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

Managing Incomplete Preference Relations in Decision Making: A Review and Future Trends

In decision making, situations where all experts are able to efficiently express their preferences over all the available options are the exception rather than the rule. Indeed, the above scenario requires all experts to possess a precise or sufficient level of knowledge of the whole problem to tackle, including the ability to discriminate the degree up to which some options are better than others. These assumptions can be seen unrealistic in many decision making situations, especially those involving a large number of alternatives to choose from and/or conflicting and dynamic sources of information. Some methodologies widely adopted in these situations are to discard or to rate more negatively those experts that provide preferences with missing values. However, incomplete information is not equivalent to low quality information, and consequently these methodologies could lead to biased or even bad solutions since useful information might not being taken properly into account in the decision process. Therefore, alternative approaches to manage incomplete preference relations that estimates the missing information in decision making are desirable and possible. This paper presents and analyses methods and processes developed on this area towards the estimation of missing preferences in decision making, and highlights some areas for future research

Trust Based Consensus Model for Social Network in an Incomplete Linguistic Information Context

A theoretical framework to consensus building within a networked social group is put forward. This article investigates a trust based estimation and aggregation methods as part of a visual consensus model for multiple criteria group decision making with incomplete linguistic information. A novel trust propagation method is proposed to derive trust relationship from an incomplete connected trust network and the trust score induced order weighted averaging operator is presented to aggregate the orthopairs of trust/distrust values obtained from different trust paths. Then, the concept of relative trust score is defined, whose use is twofold: (1) to estimate the unknown preference values and (2) as a reliable source to determine experts' weights. A visual feedback process is developed to provide experts with graphical representations of their consensus status within the group as well as to identify the alternatives and preference values that should be reconsidered for changing in the subsequent consensus round. The feedback process also includes a recommendation mechanism to provide advice to those experts that are identified as contributing less to consensus on how to change their identified preference values. It is proved that the implementation of the visual feedback mechanism guarantees the convergence of the consensus reaching process

Granular computing and optimization model-based method for large-scale group decision-making and its application

In large-scale group decision-making process, some decision makers hesitate among several linguistic terms and cannot compare some alternatives, so they often express evaluation information with incomplete hesitant fuzzy linguistic preference relations. How to obtain suitable large-scale group decision-making results from incomplete preference information is an important and interesting issue to concern about. After analyzing the existing researches, we find that: i) the premise that complete preference relation is perfectly consistent is too strict, ii) deleting all incomplete linguistic preference relations that cannot be fully completed will lose valid assessment information, iii) semantics given by decision makers are greatly possible to be changed during the consistency improving process. In order to solve these issues, this work proposes a novel method based on Granular computing and optimization model for large-scale group decision-making, considering the original consistency of incomplete hesitant fuzzy linguistic preference relation and improving its consistency without changing semantics during the completion process. An illustrative example and simulation experiments demonstrate the rationality and advantages of the proposed method: i) semantics are not changed during the consistency improving process, ii) completion process does not significantly alter the inherent quality of information, iii) complete preference relations are globally consistent, iv) final large-scale group decision-making result is acquired by fusing complete preference relations with different weights

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

Predicting missing pairwise preferences from similarity features in group decision making

