Trust based group decision making in environments with extreme uncertainty☆
Introduction
Nowadays we are living the apogee of the Internet based technologies and consequently web 2.0 communities, where a large number of users interacts in real time is a generalized phenomenon.
This type of social networks communities constitute a challenging scenario from the point of view of Group Decision Making (GDM) approaches, because it involves a large number of agents coming from different backgrounds with different levels of knowledge and influence. In this type of scenarios, there exist two main key issues that require attention. The consensus and the uncertainty in the experts’ opinions or preferences.
In many decision making situations, it is desired or even required to reach an agreement between the experts involved. To do so, in most of the occasions, it is necessary to carry out an iterative negotiation process between the experts with the objective of bringing closer their points of view to eventually reach a solution accepted by the majority of them. The higher the consensus level, the higher the agreement and consent with the final selected answer. In the literature, there exist various consensus processes that iteratively provide some advice or recommendations to the experts in order to increase the global consensus level. These types of recommendations are widely known as feedback mechanisms [1], [2], [3], [4], or when there are proposed to group of experts they are denominated as Group Recommender Systems [5]. This last one may take into account social aspects like user personality and interpersonal trust.
However, these iterative feedback approaches present the problem of experts’ non cooperative behavior [3]. That is, the experts may present a reluctance or even refuse to accept the feedback provided by the system. With this regard, it has been observed in opinion dynamics theory that people tend to accept more easily those opinions coming from confident and similar peers [6]. With this premise in mind, in [6] it has been presented a social network based consensus approach that estimates each expert’s degree of coherence with the opinion provided, widely known as consistency and his/her self-confidence to develop an inter experts similarity network with the goal of providing recommendations based on other highly confident and consistent similar experts opinions. In [7], the preference relation with self-confidence is defined.
The second important issue considered in this contribution is uncertainty in the information provided by the experts. Uncertainty may be reflected in various different ways, from the expert being unsure of the given answer [8] to the extreme case of missing information [9], [10], [11], [12], [13], [14]. For the first case, an interesting way of dealing with the inherent hesitation or vagueness in the experts’ opinions consists of taking advantage of Atanassov’s intuitionistic fuzzy sets [15], [16] by allowing the experts to explain their preferences by means of intuitionistic fuzzy preference relations (IFPRs). The particular case of extreme uncertainty in decision making scenarios is the one in which the experts are not able to provide any preference rating about an alternative, for different reasons ranging from lack of knowledge to lack of time or interest, resulting in preference relations with some of their values missing or unknown [10], [17]. Various studies remark the negative effects of not taking into consideration the incomplete information in social networks based decision making. In [18] the impact of missing data in a scientific collaboration network and in a random bipartite graph has been analyzed concluding that there are three main missing data mechanisms: “network boundary specification (non-inclusion of actors or affiliations), survey non-response, and censoring by vertex degree (fixed choice design)”. Afterward in [19] the ”effect of non-response on the structural properties of social networks, and the ability of some simple imputation techniques to treat the missing network data” have been studied pointing out that simple imputation procedures have large negative effects and demonstrating by numerous simulations the importance of estimating the missing data.
For the case of GDM with extreme uncertainty as far as the authors know it has not been proposed any consensus approach. However, not taking into consideration the unknown preferences, in the consensus process could lead to serious biased. For this aim, in the literature, various estimation approaches have been presented. Most of them use their own experts’ preferences levering the logic transitivity between them [8], [20]. An exhaustive review of these approaches has been provided in [11]. The main limitation of these transitivity based completion techniques is that they are applicable only when at least one comparative judgment about each of the alternatives is provided. Nevertheless in real world decision making [21], [22], [23], [24], very often there are situations in which not any judgment about an alternative is provided and so the transitivity properties cannot be used for the estimation. This scenario, denominated as total ignorance situations, has been considered by Alonso et al. in [9], where they proposed both individual and social strategies to estimate the missing information. As their name indicates, individual strategies estimate the missing information without considering any other information from other experts using a random initialization of the missing values and applying transitivity afterward, while social strategies take advantage of the information provided by the rest of the experts. These approaches present the disadvantage that they may provide solutions not accepted by the given experts since they might be very far from their given opinions. In [25], a method based on the concept of social influence network that deals with incomplete fuzzy preference relation by taking into account the effects of social influence in the network of decision making has been proposed.
In this contribution, we address these two main issues, consensus and uncertainty in two main steps: Firstly, in order to deal with uncertainty, we propose a new approach to estimate the missing preference opinions, expressed as intuitionistic fuzzy preference relations, able to work even in total ignorance situations. To do so, the experts are firstly clustered depending on the similarity of their preferences. Then, a new aggregation operator, the TCCI-IOWA operator that leverage the inter-experts trust, self-confidence, and consistency estimates and fuse the missing preferences in each of the clusters.
Secondly, a new feedback mechanism based on the trust propagation is proposed with the goal of increasing the consensus degree. This proposal is based on the premise that people tend to be more influenced by the opinions or behaviors of similar trusted peers [6], [26]. In addition, the proposed values to the experts, besides improving the consensus, could improve the estimated data.
The rest of the paper is set out as follows: The next section reviews some basic necessary information and backgrounds. In Section 3 the proposed approach that deals with consensus and missing information is presented. In order to illustrate the way of operation of the proposed approach, an example is presented in Section 4. Finally, in Section 5, we outline the conclusion from this work and we introduce the future research challenges.
Section snippets
Preliminaries
In order to make this contribution as self contained as possible, this section is devoted to providing some necessary definitions and backgrounds used in the rest of the paper.
The proposed algorithm
In this section, we propose a trust based decision making approach that allows estimating the missing values even in the case of total ignorance situations and as well as including a trust based feedback mechanism to increase the agreement between the experts.
Let be a set of alternatives evaluated by experts, . Each expert used a reciprocal intuitionistic fuzzy preference relation; which can be presented by . Let
An illustrative example
The feasibility and effectiveness of the proposed approach in the real world are demonstrated by a small simulated real example, which could be extended to a much larger example in the real world.
The municipality wants to build a new park in the city. For this purpose, Four zones are designated. Four experts were asked to evaluate the tenders and announce the final result. Each expert expresses his/her preferences with reciprocal intuitionistic fuzzy preference relations. In the real world,
Discussion
Nowadays thanks to the worldwide expansion of internet based technologies, many interactions between people are carried out by means of social network based communities. These cyber scenarios facilitate the communication between millions of users, in real time, no matter their backgrounds. Therefore from the point of view of group decision making, social networks constitute not only a great opportunity, but also pose various research challenges. Among them, we can highlight the anonymity of
Conclusions
In this contribution, we have introduced a consensus based approach for group decision making that deals with uncertainty in the experts opinions by taking advantage of the intuitionistic fuzzy preference relations and by estimating missing information even when no values have been provided by an expert, what is known in the specialized literature as a total ignorance situation. The main novelties introduced in this contribution are the following:
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The proposed approach is suitable to deal with
Acknowledgments
The authors would like to acknowledge the financial support from the EU project H2020-MSCA-IF-2016-DeciTrustNET-746398 and the National Spanish project TIN2016-75850-P.
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No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.knosys.2019.105168.