A bipolar consensus approach for group decision making problems
Introduction
Nowadays, the increasing complexity of the socio-economic, engineering and environmental management make less possible decision by a single decision maker considering all aspects of a problem (Yue, 2011a). Therefore, the majority of decision problems are considered currently in the group decision process. This process is generally characterized by the existence of two or more persons (i) who have different perceptions, attitudes, motivations and personality, (ii) who recognize the existence of a common problem, and (iii) attempt to reach a collective decision (Herrera, Herrera-Viedma, & Verdegay, 1996b).
Solving a group decision making (GDM) problem often goes through the following phases: elicitation phase where different characteristics of the problem are defined (objectives, alternatives, attributes, etc.), evaluation phase and a selection and recommendation phase. In the evaluation phase, the way information is managed can leads to two families of aggregation approaches, we speak of input and output aggregation (Leyva Lopez, 2010) or common value tree for all decision makers and a value tree for each decision maker (De Brucker & Macharis, 2010). In the first case, aggregation is performed at the input when the decision group is invited to agree on a common set of attributes, weights and other parameters, which amounts to solving a problem as a single decision making problem. In the second case, the individual evaluations are represented by individual value trees solved using standard process of decision support. The output aggregation is performed at the end. The present paper focuses on this second type of problem dealing with group decision making problem based on individual assessments.
Decision makers’ evaluations can be represented by preference order (where the alternatives are ranked from best to worst), a utility function (where the alternatives are represented by real value –physical or monetary value–), or a frequently used preference relation (where alternatives are evaluated by pairwise comparison) (Herrera, Herrera-Viedma, & Chiclana, 2001). Depending on the nature of the data, the certainty of decision-makers, these preferences can be modeled by absolute evaluations when information is known or fuzzy evaluation based on the theory of fuzzy set, introduced by Zadeh (1965) in case of uncertainty in order to manage human subjectivity, imprecision and vagueness. The fuzzy evaluation is used in many areas due to the pressure, lack of knowledge and/or time.
Decision-makers’ evaluations are then integrated into decision resolution procedures to reach an agreement on the selection of the best solutions. Traditionally, GDM problems have been solved by applying an alternative selection process in which the preferences of each decision makers over the alternatives are gathered and the best alternative or subset of alternatives is chosen (Roubens, 1997). However, as a group decision members usually come from different horizons with different specialty areas and different levels of knowledge, each group member has distinct information and sharing in general a part of the objectives with other decision members (Xu & Wu, 2011). This implies that individual assessments rarely meet (Roselló et al., 2010, Ben-Arieh et al., 2009) and the divergence of opinions can generates conflict (disagreement) and/or agreement within the group decision making. The recommendation phase in this case usually requires the establishment of a “consensus” building process in order to lead actors to a common decision (Khorshid, 2010).
To achieve a common accord, a variety of consensus reaching processes have been proposed in recent years (Eklund et al., 2008, Gong et al., 2013, Herrera-Viedma et al., 2014). These approaches going from mechanist models of operational research to more sophisticated and soft computing oriented models that attempt to integrate human attitude (emotion, affect, fear, egoism, altruism, selfishness, etc.). The soft computing oriented models are used increasingly due to their ability to tolerate imprecision, uncertainty and partial truth in order to simulate human behavior with low cost (Pal & Ghosh, 2004), they allow to take into account the ambiguity in human thinking and uncertainty of the real world (Ko, Tiwari, & Mehnen, 2010).
Section snippets
Consensus building processes
Basically, group decision making aims at obtaining the consent, not necessarily the agreement of the participants by accommodating views of all parties involved to attain a decision that will yield what will be beneficial to the entire group (Herrera-Viedma et al., 2014). This is why the group consensus is usually considered as a total and final agreement between the decision members (Leyva Lopez, 2010). To reach a consensus, the researchers first proposed consensus approaches with the
Consensus approaches in GDM
As mentioned in Herrera-Viedma et al. (2014), the first mathematical approaches of consensus reaching processes started with the pioneering works by French and his collaborators in the late 1940s and early 1950s (Coch and French, 1948, French, 1956). Authors employed matrix calculus to model the time evolution and reaching of the consensus process. They also describe the impact of involving people in changes that affect them through the introduction of a simple model of how a network of
Bipolar group decision making framework modeling under interactions
This section discusses the structuring and evaluation procedure based on bipolar analysis approach. Considering Multi-Attributes Multi-Objectives Group Decision Making problem (MAMOGDM probem), the general framework of the bipolar approach is presented and the satisficing game theory used as aggregation tool in individual evaluations is briefly described. The objective of proposed model is to provide a realistic framework to achieve a consensus, taking into account the potential impact of
Consensus and selection processes
The individual bipolar measures are used by decision makers to select the best alternative or the set of the best alternatives for each one. According to the knowledge and perceptions of actors, the decision-makers choices can be contradictory. To find a common satisficing alternative(s), a consensus processes is necessary.
The reach consensus can be done in two ways: by aggregating final bipolar measures of decision makers into collective bipolar measures using Eqs. (17), (18). Then selected
Application example
In this section, we use proposed group decision making bipolar analysis approach to resolve real size wind farm implantation problem adapted from Lee, Chen, and Kang (2009).
Install a wind farm involves various actors in society such as; wind specialist, local administration and public authority. In France for example, the selection of potential implantation sites (selection of alternatives) returns generally to the local administration, which taking into account previous studies, will retain
Consensus building process based on caution index variation
The proposed model achieved with this consensus approach allows decision makers to avoid changing their evaluations. Only a concession on the caution index is required based on a selection criteria proposed in section 3.2.1 In this example, we note that the equilibrium satisficing sets of qualified majority of 67% composed of decision makers d1, d3 which consider the alternative a4 as a final solution . Depending on the relationships nature and group decision-making context,
Consensus building process based on distance measures
The second proposed process is based on distance measures that allow the analyst to identify alternatives and decision makers with strong differences. Using a feedback mechanism, decision makers have the ability to change their assessments based on recommendations made by the analyst during the discussion sessions, with the aim to converge to a common solution.
The first phase of the feedback mechanism uses proximity measures and bipolar consensus to identify respectively, divergent alternatives
Conclusion and perspectives
Considering collaborative decision problem based on individual evaluation, this paper proposes a new resolution approach to deal with group decision problems in multicriteria framework.
To more realistic model, human behavior aspects (positive and negative influences, selfish, prudence, etc.) are integrated in the evaluation and recommendation phases. Based on bipolar context, local preferences which considers the vicinity influence are expressed by selectability and rejectability measures, to
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