**TITLE**

New Fuzzy Aggregations.

Part II: Associated Probabilities in the Aggregations of the POWA

**PDF**

**KEYWORDS**

mean aggregation operators, fuzzy aggregations, fuzzy measure, capacity of order, associated probabilites, most typical value, Finite Sugeno Averaging, Finite Choquet Averaging, body of evidence, possibility measure, fuzzy numbers, fuzzy decision making.

**ABSTRACT**

The Ordered Weighted Averaging (OWA) operator was introduced by R.R. Yager [58] to provide a method for aggregating inputs that lie between the max and min operators. In this article several variants of the generalizations of the fuzzy-probabilistic OWA operator - POWA (introduced by J.M. Merigo [27,28]) are presented in the environment of fuzzy uncertainty, where different monotone measures (fuzzy measure) are used as an uncertainty measure. The considered monotone measures are: possibility measure, Sugeno −λadditive measure, monotone measure associated with Belief Structure and capacity of order two. New aggregation operators are introduced: AsPOWA and SA-AsPOWA. Some properties of new aggregation operators are proved. Concrete faces of new operators are presented with respect to different monotone measures and mean operators. Concrete operators are induced by the Monotone Expectation (Choquet integral) or Fuzzy Expected Value (Sugeno integral) and the Associated Probability Class (APC) of a monotone measure. For the new operators the information measures – Orness, Entropy, Divergence and Balance are introduced as some extensions of the definitions presented in [28].

**Cite this paper**

Gia Sirbiladze, Otar Badagadze, Gvantsa Tsulaia. (2016) New Fuzzy Aggregations. Part II: Associated Probabilities in the Aggregations of the POWA. *International Journal of Control Systems and Robotics, ***1**, 73-85