On the properties of parametric geometric OWA operator

Classical collaborative filtering algorithms generate recommendations on the basis of ratings provided by users that express their subjective preference on concrete items. The correlation of ratings is used in such schemes as an implicit measure of common interest between users, that is used to predict ratings, so that these ratings determine recommendations. The common formulae used for the computation of predicted ratings use standard weighted averaging schemes as the fixed aggregation mechanism that determines the result of the prediction. Nonetheless, the surrounding context of these rating systems suggest that an approach considering a degree of group consensus in the aggregation process may better capture the essence of the "word-of-mouth" philosophy of such systems. This paper reports on the empirical evaluation of such an alternative approach in which OWA operators with different properties are tested against a dataset to search for the better empirical adjustment. The resulting algorithm can be considered as a generalization of the original Pearson formula based algorithm that allows for the fitting of the aggregation behavior to concrete databases of ratings. The results show that for the particular context studied, higher orness degrees reduce overall error measures, especially for high ratings, which are more relevant in recommendation settings. The adjustment procedure can be used as a general-purpose method for the empirical fit of the behavior of collaborative filtering systems. C 2008 Wiley Periodicals, Inc.

show abstract

“…15 Concretely, the operators produced are geometric OWAs (GOWA), which have a fixed ratio q for adjacent weights.…”

Section: The Generalized Prediction Algorithmmentioning

confidence: 99%

Empirical assessment of a collaborative filtering algorithm based on OWA operators

Sicilia

García‐Barriocanal

Sánchez‐Alonso

2008

Int. J. Intell. Syst.

View full text Add to dashboard Cite

show abstract

“…Based on the arithmetic aggregation methods [20][21][22][23][24][25][26][27], Xu [28] and Xu and Yager [29] investigated several new intuitionistic fuzzy arithmetic aggregation operators and intuitionistic fuzzy geometric aggregation operators. Wei et al [30] proposed some intervalvalued hesitant fuzzy aggregation operators: interval-valued 2 Mathematical Problems in Engineering hesitant fuzzy weighted averaging (IVHFWA) operator, interval-valued hesitant fuzzy ordered weighted averaging (IVHFOWA) operator, interval-valued hesitant fuzzy weighted geometric (IVHFWG) operator, interval-valued hesitant fuzzy ordered weighted geometric (IVHFOWG) operator, interval-valued hesitant fuzzy power aggregation operators, interval-valued hesitant fuzzy prioritized weighted average (IVHFPWA) operator, and interval-valued hesitant fuzzy prioritized weighted geometric (IVHFPWG) operator.…”

Section: Introductionmentioning

confidence: 99%

Interval‐Valued Hesitant Fuzzy Multiattribute Group Decision Making Based on Improved Hamacher Aggregation Operators and Continuous Entropy

Liu

Zhou

Zhuang

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Under the interval-valued hesitant fuzzy information environment, we investigate a multiattribute group decision making (MAGDM) method with continuous entropy weights and improved Hamacher information aggregation operators. Firstly, we introduce the axiomatic definition of entropy for interval-valued hesitant fuzzy elements (IVHFEs) and construct a continuous entropy formula on the basis of the continuous ordered weighted averaging (COWA) operator. Then, based on the Hamacher t-norm and t-conorm, the adjusted operational laws for IVHFEs are defined. In order to aggregate interval-valued hesitant fuzzy information, some new improved interval-valued hesitant fuzzy Hamacher aggregation operators are investigated, including the improved interval-valued hesitant fuzzy Hamacher ordered weighted averaging (I-IVHFHOWA) operator and the improved interval-valued hesitant fuzzy Hamacher ordered weighted geometric (I-IVHFHOWG) operator, the desirable properties of which are discussed. In addition, the relationship among these proposed operators is analyzed in detail. Applying the continuous entropy and the proposed operators, an approach to MAGDM is developed. Finally, a numerical example for emergency operating center (EOC) selection is provided, and comparative analyses with existing methods are performed to demonstrate that the proposed approach is both valid and practical to deal with group decision making problems.

show abstract

“…The corresponding orness measure plays an important role in studies of OWA operators [2,3,4,8,9,11,12,13,14,15,21,22,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. The orness measure reflects the or-like or and-like aggregation result of an aggregation function.…”

Section: Introductionmentioning

confidence: 99%