In group decision-making (GDM), fuzzy preference relations (FPRs) refer to pairwise preferences in the form of a matrix. Within the field of GDM, the problem of estimating missing values is of utmost importance, since many experts provide incomplete preferences. In this paper, we propose a new method called the entropy-based method for estimating the missing values in the FPR. We compared the accuracy of our algorithm for predicting the missing values with the best candidate algorithm from state of the art achievements. In the proposed entropy-based method, we took advantage of pairwise preferences to achieve good results by storing extra information compared to single rating scores, for example, a pairwise comparison of alternatives vs. the alternative’s score from one to five stars. The entropy-based method maps the prediction problem into a matrix factorization problem, and thus the solution for the matrix factorization can be expressed in the form of latent expert features and latent alternative features. Thus, the entropy-based method embeds alternatives and experts in the same latent feature space. By virtue of this embedding, another novelty of our approach is to use the similarity of experts, as well as the similarity between alternatives, to infer the missing values even when only minimal data are available for some alternatives from some experts. Note that current approaches may fail to provide any output in such cases. Apart from estimating missing values, another salient contribution of this paper is to use the proposed entropy-based method to rank the alternatives. It is worth mentioning that ranking alternatives have many possible applications in GDM, especially in group recommendation systems (GRS).Andalusian Government P20 00673 PID2019-103880RB-I00 MCIN/AEI/10.13039/50110001103

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

Group decision making with incomplete reciprocal preference relations based on multiplicative consistency

This paper comprises a new iterative method for multi-person decision making based on multiplicative consistency with incomplete reciprocal preference relations (IRPRs). Additionally, multiplicative transitivity property of reciprocal preference relation (RPR) is used at the first level to estimate the unknown preference values and get the complete preference relation, then it is confirmed to be multiplicative consistent by using transitive closure formula. Following this, expert's weights are evaluated by merging consistency and trust weights. The consistency weights against the experts are evaluated through multiplicative consistency investigation of the preferences given by each expert, while trust weights play the role to measure the level of trust for an expert. The consensus process determines whether the selection procedure should start or not. If it results in negative, the feedback mechanism is used to enhance the consensus degree. At the end, a numerical example is given to demonstrate the efficiency and practicality of the proposed method

Consistency-driven methodology to manage incomplete linguistic preference relation: A perspective based on personalized individual semantics

The file attached to this record is the author's final peer reviewed version.In linguistic decision making problems there may be cased when decision makers will not be able to provide complete linguistic preference relations. However, when estimating unknown linguistic preference values in incomplete preference relations, the existing research approaches ignore the fact that words mean different things for different people, i.e. decision makers have personalized individual semantics (PISs) regarding words. To manage incomplete linguistic preference relations with PISs, in this paper we propose a consistency-driven methodology both to estimate the incomplete linguistic preference values and to obtain the personalized numerical meanings of linguistic values of the different decision makers. The proposed incomplete linguistic preference estimation method combines the characteristic of the personalized representation of decision makers and guarantees the optimum consistency of incomplete linguistic preference relations in the implementation process. Numerical examples and a comparative analysis are included to justify the feasibility of the PISs based incomplete linguistic preference estimation method

Uninorm trust propagation and aggregation methods for group decision making in social network with four tuples information

The file attached to this record is the authors accepted version. The publisher's final version of record can be found by following the DOI link below.A novel social network based group decision making (SN-GDM) model with experts' weights not provided beforehand and with the following four tuple information: trust; distrust; hesitancy; and inconsistency, is introduced. The concepts of trust score (TS) and knowledge degree (KD) are de ned and combined into a trust order space. Then, a strict trust ranking order relation of trust function values (TFs) is built in which TS and KD play a similar role to the mean and the variance in Statistics. After the operational laws of TFs for uninorm operators are built, the uninorm propagation operator is investigated. It can propagate through a network both trust and distrust information simultaneously and therefore it prevents the loss of trust information in the propagating process. When an indirect trust relationship is built, the uninorm trust weighted average (UTWA) operator and the uninorm trust ordered weighted average (UTOWA) operator are de ned and used to aggregate individual trust relationship and to obtain their associated ranking order relation. Hence, the most trusted expert is distinguished from the group, and the weights of experts are determined in a reasonable way: the higher an expert is trusted the more importance value is assigned to the expert. Therefore, the novelty of the proposed SN-GDM is that it can use indirect trust relationship via trusted third partners (TTPs) as a reliable resource to determine experts' weights. Finally, the individual trust decision making matrices are aggregated into a collective one and the alternative with the highest trust order relation is selected as the best one