王進賢952221E230018

王進賢952221E230018

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1 On Weighted P-Quantile Aggregation Jongyun Hao 1,* , Jin-Hsien Wang 2 1 Department of Applied Science, Chinese Naval Academy, Kaohsiung, Taiwan, R.O.C. 2 Department of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung, Taiwan, R.O.C. *e-mail: jongyun@mail.cna.edu.tw We consider the problem of aggregating ordinal information with quantitative or qualitative importance based on quantile operations. For bag n x x x , , , 2 1 in real or in (finite) ordinal scales, the quantile operations used in this article are operating based on the floating position index of i x that is determined by its position on the ordered sequence ) , , , ( ) ( ) 2 ( ) 1 ( n x x x , where ) ( i x is the i-th smallest element of the bag n x x x , , , 2 1 . We call this type quantile aggregation the floating position index-based quantile (p-quantile) aggregation. We study on weighted p-quantile aggregation in real scales and extend the corresponding techniques to p-quantile aggregation of ordinal information with quantitative importance. The aggregated result of the latter is represented by a general ordinal proportional 2-tuple. Based on the notion of importance transformation (that is modified from Yager s), we investigate p-quantile aggregation of ordinal information with qualitative importance. Then we use p-quantile aggregation to define floating position index-based ordered weighted averaging (P-OWA) aggregation of ordinal information with qualitative importance and apply it to the problem of multicriteria decision making.
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2 1. INTRODICTION The concept of ordered weighted averaging (OWA) was introduced by Yager 1 in 1988 as a method for aggregating information in the problem of multicriteria decision making (MCDM). It is defined based on product and addition, two operations that do not apply to (finite) ordinal scales. Later on, in Ref. 2, the concept of ordinal OWA operators was introduced based on max and min operations. To overcome the operation limitation for ordinal OWA, on the one hand, researchers had developed various tools to define different versions of ordinal OWA. For examples, based on so called smooth t-conorm, Godo and Torra 3 defined ordered weighted means on (finite) ordinal scales related to integer weights their results were generalized by Calvo and Mesiar 4 , and, based on (translational) 2-tuple representation, Herrera and Martínez 5 defined OWA aggregation of linguistic (ordinal) information such that the aggregated result is not represented by a single ordinal but by an ordinal 2-tuple their results were generalized by Wang and Hao 6 , among others. On the other hand, considering the median operator as the ordinal counterpart of the arithmetic mean, researchers had developed weighted median 7 , median-based 8 and median-like 9 aggregation to replace the role of OWA as a mean operator with compensation in the ordinal contexts. In this article we address to the topic on the aggregation of weighted ordinal information.
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王進賢952221E230018

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