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Top1. Introduction
Recommender system (RS) (Michael et al., 2011) plays a very important role in all areas of life. It responds well to the needs of users in finding information in diverse forms and variations. The traditional recommender systems (Badrul et al., 2001; Michael et al., 2011; Michael, 2007) are based on historical and user preferences. However, as the data are getting popularity and diversity, many criteria in the system are used to select the desired information; thus, raising the question of utilizing appropriate decision-making operations for interactive multi-criteria collaborative filtering recommender system (Dat et al., 2019)(Thong et al., 2019). If the relationship of important criteria is considered, the decision will give more feasible results. Over the last few years, multi-criteria recommender systems have been considered (Tri et al., 2017; Tri et al., 2018a; Tri et al., 2018b; Tri et al., 2018c). Collaborative filtering models make recommendation based on key users which are specified by the interactive multi-criteria decision with the ordered weighted averaging operator (Anath et al., 2015). Weights are assigned for important level (Naime & Sasan, 2017; Soumana et al., 2017; Yong, 2017). Mathematical operations for the rankings are specified by the weights and ratings of the user for each product (Abderrahmane et al., 2019; Ferdaous et al., 2017). However, it is impossible to comprehensively evaluate the resonance relationship of criteria to make accurate decision. It can be observed that with the decision to use Arithmetic mean, Geometric mean, and Harmonic average (Tri et al., 2017), the value of each criterion is separate in the calculation which does not affect those of the others. When using the Order Weighted Average Operator (Tri et al., 2018b), the result is the combination of those of many criteria but in isolation manners. Recommender system focuses on applying artificial neural network (Mohamed & Mohammed, 2017; Mohamed & Mohammed, 2018), machine learning (Mehrbakhsh et al., 2017; Vibhor et al., 2017), clustering (Mohammed & Rashid, 2018), and Genetic Algorithm (Esteban et al., 2019) and others (Sahu et al., 2019).
The recent recommender systems have focused on multi-criteria recommendation from a variety of data sources with weights of each criterion (Abdel-Basset et al., 2020)(Selvachandran et al., 2019)(Ngan et al., 2020)(Milica, 2013)(Giang et al., 2019)(Son et al., 2019). The technique has improved the accuracy in advisory of recent recommender systems and made their advice more and more satisfying to users' requirements. However, the criteria in recommender systems are considered to be independent of each other. Because there is no relationship between them, when a criteria changes, it does not affect the other criteria. But the reality is opposite because some criteria can affect the weights of the others. This impact has a great influence on the actual desire of the user, which the recommender system needs to address. In essence, there are always hidden relationships and influences that influencing each other. Therefore, when making a decision, it is necessary to fully calculate the interaction of the criteria for effective results. One of the methods for determining the correlation between criteria is the Choquet integral. The integral is a non-additive integral of a function with respect to a capacity based on the fuzzy measure. In recommender systems, it can be used for assigning importance to all possible groups of criteria, and thus offers a much greater flexibility for aggregation. The biggest advantage of Choquet integral which is considering the interaction between all possible combinations of criteria are applied in recommender systems to enhance the basis for consultation.