonal conflicts where the aim is to achieve consensus between the group members. This paper combines two well-known multicriteria methods, based on the notion of aggregation of preferences, in order to construct a consensus seeking methodology for collective decision-making.     

An Acceptable Consistency-Based Framework for Group Decision Making with Intuitionistic Preference Relations

This article studies acceptable consistency of intuitionistic preference relations (IPRs) and examines how to aggregate individual IPRs into a collective judgment in a group decision making (GDM) context. A consistency index is first introduced to measure the consistency level, thereby defining acceptable consistency for IPRs. If a decision-maker is unwilling or unavailable to revise his/her judgment for an IPR with unacceptable consistency, an automated approach is developed to improve its consistency to an acceptable level. The acceptably consistent IPRs are subsequently aggregated into a group opinion by using an induced ordered weighted averaging operator. A procedure is then proposed to solve GDM problems with IPRs. An illustrative example is presented to demonstrate the effectiveness and applicability of the proposed approach.     

Continuous Ordered Weighted Distance Measure and Its Application to Multiple Attribute Group Decision Making

We develop a new distance measure called the continuous ordered weighted distance (COWD) measure by using the continuous ordered weighted averaging (COWA) operator in the interval distance. We study some properties and different families of the COWD measure. We further generalize the COWD measure. The prominent characteristics of the COWD measure are that it is not only a generalization of some widely used distance measures and the continuous generalized OWA operator, but also it can deal with interval deviations in aggregation on interval arguments by using a controlled parameter. The desirable characteristics make the COWD measure be suitable to wide range situations, such as decision making, engineering and economics. In the end, we develop the new approach to group decision making in investment selection.