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The authors' previously published research delved into the theory of software product quality modelling, model views, concepts, and terminologies. They also analysed this specific field from the point of view of uncertainty, and possible descriptions based on fuzzy set theory and fuzzy logic. Laying a theoretical foundation was necessary; however, software professionals need a more tangible and practical approach for their everyday work. Consequently, the authors devote this paper to filling in this gap; it aims to illustrate how to interpret and utilise the previous findings, including the established taxonomy of the software product quality models. The developed fuzzy model's simplification is also presented with a Generalized Additive Model approximation. The paper does not require any formal knowledge of uncertainty computations and reasoning under uncertainty, nor does it need a deep understanding of quality modelling in terms of terminology, concepts, and meta-models, which were necessary to prepare the taxonomy and relevance ranking. The paper investigates how to determine the validity of statements based on a given software product quality model; moreover, it considers how to tailor and adjust quality models to the particular project's needs. The paper also describes how to apply different software product quality models for different quality views to take advantage of the automation potential offered for the measurement and assessment of source code quality. Furthermore, frequent pitfalls are illustrated with their corresponding resolutions, including an unmeasured quality property that is found to be important and needs to be included in the measurement and assessment process. [ABSTRACT FROM AUTHOR]

• A new simulation methodology, intended bounded rationality methodology, is proposed. • Evaluation cost-benefit of different aspects of decision support techniques. • Classification of errors that a decision support technique can generate is proposed. • Consistent erroneous judgments and inconsistent correct judgments are possible. • A case where consistency condition in AHP provides maximum 5% of the expected return. Expert's judgments have been crucial in the development of decision theory; however, what criterion to use in the selection of experts remains an issue to address. Decision support techniques proposed to improve the quality of expert judgment decision making consider a demonstrated inconsistency of the judgments expressed by an expert as a criterion of exclusion in the decision-making process of such expert. Although consistency appears to be a desirable condition to qualify as "expert", little is known about the quality of the decisions made imposing consistency as the expert qualifying condition. This paper proposes a simulation methodology, based on an automaton programmed to make decisions in an intended but bounded rational way, to assess the cost-benefit of different aspects of decision support techniques. Within this methodology, the imposition of the consistency condition in the selection of experts is studied. In particular, the paper shows with a case study example that the Analytical hierarchy process (AHP) decision support technique expected payoff is at most 5% higher when implementing Saaty's consistency criterion of the expert's judgments than when the consistency criterion is not considered. [ABSTRACT FROM AUTHOR]

This article proposes a framework of consensus reaching process based on interval-valued number with self-confidence involving two feedback mechanisms: (1) the ordinal feedback mechanism (OFM), and (2) the joint feedback mechanism (JFM). Firstly, a new concept called the interval-valued number with self-confidence (IVN-SC) is defined, which allows experts to express self-confidence (SC) when providing their evaluations by interval-valued number (IVN). In OFM, three types of discordant behaviours are explored from the perspective of IVN consensus and SC consensus, and then the corresponding personalized mechanisms for discordant behaviours are implemented to guarantee they both reach consensus threshold. While in JFM, the comprehensive consensus degree by combing the IVN and SC is presented to measure the agreement level among experts, and then a joint optimization model with IVN-SC is activated to support the discordant experts to reach the threshold value of group consensus. It explores that the JFM is less strict than the OFM because the former contains the compensatory aggregation operator while the latter does not. Finally, an illustrative example and comparative analysis are devised to testify the effectiveness of the proposed models. • A new concept of interval-valued number with self-confidence is defined. • An ordinal feedback mechanism for consensus is developed. • A joint feedback mechanism to support consensus is investigated. [ABSTRACT FROM AUTHOR]

This article proposes a framework for bilateral negotiation mechanism to deal the case the concordant decision-makers (DMs) coalition cannot be constructed, which resolves the limitations of the existing group decision making methods. Bilateral negotiation means a process in which any two involved DMs change their own opinions based on each other's opinions, avoiding the formation of group coalitions and the coercion of individual DMs. It can not only improve group consensus by interaction between individual DMs, but also considers the limited compromise behavior of DMs in the consensus bargaining process. The key contributions of this article contain: (1) It investigates the concept of ' harmony threshold ' by combining the consensus levels of individual DMs and the number of group members to explain the limited compromise behavior of DMs. (2) it proposes a novel bilateral negotiation consensus mechanism with personalized compromise behavior with the group consensus threshold as the objective function and personalized harmony thresholds as constraints to help any two discording DMs partly to adopt each other's opinions. And (3) It develops the ranking difference level (RDL) to measure the deviation degree between the final ranking of alternatives and all the DMs' original rankings of alternatives. The research found that the proposed mechanism can reduce consensus cost by 40% and ranking difference by 5%. [ABSTRACT FROM AUTHOR]

