Some Issues on Incomplete Fuzzy Preference Relations

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Project title

Code/計畫編號

NSC96-2416-H019-004-MY2

Translated Name/計畫中文名

不完整模糊偏好關係之研究

Project Coordinator/計畫主持人

Hsuan-Shih Lee

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Shipping and Transportation Management

Website

https://www.grb.gov.tw/search/planDetail?id=1616926

Year

2008

Start date/計畫起

01-08-2008

Expected Completion/計畫迄

31-07-2009

Bugetid/研究經費

907千元

ResearchField/研究領域

管理科學

" 模糊偏好關係一直是決策者表達方案偏好非常好的工具之一，也引起了研究學者很多的注意。Z. S. Xu 與Enrique Herrera-Viedma 是這個領域中非常活躍的研究學者。最近，他們發表了兩篇論文，處理不完整模糊偏好關係，亦即關係中有些元素是未知的。Xu 試圖運用目標規劃方法直接由不完整模糊偏好關係決定方案之優先權重。然而，Xu 所提之定義並不健全，用以建立數學規劃模式之偏好關係與優勢向量對應關係式也不正確。E. Herrera-Viedma 等人試圖依據加法遞移性，由不完整模糊偏好關係建構一完整模糊偏好關係。他們發展出三項未知元素推估算式，並且提出一個足以推估出完整模糊偏好關係之充分條件。我們發現尚存在其他推估算式，以及推估出完整模糊偏好關係之充分且必要條件。此外，Xu 與E. Herrera-Viedma 等人的論文中，只考慮區間尺度。在AHP 中，採用的是比例尺度。如何將相關研究成果推展至偏好關係值係由比例尺度表示之不完整模糊偏好關係上是一項重要的議題。在本研究計畫裏，我們將對這些議題加以探討。 "" Fuzzy preference relation has been one of the promising tools for conveying the preference of decision makers in regards to alternatives and drawn a lot of attentions from researchers. Z. S. Xu and Enrique Herrera-Viedma are active researchers in this area. Recently, they have published two papers to deal with incomplete fuzzy preference relations where some entries are unknown. Xu tried to prioritize alternatives directly from the incomplete fuzzy preference relation with goal programming method. However, the definitions he provided are not robust and the equation for establishing the programming model is incorrect. On the other hand, E. Herrera-Viedma et al. tried to construct complete fuzzy preference relation from an incomplete one. E. Herrera-Viedma et al. have developed three equations to estimate unknown entries based on additive transitivity. A sufficient condition for an incomplete fuzzy preference relation to be completed was also given in their paper. We find that there exit other estimation equation and a necessary and sufficient condition for an incomplete fuzzy preference relation to be completed. Furthermore, in the papers of Xu and E. Herrera-Viedma et al. only interval scales are considered. In AHP, ratio scales are assumed. How to extend the results of incomplete fuzzy preference relations consisting of interval scales to the cases where preference values are in terms of ratio scales is an important issue. All these issues are going to be addressed in this project. "

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Some Issues on Incomplete Fuzzy Preference Relations

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