Associated Probabilities’ Aggregations in Fuzzy Collaborative Filtering Recommender System Prediction

In this article, the expert evaluations transformed in the multi-attribute decision-making (MADM) model are presented in the discrimination q-rung picture linguistic fuzzy numbers (q-RPLFNs). In the construction of a second-order additive fuzzy measure (TOAFM) the attributes’ interaction indexes and Shapley values are taken into account. The Shapley entropy maximum principle for identification of associated probabilities class (APC) of a TOAFM is constructed. Based on the APC of the TOAFM, a new aggregation operators’ class is constructed which represents some hybrid extensions of ordered weighted averaging (OWA), geometric (OWG), the Choquet integral averaging (CA) and geometric (CG) operators under discrimination q-rung orthopair fuzzy (q-ROF) and q-rung picture linguistic fuzzy (q-RPLF) information. These operators, constructed for the q-RPLF and q-ROF environments, take into account the overall pair interactions among attributes. Main properties on the correctness of extensions are proved: for the lower and upper capacities of order 2, all constructed operators consequently coincide with q-ROF and q-RPLF Choquet averaging and geometric operators, respectively. Constructed operators in the evaluation of prediction of fuzzy Collaborative Filtering Recommender Systems (CFRS) are used. New symmetric discrimination measures as some extensions of discrimination measures for the fuzzy CFRS are proposed. Users’ profile data by the constructed operators in the new similarity measure under q-rung picture linguistic environment are aggregated. The developed new approach is schematically described in such a way that it can be “embedded” in any existing CFRS model. An example is given to illustrate the results, for which the software designed to aggregate profile data for similarity comparison provides the use of new and well-known classical aggregation operators.