This article proposes a framework for bilateral negotiation mechanism to deal the case the concordant decision-makers (DMs) coalition cannot be constructed, which resolves the limitations of the existing group decision making methods. Bilateral negotiation means a process in which any two involved DMs change their own opinions based on each other's opinions, avoiding the formation of group coalitions and the coercion of individual DMs. It can not only improve group consensus by interaction between individual DMs, but also considers the limited compromise behavior of DMs in the consensus bargaining process. The key contributions of this article contain: (1) It investigates the concept of ' harmony threshold ' by combining the consensus levels of individual DMs and the number of group members to explain the limited compromise behavior of DMs. (2) it proposes a novel bilateral negotiation consensus mechanism with personalized compromise behavior with the group consensus threshold as the objective function and personalized harmony thresholds as constraints to help any two discording DMs partly to adopt each other's opinions. And (3) It develops the ranking difference level (RDL) to measure the deviation degree between the final ranking of alternatives and all the DMs' original rankings of alternatives. The research found that the proposed mechanism can reduce consensus cost by 40% and ranking difference by 5%. [ABSTRACT FROM AUTHOR]

The manifestation of the intensity in the judgment of one alternative versus another in the peer comparison processes is a central element in some decision support techniques, such as the Analytical Hierarchy Process (AHP). However, its contribution regarding quality (expected performance) with respect to the priority vector has not been evaluated so far. Using the Intentional Bounded Rationality Methodology (IBRM), this work analyzes the gains obtained from requiring the decision-maker to report an intensity judgment in pairs (AHP) with respect to a technique that only requires expressing a preference (Ordering). The results show that when decision-makers have low levels of expertise, it is possible that a less informative and computational cheap technique (Ordering) performs better than a more informative and computational expensive one (AHP). When decision-makers have medium and high levels of expertise, AHP technique obtains modest gains with respect to the Ordering technique. This study proposes a cost-benefit analysis of decision support techniques contrasting the gains of a technique that requires more resources (AHP) against other that require less resources (Ordering). Our results can change the managing approach of the information obtained from experts' judgments. [ABSTRACT FROM AUTHOR]

This article investigates a minimum cost-maximum consensus jointly driven feedback mechanism under a harmonious power structure by twofold group and individual attention recommendations for building social network consensus. Harmonious power structure is first constructed with subgroup-centrality-IOWA operator by (i) extracting subgroup importance rankings through social network analysis, and (ii) minimising group structure conflict to search the harmony weight allocation. Subsequently, a twofold attention recommendation approach that balances group attention and individual attention is proposed to generate feedback recommendations for the feedback recipients. Based on this, optimisation models that minimise individual adjustment cost and maximise group consensus are constructed, jointly driving the feedback mechanism. Finally, a demonstration example is provided to illustrate the efficacy of the proposed model. • It determines the harmony power structure of subgroup. • It proposes a twofold attention recommendation method. • It instigates a joint cost-consensus driven feedback mechanism. [ABSTRACT FROM AUTHOR]

• How differences in expertise, diversity, and group decision procedures affect the decision quality. • Alternatives in the strategic decision are often not observable preventing empirical studies obtain complete results. • A new simulation methodology, Intended Bounded Rationality Methodology, is used. • Concentrated decision power can be an acceptable system. This paper proposes to analyze how the differences in expertise, diversity, and group decision procedures affect the quality of the strategic decision of steering committees. Strategic decisions are difficult to anticipate, and performances of the alternatives are often not observable in their entirety, which prevent researchers from obtaining controlled empirical studies. This paper proposes to analyze the performance of steering committees where managers can err in their decisions using the Intentional Bounded Rationality (IBR). The majority procedure improves the committee's performance concerning authority when the level of diversity and expertise increases. However, in situations of low expertise, the gains over authority narrow. This work provides guidance in terms of trade-offs between the mentality of managers, their expertise, group decision procedures, and diversity, which in the empirical works are contradictory. This study contributes to current theorizations of committee management using the IBR methodology, which is new and allows quantifying the contribution of the distinct characteristics of the committee. [ABSTRACT FROM AUTHOR]

• Novel framework that estimate trust and reputation, (global reputation, and pairwise trust) between agents in a social network. • Assessing user's Reputation by evaluating their relationships and their position in the network. • User behavior tracking to isolate malicious agents. • Double supervised personalized feedback to rate interactions between users. 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' confidence 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 profile 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 confirming that the proposed approach supports robust trust and reputation establishment among the users, even in social network under the presence of malicious users. [ABSTRACT FROM AUTHOR]

• This study contributes to consensus generation within a social network framework. • The concept of eigenvector-like centrality measure is implemented within a hierarchical clustered preference similarity network. • A new centrality influence score measure is developed for the purpose of identifying the network influencer. • A new similarity social influence network feedback mechanism is designed. Consensus group decision making (CGDM) allows the integration within this area of study of other advanced frameworks such as Social Network Analysis (SNA), Social Influence Network (SIN), clustering and trust-based concepts, among others. These complementary frameworks help to bridge the gap between their corresponding theories in such a way that important elements are not overlooked and are appropriately taken into consideration. In this paper, a new influence-driven feedback mechanism procedure is introduced for a preference similarity network clustering based consensus reaching process. The proposed influence-driven feedback mechanism aims at identifying the network influencer for the generation of advices. This procedure ensures that valuable recommendations are coming from the expert with most similar preferences with the other experts in the group. This is achieved by adapting, from the SIN theory into the CGDM context, an eigenvector-like measure of centrality for the purpose of: (i) measuring the influence score of experts, and (ii) determining the network influencer. Based on the initial evaluations on a set of alternatives provide by the experts in a group, the proposed influence score measure, which is named the σ-centrality , is used to define the similarity social influence network (SSIN) matrix. The σ-centrality is obtained by taking into account both the endogenous (internal network connections) and exogenous (external) factors, which means that SSIN connections as well as the opinion contribution from third parties are permitted in the nomination of the network influencer. The influence-driven feedback mechanism process is designed based on the satisfying of two important conditions to ensure that (1) the revised consensus degree is above the consensus threshold and that (2) the clustering solution is improved. [ABSTRACT FROM AUTHOR]

