One of the most widely adopted approaches to define weights for Ordered Weighting Averaging (OWA) operators consists of using biparametric linear increasing fuzzy linguistic quantifiers. However, several shortcomings appear when using these quantifiers because depending on the values of these parameters, the aggregations could be biased or the extreme values might be completely ignored. In this contribution, the use of Extreme Values Reductions (EVRs) as fuzzy linguistic quantifiers is proposed to define weights for OWA operators in order to provide more realistic aggregations. First, the impact of the parameters of these linear fuzzy linguistic quantifiers in the OWA aggregations is studied. After that, EVR-OWA operators are introduced as those OWA operators whose weights are computed by using an EVR as fuzzy linguistic quantifier. It will be shown that when using EVR-OWA operators to fuse information, the aggregations are non-biased, take into account more information and the intermediate values are prioritized before the extreme ones. After proposing several families of EVRs, the generalising potential of the EVR-OWA operators is shown by proving that every family of symmetric weights for OWA operators that prioritize the intermediate information are the weights obtained from a certain EVR. Finally, an illustrative example is provided.

This study develops a power-average-operator-based hybrid multiattribute online product recommendation model that considers the consumer's risk attitude to rank categoric product options as a complement to existing recommender systems. Online production recommendation plays a key role in the development of e-commerce, and can greatly improve consumers' shopping experiences. However, few online shopping sites provide interactive decision aids for consumers such that they can articulate their preferences towards multiple selection attributes with the purpose of mitigating choice difficulty and improving decision quality. Additionally, consumers' risk attitudes to online shopping dramatically impact their product choices. In the model proposed in this paper, the risk attitude-based power average (RAPA) operator is used to integrate the risk attitude of the decision-maker into the information fusion process of multiple attribute decision-making. Subsequently, the risk attitude function, with several basic types, is introduced to quantify the risk attitude of the decision-maker for use in the RAPA operator. A proportional hesitant fuzzy 2-tuple linguistic term set (PHF2TLTS) is constructed by incorporating a binary of linguistic information aiming to comprehensively analyze the hybrid product information. With a focus on the information fusion process, the proportional hesitant 2-tuple linguistic RAPA operator and weighted proportional hesitant 2-tuple linguistic RAPA operator are introduced to aggregate a given set of PHF2TLTSs. The validity of the proposed model is demonstrated using an illustrative example, a comparison with existing approaches and detailed explanations of the performance differences.

Consensus Reaching Processes (CRPs) deal with those group decision-making situations in which conflicts among experts' opinions make difficult the reaching of an agreed solution.This situation, worsens in largescale group decision situations, in which opinions tend to be more polarized, because in problems with extreme opinions it is harder to reach an agreement.Several studies have shown that experts' preferences may not always follow a linear scale, as it has commonly been assumed in previous CRP.Therefore, the main aim of this paper is to study the effect of modeling this nonlinear behavior of experts' preferences (expressed by fuzzy preference relations) in CRPs.To do that, the experts' preferences will be remapped by using nonlinear deformations which amplify or reduce the distance between the extreme values.We introduce such automorphisms to remap the preferences as Extreme Values Amplifications (EVAs) and Extreme Values Reductions (EVRs), study their main properties and propose several families of these EVA and EVR functions.An analysis about the behavior of EVAs and EVRs when are implemented in a generic consensus

Group recommender systems (GRSs) recommend items that are used by groups of people because certain activities, such as listening to music, watching a movie, dining in a restaurant, etc., are social events performed by groups of people sharing their tastes, and their choices affect all of them. GRSs help groups of people making choices in overloaded search spaces according to all group members preferences. A common GRS scheme aggregates users preferences to generate a group preference profile. However, the aggregation process may imply a loss of information, negatively affecting different properties of the GRS such as diversity of group recommendations, which is an important quality factor because of such recommendations are targeted to groups formed by users with individual and possibly conflicting preferences. To avoid and manage the loss of information caused by aggregation, this paper proposes to keep all group members preferences by using hesitant fuzzy sets (HFSs) and interpreting such information like the group hesitation about their preferences that will be used in the group recommendation process. To evaluate the performance and rank quality of the HFS GRS proposal, a case study is carried out.

The necessity of dealing with uncertainty in real world problems has been a long-term research challenge that has originated different methodologies and theories. Fuzzy sets along with their extensions, such as type-2 fuzzy sets, interval-valued fuzzy sets, and Atanassov's intuitionistic fuzzy sets, have provided a wide range of tools that are able to deal with uncertainty in different types of problems. Recently, a new extension of fuzzy sets so-called hesitant fuzzy sets has been introduced to deal with hesitant situations, which were not well managed by the previous tools. Hesitant fuzzy sets have attracted very quickly the attention of many researchers that have proposed diverse extensions, several types of operators to compute with such types of information, and eventually some applications have been developed. Because of such a growth, this paper presents an overview on hesitant fuzzy sets with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.