2 nd PRESENTATION Generalized mean operator Yuh-Yuan Guh, Rung-Wei Po, E. Stanley Lee Generalized mean operator Prof. Ta Chung Chu Student: Santiwatthana Charindech (AOR, 陳正德 ) Chen Chih-Kai ( 陳智凱 )

Generalized mean operator In this study the researcher considered the aggregation step as a fuzzy variable and uses generalized means function to fuzzify the aggregation operator With operation means operator, the model can flexibly reflect any DM’s evaluation attitude and also the model can make an objective evaluation that approaches a real decision making situation.

Fuzzy weight average within a generalized means function Here score ( ) and weight ( ) are fuzzy number, for each,within the corresponding intervals: – corresponding intervals for denoted by Assume y is Fuzzy weight average function The Fuzzy weight average function with generalized mean operator can be denoted by:

while, the minimum operator, the harmonic mean operator, the geometric mean operator, the arithmetic mean operator, the maximum operator. The weighted generalized mean operator is one kind of averaging operator by varying the parameter value p, the weighted generalized means operator can produce various different aggregation operators We make use different values of p to enumerate different decision attitudes for the DM. For example, if the DM takes a more open attitude in evaluation, this implies that a higher value p should be adopted for the weighted generalized means function, and the function will give a higher aggregated index toward the maximum value that the function can produce

Consider the influence of value p on a generalized mean function 1. Where, since and We have Define upper bond and lower bond for each interval being while where and

Take the Napierian logarithm for and So we get

2. Where, since and We have and