Consistency based completion approaches of incomplete preference relations in uncertain decision contexts.

Uncertainty, hesitation and vagueness are inherent to human beings when articulating opinions and preferences. Therefore in decision making situations it might well be the case that experts are unable to express their opinions in an accurate way. Under these circumstances, various families of preference relations (PRs) have been proposed (linguistic, intuitionistic and interval fuzzy PRs) to allow the experts to manifest some degree of hesitation when enunciating their opinions. An extreme case of uncertainty happens when an expert is unable to differentiate the degree up to which one preference is preferred to another. Henceforth, incomplete preference relations are possible. It is worth to bear in mind that incomplete information does not mean low quality information, on the contrary, in many occasions experts might prefer no to provide information in other to keep consistency. Consequently mechanism to deal with incomplete information in decision making are necessary. This contribution presents the main consistency based completion approaches to estimate incomplete preference values in linguistic, intuitionistic and interval fuzzy PRs

Choice degrees in decision-making: A comparison between intuitionistic and fuzzy preference relations approaches

Preference modelling based on Atanassov’s intuitionistic fuzzy sets are gaining increasing relevance in the field of group decision making as they provide experts with a flexible and simple tool to express their preferences on a set of alternative options, while allowing, at the same time, to accommodate experts’ preference uncertainty, which is inherent to all decision making processes. A key issue within this framework is the provision of efficient methods to rank alternatives, from best to worse, taking into account the peculiarities that this type of preference representation format presents. In this contribution we analyse the relationships between the main method proposed and used by researchers to rank alternatives using intuitionistic fuzzy sets, the score degree function, and the well known choice degree based on Orlovsky’s non-dominance concept for the case when the preferences are expressed by means of fuzzy preference relations. This relationship study will provide the necessary theoretical results to support the implementation of Orlovsky’s non-dominance concept to define the fuzzy quantifier guided non-dominance choice degree for intuitionistic fuzzy preference relations

A social network based approach for consensus achievement in multiperson 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.Nowadays we are living the apogee of the Internet based technologies and consequently web 2.0 communities, where a large number of users interact in real time and share opinions and knowledge, is a generalized phenomenon. This type of social networks communities constitute a challenge scenario from the point of view of Group Decision Making approaches, because it involves a large number of agents coming from different backgrounds and/or with different level of knowledge and influence. In these type of scenarios there exists two main key issues that requires attention. Firstly, the large number of agents and their diverse background may lead to uncertainty and or inconsistency and so, it makes difficult to assess the quality of the information provided as well as to merge this information. Secondly, it is desirable, or even indispensable depending on the situation, to obtain a solution accepted by the majority of the members or at least to asses the existing level of agreement. In this contribution we address these two main issues by bringing together both decision Making approaches and opinion dynamics to develop a similarity-confidence-consistency based Social network that enables the agents to provide their opinions with the possibility of allocating uncertainty by means of the Intuitionistic fuzzy preference relations and at the same time interact with like-minded agents in order to achieve an agreement

Dealing with Incomplete Information in Linguistic Group Decision Making by Means of Interval Type-2 Fuzzy Sets

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.Nowadays in the social network based decision making processes, as the ones involved in e-commerce and e-democracy, multiple users with di erent backgrounds may take part and diverse alternatives might be involved. This diversity enriches the process but at the same time increases the uncertainty in the opinions. This uncertainty can be considered from two di erent perspectives: (i) the uncertainty in the meaning of the words given as preferences, that is motivated by the heterogeneity of the decision makers, (ii) the uncertainty inherent to any decision making process that may lead to an expert not being able to provide all their judgments. The main objective of this contribution is to address these two type of uncertainty. To do so the following approaches are proposed: Firstly, in order to capture, process and keep the uncertainty in the meaning of the linguistic assumption the Interval Type 2 Fuzzy Sets are introduced as a way to model the experts linguistic judgments. Secondly, a measure of the coherence of the information provided by each decision maker is proposed. Finally, a consistency based completion approach is introduced to deal with the uncertainty presented in the expert judgments. The proposed approach is tested in an e-democracy decision making scenario

DeciTrustNET: A graph based trust and reputation framework for social networks

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.The world wide success of large scale social information systems with diverse purposes, such as e-commerce platforms, facilities sharing communities and social networks, make them a very promising paradigm for large scale information sharing and management. However the anonymity, distributed and open nature of these frameworks, that, on the one hand, foster the communication capabilities of their users, may contribute, on the other hand, to the propagation of low quality information, attacks and manipulations from users with malicious intentions. All of these risks could end up decreasing users' con dence in these systems and in a reduction of their utilisation. With these issues in mind, the objective of this contribution is to create DeciTrustNET, a trust and reputation based framework for social networks that takes into consideration the users relationships, the historic evolution of their reputations and their pro le similarity to develop a tamper resilient network that guarantees trustworthy communications and transactions. An extensive experimental analysis of the developed framework has been carried out con rming that the proposed approach supports robust trust and reputation establishment among the users, even in social network under the presence of malicious users