Group Recommender Systems are special kinds of Recommender Systems aimed at suggesting items to groups rather than individuals taking into account, at the same time, the preferences of all (or the majority of) members. Most existing models build recommendations for a group by aggregating the preferences for their members without taking into account social aspects like user personality and interpersonal trust, which are capable of affecting the item selection process during interactions. To consider such important factors, we propose in this paper a novel approach to group recommendations based on fuzzy influence-aware models for Group Decision Making. The proposed model calculates the influence strength between group members from the available information on their interpersonal trust and personality traits (possibly estimated from social networks). The estimated influence network is then used to complete and evolve the preferences of group members, initially calculated with standard recommendation algorithms, toward a shared set of group recommendations, simulating in this way the effects of influence on opinion change during social interactions. The proposed model has been experimented and compared with related works. • Group recommender systems suggest items to be consumed by groups of users. • Individual preferences of any group member must be taken into account. • Considering social influence between group members leads to better recommendations. • Influence strength can be estimated from information retrieved in social networks. • Fuzzy decision making allows the influence-based aggregation of individual preferences. [ABSTRACT FROM AUTHOR]

Tracking the head in a video stream is a common thread seen within computer vision literature, supplying the research community with a large number of challenging and interesting problems. Head pose estimation from monocular cameras is often considered an extended application after the face tracking task has already been performed. This often involves passing the resultant 2D data through a simpler algorithm that best fits the data to a static 3D model to determine the 3D pose estimate. This work describes the 2.5D constrained local model, combining a deformable 3D shape point model with 2D texture information to provide direct estimation of the pose parameters, avoiding the need for additional optimization strategies. It achieves this through an analytical derivation of a Jacobian matrix describing how changes in the parameters of the model create changes in the shape within the image through a full-perspective camera model. In addition, the model has very low computational complexity and can run in real-time on modern mobile devices such as tablets and laptops. The point distribution model of the face is built in a unique way, so as to minimize the effect of changes in facial expressions on the estimated head pose and hence make the solution more robust. Finally, the texture information is trained via local neural fields—a deep learning approach that utilizes small discriminative patches to exploit spatial relationships between the pixels and provide strong peaks at the optimal locations. [ABSTRACT FROM AUTHOR]

Highlights • A new consensus model based on influence from a social network is defined. • The most influential experts' opinions are used to generate recomendations. • The model is able to identify and isolate malicious behaviour experts. Abstract 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. [ABSTRACT FROM AUTHOR]

Abstract In order to avoid misleading decision solutions in group decision making (GDM) processes, in addition to consensus, which is obviously desirable to guarantee that the group of experts accept the final decision solution, consistency of information should also be sought after. For experts' preferences represented by reciprocal fuzzy preference relations, consistency is linked to the transitivity property. In this study, we put forward a new consensus approach to solve GDM with reciprocal preference relations that implements rationality criteria of consistency based on the transitivity property with the following twofold aim prior to finding the final decision solution: (A) to develop a consistency control module to provide personalized consistency feedback to inconsistent experts in the GDM problem to guarantee the consistency of preferences; and (B) to design a consistent preference network clustering based consensus measure based on an undirected weighted consistent preference similarity network structure with undirected complete links, which using the concept of structural equivalence will allow one to (i) cluster the experts; and (ii) measure their consensus status. Based on the uninorm characterization of consistency of reciprocal preferences relations and the geometric average, we propose the implementation of the geo-uninorm operator to derive a consistent based preference relation from a given reciprocal preference relation. This is subsequently used to measure the consistency level of a given preference relation as the cosine similarity between the respective relations' essential vectors of preference intensity. The proposed geo-uninorm consistency measure will allow the building of a consistency control module based on a personalized feedback mechanism to be implemented when the consistency level is insufficient. This consistency control module has two advantages: (1) it guarantees consistency by advising inconsistent expert(s) to modify their preferences with minimum changes; and (2) it provides fair recommendations individually, depending on the experts' personal level of inconsistency. Once consistency of preferences is guaranteed, a structural equivalence preference similarity network is constructed. For the purpose of representing structurally equivalent experts and measuring consensus within the group of experts, we develop an agglomerative hierarchical clustering based consensus algorithm, which can be used as a visualization tool in monitoring current state of experts' group agreement and in controlling the decision making process. The proposed model is validated with a comparative analysis with an existing literature study, from which conclusions are drawn and explained. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the Type-Reduced Set (TRS) of the continuous type-2 fuzzy set is considered as an object in its own right. The structures of the TRSs of both the interval and generalised forms of the type-2 fuzzy set are investigated. In each case the respective TRS structure is approached by first examining the TRS of the discretised set. The TRS of a continuous interval type-2 fuzzy set is demonstrated to be a continuous horizontal straight line, and that of a generalised type-2 fuzzy set, a continuous, convex curve. This analysis leads on to the concept of truncation, and the definition of the truncation grade. The truncated type-2 fuzzy set is then defined, whose TRS (and hence defuzzified value) is identical to that of the non-truncated type-2 fuzzy set. This result is termed the Type-2 Truncation Theorem , an immediate corollary of which is the Type-2 Equivalence Theorem which states that the defuzzified values of type-2 fuzzy sets that are equivalent under truncation are equal. Experimental corroboration of the equivalence of the non-truncated and truncated generalised type-2 fuzzy set is provided. The implications of these theorems for uncertainty quantification are explored. The theorem's repercussions for type-2 defuzzification employing the α -Planes Representation are examined; it is shown that the known inaccuracies of the α -Planes Method are deeply entrenched. [ABSTRACT FROM AUTHOR]

