Transcript 下載/瀏覽

2nd 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
the corresponding intervals:
– corresponding intervals for
denoted by
– corresponding intervals for
denoted by
• Assume y is Fuzzy weight average function
,within
• 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
• We have
, since
and
• Define upper bond and lower bond for each
while
where
and
interval being
Take the Napierian logarithm for
So we get
and
2. Where
We have
and
, since
and