Received two pieces of good news today, with a new paper submitted to Knowledge-Based Systems having been accepted and also an update of our contribution to the Recommender Systems Handbook.
Title: A penalty-based aggregation operator for non-convex intervals
Authors: G. Beliakov and S. James
In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets, and other new domains pose a number of difficulties.
The aggregation of non-convex or discontinuous intervals is usually approached in line with the extension principle, i.e. by aggregating all real-valued input vectors lying within the interval boundaries and taking the union as the final output. Although this is consistent with the aggregation of convex interval inputs, in the non-convex case such operators are not idempotent and may result in outputs which do not faithfully summarize or represent the set of inputs. After giving an overview of the treatment of non-convex intervals and their associated interpretations, we propose a novel extension of the arithmetic mean based on penalty functions that provides a representative output and satisfies idempotency.
Title: Aggregation functions for recommender systems (in Recommender Systems Handbook, 2nd Ed. by Springer)
Authors: G. Beliakov, T. Calo and S. James
This chapter gives an overview of aggregation functions and their use in recommender systems. The classical weighted average lies at the heart of various recommendation mechanisms, often being employed to combine item feature scores or predict ratings from similar users. Some improvements to accuracy and robustness can be achieved by aggregating different measures of similarity or using an average of recommendations obtained through different techniques. Advances made in the theory of aggregation functions therefore have the potential to deliver increased performance to many recommender systems. We provide definitions of some important families and properties, sophisticated methods of construction, and various examples of aggregation functions in the domain of recommender systems.