Association rule mining (ARM) aims to find out association rules that satisfy predefined minimum support and confidence from a given database. However, in many cases ARM generates extremely large number of association rules, which are impossible for end users to comprehend or validate, thereby limiting the usefulness of data mining results. In this paper, we propose a new mining algorithm based on animal migration optimization (AMO), called ARM–AMO, to reduce the number of association rules. It is based on the idea that rules which are not of high support and unnecessary are deleted from the data. Firstly, Apriori algorithm is applied to generate frequent itemsets and association rules. Then, AMO is used to reduce the number of association rules with a new fitness function that incorporates frequent rules. It is observed from the experiments that, in comparison with the other relevant techniques, ARM–AMO greatly reduces the computational time for frequent item set generation, memory for association rule generation, and the number of rules generated. [ABSTRACT FROM AUTHOR]

To assess the overall experience of a patient in a hospital, many factors must be analyzed; nonetheless, one of the key aspects is the performance of nurses as they closely interact with patients on many occasions. Nurses carry out many tasks that could be assessed to understand the patient's satisfaction and consequently, the effectiveness of the offered services. To assess their performance, traditionally, expensive, and time-consuming methods such as questionnaires and interviews have been used; nevertheless, the development of social networks has allowed the patients to convey their opinions in a free and public manner. For that reason, in this study, a comprehensive analysis has been performed based on patients' opinions collected from a feedback platform for health and care services, to discover the topics about nurses the patients are more interested in. To do so, a topic modeling technique has been proposed. After this, sentiment analysis has been applied to classify the topics as satisfactory or unsatisfactory. Finally, the results have been compared with what the patients think about doctors. The results highlight what topics are most relevant to assess the patient satisfaction and to what extent. The results remark that the opinion about nurses is, in general, more positive than about doctors. [ABSTRACT FROM AUTHOR]

There are situations in which lexicon-based methods for Sentiment Analysis (SA) are not able to generate a classification output for specific instances of a given dataset. Most often, the reason for this situation is the absence of specific terms in the sentiment lexicon required in the classification effort. In such cases, there were only two possible paths to follow: (1) add terms to the lexicon (off-line process) by human intervention to guarantee no noise is introduced into the lexicon, which prevents the classification system to provide an immediate answer; or (2) use the services of a word-frequency dictionary (on-line process), which is computationally costly to build. This paper investigates an alternative approach to compensate for the lack of ability of a lexicon-based method to produce a classification output. The method is based on the combination of the classification outputs of non lexicon-based tools. Specifically, firstly the outcome values of applying two or more non-lexicon classification methods are obtained. Secondly, these non-lexicon outcomes are fused using a uninorm based approach, which has been proved to have desirable compensation properties as required in the SA context, to generate the classification output the lexicon based approach is unable to achieve. Experimental results based on the execution of two well-known supervised machine learning algorithms, namely Naïve Bayes and Maximum Entropy, and the application of a cross-ratio uninorm operator are presented. Performance indices associated to options (1) and (2) above are compared against the results obtained using the proposed approach for two different datasets. Additionally, the performance of the proposed cross-ratio uninorm operator based approach is also compared when the aggregation operator used is the arithmetic mean instead. It is shown that the combination of non lexicon-based classification methods with specific uninorm operators improves the classification performance of lexicon-based methods, and it enables the offering of an alternative solution to the SA classification problem when needed. The proposed aggregation method could be used as well as a replacement of ensemble averaging techniques commonly applied when combining the results of several machine learning classifiers’ outputs. [ABSTRACT FROM AUTHOR]

