A New Approach for Fairness Increment of Consensus-driven Group Recommender Systems Based on Choquet Integral

It has been witnessed in recent years for the rising of Group recommender systems (GRSs) in most e-commerce and tourism applications like Booking.com, Traveloka.com, Amazon, etc. One of the most concerned problems in GRSs is to guarantee the fairness between users in a group so-called the consensus-driven group recommender system. This paper proposes a new flexible alternative that embeds a fuzzy measure to aggregation operators of consensus process to improve fairness of group recommendation and deals with group member interaction. Choquet integral is used to build a fuzzy measure based on group member interactions and to seek a better fairness recommendation. The empirical results on the benchmark datasets show the incremental advances of the proposal for dealing with group member interactions and the issue of fairness in Consensus-driven GRS.

A multi-criterion group decision-making method based on regret theory under 2-tuple linguistic environment

PurposeThe purpose of this paper is to develop a multi-criterion group decision-making (MCGDM) method by combining the regret theory and the Choquet integral under 2-tuple linguistic environment and apply the proposed method to deal with the supplier selection problem.Design/methodology/approachWhen making a decision, the decision-maker is more willing to choose the alternative(s) which is preferred by the experts so as to avoid the regret. At the same time, the correlative relationships among the criterion set can be sufficiently described by the fuzzy measures, later the evaluations of a group of criteria can be aggregated by means of the Choquet integral. Hence, the authors cope with the MCGDM problems by combining the regret theory and the Choquet integral, where the fuzzy measures of criteria are partly known or completely unknown and the evaluations are expressed by 2-tuples. The vertical and the horizontal regret-rejoice functions are defined at first. Then, a model aiming to determine the missing fuzzy measures is constructed. Based on which, an MCGDM method is proposed. The proposed method is applied to tackle a practical decision-making problem to verify its feasibility and the effectiveness.FindingsThe vertical and the horizontal regret-rejoice functions are defined. The relationships of the fuzzy measures are expressed by the sets. A model is built for determining the fuzzy measures. Based on which, an MCGDM method is proposed. The results show that the proposed method can solve the MCGDM problems within the context of 2-tuple, where the decision-maker avoids the regret and the criteria are correlative.Originality/valueThe paper proposes an MCGDM method by combining the regret theory and the Choquet integral, which is suitable for dealing with a variety of decision-making problems.

Associated probabilities aggregations in multistage investment decision-making

PurposeThe attributes that influence the selection of applicants and the relevant crediting decisions are naturally distinguished by interactions and interdependencies. A new method of possibilistic discrimination analysis (MPDA) was developed for the second stage to address this phenomenon. The method generates positive and negative discrimination measures for each alternative applicant in relation to a particular attribute. The obtained discrimination pair reflects the interaction of attributes and represents intuitionistic fuzzy numbers (IFNs). For the aggregation of applicant's discrimination intuitionistic fuzzy assessments (with respect to attributes), new intuitionistic aggregation operators, such as AsP-IFOWA and AsP-IFOWG, are defined and studied. The new operators are certain extensions of the well-known Choquet integral and Yager OWA operators. The extensions, in contrast to the Choquet aggregation, take into account all possible interactions of the attributes by introducing associated probabilities of a fuzzy measure.Design/methodology/approachFor optimal planning of investments distribution and decreasing of credit risks, it is crucial to have selected projects ranked within deeply detailed investment model. To achieve this, a new approach developed in this article involves three stages. The first stage is to reduce a possibly large number of applicants for credit, and here, the method of expertons is used. At the second stage, a model of improved decisions is built, which reduces the risks of decision making. In this model, as it is in multi-attribute decision-making (MADM) + multi-objective decision-making (MODM), expert evaluations are presented in terms of utility, gain, and more. At the third stage, the authors construct the bi-criteria discrete intuitionistic fuzzy optimization problem for making the most profitable investment portfolio with new criterion: 1) Maximization of total ranking index of selected applicants' group and classical criterion and 2) Maximization of total profit of selected applicants' group.FindingsThe example gives the Pareto fronts obtained by both new operators, the Choquet integral and Yager OWA operators also well-known TOPSIS approach, for selecting applicants and awarding credits. For a fuzzy measure, the possibility measure defined on the expert evaluations of attributes is taken.Originality/valueThe comparative analysis identifies the applicants who will receive the funding sequentially based on crediting resources and their requirements. It has become apparent that the use of the new criterion has given more credibility to applicants in making optimal credit decisions in the environment of extended new operators, where the phenomenon of interaction of all attributes was also taken into account.

Recognition of Electroencephalography-Related Features of Neuronal Network Organization in Patients With Schizophrenia Using the Generalized Choquet Integrals

In this study, we focused on the verification of suitable aggregation operators enabling accurate differentiation of selected neurophysiological features extracted from resting-state electroencephalographic recordings of patients who were diagnosed with schizophrenia (SZ) or healthy controls (HC). We built the Choquet integral-based operators using traditional classification results as an input to the procedure of establishing the fuzzy measure densities. The dataset applied in the study was a collection of variables characterizing the organization of the neural networks computed using the minimum spanning tree (MST) algorithms obtained from signal-spaced functional connectivity indicators and calculated separately for predefined frequency bands using classical linear Granger causality (GC) measure. In the series of numerical experiments, we reported the results of classification obtained using numerous generalizations of the Choquet integral and other aggregation functions, which were tested to find the most appropriate ones. The obtained results demonstrate that the classification accuracy can be increased by 1.81% using the extended versions of the Choquet integral called in the literature, namely, generalized Choquet integral or pre-aggregation operators.

Using the Choquet Integral for the Determination of the Anxiety Degree

This paper introduces a mathematical model describing how the EEG type waves are processed in order to characterize the level of anxiety. The electroencephalogram (EEG) is a recording of the electrical activity of the brain. The main frequencies of the human EEG waves are: Delta, Theta, Alpha (Low Alpha and High Alpha), Beta (Low Beta and High Beta), Gamma. Psychologists' studies show that there is an interactive relationship between anxiety and two factors in the Big Five theory, namely, extraversion and neuroticism. The specialists in psychology state that the anxiety is characterized by LowAlpha, HighAlpha, LowBeta and HighBeta waves. In this regard, we developed a mathematical model through which EEG waves are processed in order to determine the level of anxiety. Our main idea is to use the Choquet integral with respect to a suitable monotone measure in order to characterize the level of anxiety. This measure was obtained using the measurements of the values of EEG waves made on 70 subjects and the corresponding levels of anxiety (established by psychologists) of these subjects. In order to verify our mathematical model (aggregation tool) we used it to determine the level of anxiety of 10 other subjects, comparing our results with the results provided by psychologists (the comparison validated our results).

Standards for the Weighting of Criteria and the Measurement of Interaction

This article discusses the need for standards for the assignment of importance to criteria and the measurement of interaction between them in multiple criteria analyses of complex systems. A strategy for criteria evaluation is considered that is suitable to account for the interaction among a wide variety of imprecisely assessed criteria applied simultaneously. It is based on the results of collecting sample information on preferences according to the specified criteria instead of merely an abstract comparison of the criteria. The comparison of alternatives is based on objectives that determine the formation of preferences. It is facilitated by a rating in terms of preference probabilities. Probabilistic standards grant homogeneity of measurements by different criteria, which is useful for the combination of the criteria. These standards apply to a sampling evaluation conducted via pairwise trichotomic comparison of the alternatives according to each criterion, followed by the combination of these multiple evaluations into a single global score by means of the Choquet Integral with respect to a capacity determined by applying preference concentration to the sets of probabilistic assessments. Examples of practical application are discussed.