Confidence Based Consensus in Environments with High Uncertainty and Incomplete Information

With the incorporation of web 2.0 frameworks the complexity of decision making situations has exponentially increased, involving in many cases many experts, and a potentially huge number of different alternatives, leading the experts to present uncertainty with the preferences provided. In this context, intuitionistic fuzzy preference relations play a key role as they provide the experts with means to allocate the uncertainty inherent in their proposed opinions. However, in many occasions the experts are unable to give a preference due to different reasons, there- fore effective mechanisms to cope with missing information are more than necessary. In this contribution, we present a new group decision making (GDM) approach able to estimate the missing information and at the same time implements a mechanism to bring the experts’ opinions closer in an iterative process in which the experts’ confidence plays a key role

GDMR A new framework in R to suppot Fuzzy Group Decision Making processes

This is a summary of our article published in Information Science [12] to be part of the MultiConference CAEPIA'15 KeyWorks

A personalized consensus feedback mechanism based on maximum harmony degree

This work was sponsored by National Natural Science Foundation of China (NSFC) (No.71971135,71571166), EU project H2020-MSCA-IF-2016-DeciTrustNET-746398 and FEDER funds provided in the National Spanish project TIN2016-75850-R.This article proposes a framework of personalized feedback mechanism to help multiple inconsistent experts to reach consensus in group decision making by allowing to select different feedback parameters according to individual consensus degree. The general harmony degree (GHD) is defined to determine the before/after feedback difference between the original and revised opinions. It is proved that the GHD index is monotonically decreasing with respect to the feedback parameter, which means that higher parameters values will result in higher changes of opinions. An optimisation model is built with the GHD as the objective function and the consensus thresholds as constraints, with solution being personalized feedback advices to the inconsistent experts that keep a balance between consensus (group aim) and independence (individual aim). This approach is, therefore, more reasonable than the unpersonalized feedback mechanisms in which the inconsistent experts are forced to adopt feedback generated with only consensus target without considering the extent of the changes acceptable by individual experts. Furthermore, the following interesting theoretical results are also proved: (1) the personalized feedback mechanism guarantees that the increase of consensus level after feedback advices are implemented; (2) the GHD by the personalized feedback mechanism is higher than that of the unpersonalized one; and (3) the personalized feedback mechanism generalises the unpersonalized one as it is proved the latter is a particular type of the former. Finally, a numerical example is provided to model the feedback process and to corroborates these results when comparing both feedback mechanism approaches.National Natural Science Foundation of China (NSFC) 71971135 71571166European Commission H2020-MSCA-IF-2016-DeciTrustNET-746398 TIN2016-75850-

Confidence-consistency driven group decision making approach with incomplete reciprocal intuitionistic preference relations

This is the reference for the online corrected proof versionIntuitionistic preference relations constitute a flexible and simple representation format of experts’ preference on a set of alternative options, while at the same time allowing to accommodate degrees of hesitation inherent to all decision making processes. In comparison with fuzzy preference relations, the use of intuitionistic fuzzy preference relations in decision making is limited, which is mainly due to the computational complexity associated to using membership degree, non-membership degree and hesitation degree to model experts’ subjective preferences. In this paper, the set of reciprocal intuitionistic fuzzy preference relations and the set of asymmetric fuzzy preference relations are proved to be mathematically isomorphic. This result can be exploited to use methodologies developed for fuzzy preference relations to the case of intuitionistic fuzzy preference relations and, ultimately, to overcome the computation complexity mentioned above and to extend the use of reciprocal intuitionistic fuzzy preference relations in decision making. In particular, in this paper, this isomorphic equivalence is used to address the presence of incomplete reciprocal intuitionistic fuzzy preference relations in decision making by developing a consistency driven estimation procedure via the corresponding equivalent incomplete asymmetric fuzzy preference relation procedure. Additionally, the hesitancy degree of the reciprocal intuitionistic fuzzy preference relation is used to introduce the concept of expert’s confidence from which a group decision making procedure, based on a new aggregation operator that takes into account not only the experts’ consistency but also their confidence degree towards the opinion provided, is proposed

Confidence based consensus model for intuitionistic fuzzy preference relations

Intuitionistic fuzzy preference relation are gaining increasing relevance in the field of group decision making as they provide experts to allocate the uncertainty inherent in their proposed opinions. A key issue in this field is to reach a solution accepted by the majority of the member of the group. The consensus process to those experts who present higher levels of confidence with the provided opinion. In this contribution we analyse the consensus methods that exists for Intuitionistic Fuzzy Preference Relations and we present a new confidence-consistency based consensus model. Moreover to rank the alternatives we present the implementation of Orlovsky’s non-dominance concept to define the fuzzy quantifier guided non-dominance choice degree for intuitionistic fuzzy preference relations