A theoretical visual interaction framework to model consensus in social network group decision making (SN-GDM) is put forward with following three main components: (1) construction of trust relationship; (2) trust based recommendation mechanism; and (3) visual adoption mechanism. To do that, dual trust propagation is investigated to connect incomplete trust relationship by trusted third partners, in a way that it can fit our intuition in these cases: trust values decrease while distrust values increase. Trust relationship is proposed to be used in determining the trust degree of experts and in aggregating individual opinions into a collective one. Three levels of consensus degree are defined and used to identify the inconsistent experts. A trust based recommendation mechanism is developed to generate advices according to individual trust relationship, making recommendations more likeable to be implemented by the inconsistent experts to achieve higher levels of consensus. Therefore, it has an advantage with respect to existing interaction models because it does not force the inconsistent experts to accept advices irrespective of their trust on them. Finally, a visual adoption mechanism, which provides visual information representations on experts’ individual consensus positions before and after adopting the recommendation advices, is presented and analysed theoretically. Experts can select their appropriate feedback parameters to achieve a balance between group consensus and individual independence. Consequently, the proposed visual interaction model adds real and needed flexibility in guiding the consensus reaching process in SN-GDM. [ABSTRACT FROM AUTHOR]

The objective of this article is to present a hybrid approach to the Sentiment Analysis problem at the sentence level. This new method uses natural language processing (NLP) essential techniques, a sentiment lexicon enhanced with the assistance of SentiWordNet, and fuzzy sets to estimate the semantic orientation polarity and its intensity for sentences, which provides a foundation for computing with sentiments. The proposed hybrid method is applied to three different data-sets and the results achieved are compared to those obtained using Naïve Bayes and Maximum Entropy techniques. It is demonstrated that the presented hybrid approach is more accurate and precise than both Naïve Bayes and Maximum Entropy techniques, when the latter are utilised in isolation. In addition, it is shown that when applied to datasets containing snippets, the proposed method performs similarly to state of the art techniques. [ABSTRACT FROM AUTHOR]

Intuitionistic 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. [ABSTRACT FROM AUTHOR]

Group decision making is part of every organizational life. It is a type of participatory process in which multiple decision makers acting collectively, analyze problems, consider and evaluate several alternatives, and select from among the alternatives a solution. In such a situation, an important issue is the level of agreement or consensus achieved among the group of decision makers before obtaining the solution. In the beginning, consensus was meant as a full and unanimous agreement. Regrettably, this stringent concept of consensus in many cases is a utopia. As a result, and from a pragmatic point of view, it makes more sense to speak about a degree of consensus and, here, the theory of fuzzy sets has delivered new tools for the analysis of such imprecise phenomena like consensus. Given the significance of reaching an accepted solution by all the decision makers, consensus is a major aim of group decision making problems and, in such a way, it has obtained a great attention in the literature. However, there still exist several dares which have to be tackled by the researchers. The purpose of this paper is to bring out several issues that represent challenges that have to be faced. [ABSTRACT FROM AUTHOR]

• A weight method with the criteria variability to choose subgroup representatives. • Two consensus measurements for individual-guided and moderator-guided consensus. • Cloud model-based consensus optimisation with preference consistency. • A consensus hybrid strategy framework considering compromise behaviors. Large-scale group decision-making (LSGDM) is characterised by a large number of experts and a complex consensus reaching process. Clustering is used to divide the large group into a number of manageable subgroups; however, the simultaneous presence of all subgroup members at the negotiation process is rare. Thus, the selection of subgroup representatives for a smooth negotiation is necessary. Few LSGDM consensus recommendation optimisation models truly consider the problems of subgroup representative selection in their strategy to reach a consensus. This article proposes LSGDM consensus hybrid strategy framework with three-dimension clustering optimisation based on normal cloud models (NCMs) whose aims are threefold: (1) the use of NCMs to represent the imprecision of linguistic preferences provided in real complex decision scenarios with a large number of experts; (2) to establish a clustering optimisation method to choose subgroup representatives using three sensible criteria: preference similarity level within the subgroup, preference precision level, and preference consistency level; and (3) to establish two consensus recommendation optimisation strategies for individual negotiation-guided and moderator-guided consensus reaching, respectively. The feasibility and applicability of the proposed method are illustrated via a power curtailment policy assessment example, then some sensitive and comparative analyses are conducted to explicit the effectiveness and advantages of the proposed consensus hybrid strategies. [ABSTRACT FROM AUTHOR]

A bargaining game is used to develop feedback mechanism for dynamic social networks group decision making (SN-GDM). The dynamic trust relationships between experts are updated by the change of their consensus state after each round of interaction. Then, a maximum entropy model based on individual interactive relationship and fairness is established to determine the comprehensive weight of each expert, which considers: (1) the individual weight by influence of expert; (2) the interaction weight by social relationships of experts. Hence, 2-tuple linguistic collective evaluation matrix of the 2-additive Choquet integral under Möbius transform is put forward. Further, the equilibrium solution of two experts in the bargaining game is established, and then this equilibrium recommendation will be accepted by both experts. Consequently, a bargaining game based feedback mechanism driven by trust relationship is proposed to reflect the interaction behaviors between the inconsistent expert and her/his most trusted consistent one, and therefore the recommendation advices are generated for them to promote consensus in SN-GDM. Finally, a sustainable supplier selection example demonstrates the effectiveness of the proposed approach. • The dynamic trust relationship is updated by new consensus state. • A maximum entropy model is proposed to assign expert weight. • The bargaining game based feedback mechanism is put forward. [ABSTRACT FROM AUTHOR]

