Yager presented the Ordered Weighted Averaging (OWA) operator to provide a method for aggregating information of decision-making. Yager and Filev further presented the Induced Ordered Weighted Averaging (IOWA) operato...Yager presented the Ordered Weighted Averaging (OWA) operator to provide a method for aggregating information of decision-making. Yager and Filev further presented the Induced Ordered Weighted Averaging (IOWA) operator. In this paper, we propose a Generalized Induced Ordered Weighted Geometric (GIOWG) operator and establish a simple objective-programming model to learn the associated weighting vector from observational data. Each object processed by the GIOWG operator consists of three components, where the first component represents the importance degree or character of the second component, and the second component is used to induce an ordering, through the first component, over the third components which are then aggregated. The desirable properties, such as commutativity, idempotency and monotonicity, etc., associated wlth the GIOWG operator are studied in detail, and some numerical examples are given to show the practicality and effectiveness of the developed operator.展开更多
文摘Yager presented the Ordered Weighted Averaging (OWA) operator to provide a method for aggregating information of decision-making. Yager and Filev further presented the Induced Ordered Weighted Averaging (IOWA) operator. In this paper, we propose a Generalized Induced Ordered Weighted Geometric (GIOWG) operator and establish a simple objective-programming model to learn the associated weighting vector from observational data. Each object processed by the GIOWG operator consists of three components, where the first component represents the importance degree or character of the second component, and the second component is used to induce an ordering, through the first component, over the third components which are then aggregated. The desirable properties, such as commutativity, idempotency and monotonicity, etc., associated wlth the GIOWG operator are studied in detail, and some numerical examples are given to show the practicality and effectiveness of the developed operator.