The mathematical modelling and representation of Tanino’s multiplicative transitivity property to the case of intuitionistic reciprocal preference relations (IRPRs) is derived via Zadeh’s extension principle and the representation theorem of fuzzy sets. This result guarantees the correct generalisation of the multiplicative transitivity property of reciprocal preference relations (RPRs), and it allows the multiplicative consistency (MC) property of IRPRs to be defined. The MC property used in decision making problems is threefold: (1) to develop a consistency based procedure to estimate missing values in IRPRs using an indirect chain of alternatives; (2) to quantify the consistency index (CI) of preferences provided by experts; and (3) to build a novel consistency based induced ordered weighted averaging (MC-IOWA) operator that associates a higher contribution in the aggregated value to the more consistent information. These three uses are implemented in developing a consensus model for GDM problems with incomplete IRPRs in which the level of agreement between the experts’ individual IRPRs and the collective IRPR, which is referred here as the proximity index (PI), is combined with the CI to design a feedback mechanism to support experts to change some of their preference values using simple advice rules that aim at increasing the level of agreement while, at the same time, keeping a high degree of consistency. In the presence of missing information, the feedback mechanism implements the consistency based procedure to produce appropriate estimate values of the missing ones based on the given information provided by the experts. Under the assumption of constant CI values, the feedback mechanism is proved to converge to unanimous consensus when all experts are provided with recommendations and these are fully implemented. Additionally, visual representation of experts’ consensus position within the group before and after implementing their feedback advice is also provided, which help an expert to revisit his evaluations and make changes if considered appropriate to achieve a higher consensus level. Finally, an IRPR fuzzy majority based quantifier-guided non-dominance degree based prioritisation method using the associated score reciprocal preference relation is proposed to obtain the final solution of consensus. [ABSTRACT FROM AUTHOR]

The judgments of decision-makers are frequently the best way to process the information on complex alternatives. However, the performances of the alternatives are often not observable in their entirety, which prevents researchers from conducting controlled empirical studies. This paper justifies a functional representation that, due to its good predictive results, has been widely used ad hoc in studies in different branches of knowledge; it formalizes aspects of the human mental structure that influence the ability of people to decide and the intentional bounded rationality, and it subsequently analyzes how the reliability of decision-makers is affected by the difficulty of the problem and the expertise and beliefs of the decision-maker. The main research objective of this paper is to derive explicitly a general functional form that represents the behavior of a decision-maker linked to their way of thinking. This functional form allows a laboratory to be created to study a priori the performance of human decisions, i.e., the probability of choosing each of the alternatives, once the returns of the alternatives, the level of expertise, and the initial beliefs of the decision-maker are known exogenously. This laboratory will allow (1) the evaluation of decision support techniques; (2) the creation of agent-based models that anticipate group performances due to individual interactions; and (3) the development of other investigations based on statistical simulations. [ABSTRACT FROM AUTHOR]

This paper proposes a consensus-trust driven framework of bidirectional interaction for social network large-group decision making. Firstly, the concepts of interaction consensus threshold and interaction trust threshold are defined, which are used to discriminate the interaction modes between subgroups into four categories. Corresponding hybrid feedback strategies are designed in which the consensus level and trust level of subgroups are regarded as reliable resources to facilitate the achievement of group consensus. Secondly, a minimum adjustment bidirectional feedback model considering cohesion is developed to help the interacting subgroups reach mutual consensus with minimum opinion modification. Finally, the proposed consensus framework is applied to a blockchain platform selection problem in supply chain to demonstrate the effectiveness and applicability of the model. [ABSTRACT FROM AUTHOR]

Abstract: A social network analysis (SNA) trust–consensus based group decision making model with interval-valued fuzzy reciprocal preference relation (IFRPR) is investigated. The main novelty of this model is that it determines the importance degree of experts by combining two reliable resources: trust degree (TD) and consensus level (CL). To do that, an interval-valued fuzzy SNA methodology to represent and model trust relationship between experts and to compute the trust degree of each expert is developed. The multiplicative consistency property of IFRPR is also investigated, and the consistency indexes for the three different levels of an IFRPR are defined. Additionally, similarity indexes of IFRPR are defined to measure the level of agreement among the group of experts. The consensus level is derived by combining both the consistency index and similarity index, and it is used to guide a feedback mechanism to support experts in changing their opinions to achieve a consensus solution with a high degree of consistency. Finally, a quantifier guided non-dominance possibility degree (QGNDPD) based prioritisation method to derive the final trust–consensus based solution is proposed. [Copyright &y& Elsevier]

Execution tracing is a tool used in the course of software development and software maintenance to identify the internal routes of execution and state changes while the software operates. Its quality has a high influence on the duration of the analysis required to locate software faults. Nevertheless, execution tracing quality has not been described by a quality model, which is an impediment while measuring software product quality. In addition, such a model needs to consider uncertainty, as the underlying factors involve human analysis and assessment. The goal of this study is to address both issues and to fill the gap by defining a quality model for execution tracing. The data collection was conducted on a defined study population with the inclusion of software professionals to consider their accumulated experiences; moreover, the data were processed by genetic algorithms to identify the linguistic rules of a fuzzy inference system. The linguistic rules constitute a human-interpretable rule set that offers further insights into the problem domain. The study found that the quality properties accuracy, design and implementation have the strongest impact on the quality of execution tracing, while the property legibility is necessary but not completely inevitable. Furthermore, the quality property security shows adverse effects on the quality of execution tracing, but its presence is required to some extent to avoid leaking information and to satisfy legal expectations. The created model is able to describe execution tracing quality appropriately. In future work, the researchers plan to link the constructed quality model to overall software product quality frameworks to consider execution tracing quality with regard to software product quality as a whole. In addition, the simplification of the mathematically complex model is also planned to ensure an easy-to-tailor approach to specific application domains. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the problem of choosing the most appropriate classification from a given set of classifications of a set of patterns. This is a relevant topic on unsupervised systems and clustering analysis because different classifications can in general be obtained from the same data set. The provided methodology is based on five fuzzy criteria which are aggregated using an Ordered Weighted Averaging (OWA) operator. To this end, a novel multi-criteria decision making (MCDM) system is defined, which assesses the degree up to which each criterion is met by all classifications. The corresponding single evaluations are then proposed to be aggregated into a collective one by means of an OWA operator guided by a fuzzy linguistic quantifier, which is used to implement the concept of fuzzy majority in the selection process. This new methodology is applied to a real marketing case based on a business to business (B2B) environment to help marketing experts during the segmentation process. As a result, a segmentation containing three segments consisting of 35, 98 and 127 points of sale respectively is selected to be the most suitable to endorse marketing strategies of the firm. Finally, an analysis of the managerial implications of the proposed methodology solution is provided. [Copyright &y& Elsevier]

Abstract: A novel intuitionistic fuzzy set (IFS) score function and an intuitionistic fuzzy preference relation (IFPR) quantifier guided non-dominance based prioritisation method are introduced. Based on Yager’s continuous OWA (COWA) operator, the interval-valued intuitionistic fuzzy COWA (IVIF-COWA) operator is defined, and a new attitudinal expected score function for interval-valued intuitionistic fuzzy numbers (IVIFNs) is introduced. The novelty of this attitudinal expected score function is that it allows the comparison of IVIFNs by taking into account of the decision makers’ attitudinal character. Moreover, we show that the new attitudinal expected score function extends: (i) the IFS score function introduced in this paper, which is mathematically equivalent to Chen and Tan’s score function ; and (ii) Xu and Chen’s score function for IVIFNs . Using the proposed score functions, a method is developed to construct FPRs from a given IFPR and IVIFPR, respectively. When the hesitancy degree function is null, we prove that the score FPRs coincide with their respective IFPR and IVIFPR. Finally, a ranking sensitivity analysis of the attitudinal expected score function with respect to the attitudinal parameter is provided. [Copyright &y& Elsevier]

Abstract: For intuitionistic fuzzy sets, it is argued that three dimensional distance functions are not necessary because two dimensional distance functions already provide a simple and concise expression of the distance between two intuitionistic fuzzy sets. However, we show that a three dimensional interpretation of intuitionistic fuzzy sets could give different comparison results to the ones obtained with their two dimensional counterparts. In addition to the existing distances, we define a three dimensional Hausdorff distance and compare its consistency with its two dimensional counterpart, which shows the usefulness of the three dimensional functions to model and provide the expression of the distance between two intuitionistic fuzzy sets. [Copyright &y& Elsevier]

This article investigates multiplicative consistency ascertaining, inconsistency repairing, and weights derivation for hesitant multiplicative preference relations (HMPRs). First, the completely multiplicative consistency and weakly multiplicative consistency of HMPRs are defined. Based on them, 0–1 mixed programming models and simple algebraic operations are proposed to ascertain the multiplicative consistency of HMPRs. Then, some goal programming models are developed to generate the weights from consistent HMPRs and to revise inconsistent HMPRs. An integrated procedure to manage the multiplicative consistencies of HMPRs is designed. The proposed methods are also extended to accommodate incomplete HMPRs, and to estimate missing values. Finally, some numerical examples, a comparative analysis with existent approaches, and a simulation analysis are included to illustrate the practicality and effectiveness of the developed models. [ABSTRACT FROM AUTHOR]

This note analyzes two methods for calculating missing values of an incomplete reciprocal fuzzy preference relation. The first method by Herrera-Viedma et al. appeared in the IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS [vol. 37, no. 1(2007) 176-1891, while the second one by Fedrizzi and Giove appeared later in the European Journal of Operational Research [vol. 183 (2007) 303-313]. The underlying concept driving both methods is the additive consistency property. We show that both methods, although different, are very similar. Both methods derive the same estimated values for the independent-missing-comparison case, while they differ in the dependent-missing-comparison case. However, it is shown that a modification of the first method coincides with the second one. Regarding the total reconstruction of an incomplete preference relation, it is true that the second method performs worse than the first one. When Herrera-Viedma et al.'s method is unsuccessful, Fedrizzi-Giove's method is as well. However, in those cases when Fedrizzi-Giove's method cannot guarantee the successful reconstruction of an incomplete preference relation, we have that Herrera-Viedma et al.'s method can. These results lead us to claim that both methods should be seen as complementary rather than competitors in their application, and as such, we propose a reconstruction policy of incomplete fuzzy preference relations using both methods. By doing this, the only unsuccessful reconstruction case is when there is a chain of missing pairwise comparisons involving each one of the feasible alternatives at least once. [ABSTRACT FROM AUTHOR]

Abstract: The OWA operator proposed by Yager has been widely used to aggregate experts’ opinions or preferences in human decision making. Yager''s traditional OWA operator focuses exclusively on the aggregation of crisp numbers. However, experts usually tend to express their opinions or preferences in a very natural way via linguistic terms. These linguistic terms can be modelled or expressed by (type-1) fuzzy sets. In this paper, we define a new type of OWA operator, the type-1 OWA operator that works as an uncertain OWA operator to aggregate type-1 fuzzy sets with type-1 fuzzy weights, which can be used to aggregate the linguistic opinions or preferences in human decision making with linguistic weights. The procedure for performing type-1 OWA operations is analysed. In order to identify the linguistic weights associated to the type-1 OWA operator, type-2 linguistic quantifiers are proposed. The problem of how to derive linguistic weights used in type-1 OWA aggregation given such type of quantifier is solved. Examples are provided to illustrate the proposed concepts. [Copyright &y& Elsevier]

Dealing with incomplete information is an important problem in decision making. In this paper, we present a short discussion on this topic and a new estimation method of missing values in an incomplete fuzzy preference relation which is based on the modelling of consistency of preferences via a representable uninorm. [ABSTRACT FROM AUTHOR]

In group decision making (GDM) processes, prior to the selection of the best alternative(s), it would be desirable that experts achieve a high degree of consensus or agreement between them. Due to the complexity of most decision making problems, individuals' preferences may not satisfy formal properties. ‘Consistency’ is one of such properties, and it is associated with the transitivity property. Obviously, when carrying out a rational decision making, consistent information, i.e. information which does not imply any kind of contradiction, is more appropriate than information containing some contradictions. Therefore, in a GDM process, consistency should also be sought after. In this paper we present a consensus model for GDM problems that proceeds from consistency to consensus. This model integrates a novel consistency reaching module based on consistency measures. In particular, the model generates advice on how experts should change their preferences in order to increase their consistency. Also, the consensus model is considered adaptive because the search for consensus is adapted to the level of agreement achieved at each consensus round. [ABSTRACT FROM AUTHOR]

In decision-making problems there may be cases in which experts do not have an in-depth knowledge of the problem to be solved. In such cases, experts may not put their opinion forward about certain aspects of the problem, and as a result they may present incomplete preferences, i.e., some preference values may not be given or may be missing. In this paper, we present a new model for group decision making in which experts' preferences can be expressed as incomplete fuzzy preference relations. As part of this decision model, we propose an iterative procedure to estimate the missing information in an expert's incomplete fuzzy preference relation. This procedure is guided by the additive-consistency (AC) property and only uses the preference values the expert provides. The AC property is also used to measure the level of consistency of the information provided by the experts and also to propose a new induced ordered weighted averaging (IOWA) operator, the AC-IOWA operator, which permits the aggregation of the experts' preferences in such a way that more importance is given to the most consistent ones. Finally, the selection of the solution set of alternatives according to the fuzzy majority of the experts is based on two quantifier-guided choice degrees: the dominance and the nondominance degree. [ABSTRACT FROM AUTHOR]

Qualified Securities for Short-sale Refinancing (QSSR) is a unique trading mechanism that has exogenously increased the supply of loanable securities in Chinese stock markets. Using difference-in-differences (DID) methodology, this paper is the first to investigate whether and to what extent additions to the QSSR eligibility list affect short selling activities and stock price behaviors. The paper finds that stocks added to the QSSR list exhibit better liquidity and less negative skewness in returns than non-QSSR stocks. However, QSSR stocks are more volatile and display a higher frequency of extreme negative returns. In addition, on average, QSSR stocks experience larger negative abnormal returns (ARs) and cumulative abnormal returns (CARs) relative to non-QSSR stocks, and the difference in CARs is positively related to investor heterogeneity. The results indicate that short selling has mixed effects on stock prices. Removing short-sale constraints can improve liquidity and reduce price bubbles, but can also increase return volatility and amplify market crashes. [ABSTRACT FROM AUTHOR]

This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of the fuzzy set (FS), but it also includes the concepts of the intuitionistic fuzzy set (IFS), the Pythagorean fuzzy set (PFS) and the p-rung orthopair fuzzy set (p-ROFS). In order to explore the features of the E-FS concept, set and algebraic operations on E-FSs, average and geometric operations of E-FSs are studied and an E-FS score function is defined. The superiority of the E-FS concept is further confirmed with a score-based decision making technique in which the concepts of FS, IFS, PFS and p-ROFS do not make sense. [ABSTRACT FROM AUTHOR]