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今天小編為您帶來精讀博士論文《廣義乘性偏好資訊下考慮專家共識的多屬性群決策方法》6.1标準猶豫乘性偏好關系及其距離測度。
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Today, the editor brings the " 6.1 standard hesitation multiplicative preference relation and its distance measure of the intensively read PhD thesis 'A Multi-Attribute Group Decision-Making approach considering expert consensus under generalised nultiplicative preference information'".
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一、内容摘要（Content Summary）
本期推文将從思維導圖、精讀内容、知識補充三個方面介紹精讀博士論文《廣義乘性偏好資訊下考慮專家共識的多屬性群決策方法》的6.1标準猶豫乘性偏好關系及其距離測度。
This issue of the article will introduce the 6.1 standard hesitation multiplicative preference relation and its distance measure from three aspects: mind mapping, in-depth reading content, and supplementary knowledge, focusing on the doctoral dissertation "Multi-attribute Group Decision-making Method Considering Expert Consensus under Generalized Multiplicative Preference Information".
二、思維導圖（Mind Mapping）
三、精讀内容（Detailed Reading Content）
（一）章節前言（Chapter Introduction）
在該章節的前言，作者首先對猶豫乘性偏好資訊（HMPR）進行了相應的研究綜述，并進行了研究評述。而實際決策中，專家可能對于偏好資訊的取值猶豫不決而運用猶豫乘性偏好資訊完成評估工作，此時對于個體資訊的一緻性與群體共識水準提出了更高的要求，是以，本章旨在提出考慮HMPR的一緻性與共識的多屬性群決策（MAGDM）方法。
In the introduction of this chapter, the author provides a comprehensive review and evaluation of the research on hesitant multiplicative preference relations (HMPR). In practical decision-making, experts may exhibit hesitancy in determining preference values and utilize hesitant multiplicative preference information to carry out evaluations. Under such circumstances, higher requirements are placed on the consistency of individual information and the level of consensus within a group. Therefore, the aim of this chapter is to propose a multi-attribute group decision-making (MAGDM) approach that considers the consistency and consensus of HMPR.
然後，作者介紹了目前考慮一緻性與共識的HMPR下的MAGDM方法的不足。接着，介紹了本章節的研究貢獻：本章建構了一種基于HMPR的一緻性與共識的優化模型，并在此基礎上提出了MAGDM方法。最後，介紹了本章的章節安排。
Subsequently, the author discusses the limitations of existing MAGDM methods that consider consistency and consensus under HMPR. The research contributions of this chapter are then presented, which include the construction of an optimization model based on HMPR that considers consistency and consensus, and the development of the MAGDM method based on this model. Finally, the chapter concludes with an overview of its structure.
（二）标準猶豫乘性偏好關系及其距離測度（Standard Hesitant Multiplicative Preference Relations and Their Distance Measures）
在第2章中已經介紹了有關猶豫乘性集與HMPR的相關概念，本小節将在此基礎上回顧最小化原始标準化猶豫乘性偏好關系（NHMPR）的定義，并建構不同 NHMPR之間的改進距離以完善後續研究。由于實際中MAGDM問題的複雜程度不斷提高，來自不同研究背景的專家将極有可能運用不同元素數量的猶豫乘性數來評估備選方案，是以可能造成的後果是運算複雜程度急劇增加。為了克服這個不足，即統一猶豫乘性數中的元素數量，有研究者提出了猶豫乘性數的标準化方法。
In Chapter 2, relevant concepts pertaining to hesitant multiplicative sets and HMPR have already been introduced. This subsection builds upon the previous knowledge by revisiting the definition of minimizing normalized hesitant multiplicative preference relations (NHMPR) and constructing improved distance measures between different NHMPR to enhance further research. As the complexity of MAGDM problems in practice continues to increase, experts from different research backgrounds may employ hesitant multiplicative numbers with different element quantities for evaluating alternative solutions. Consequently, this can lead to a significant increase in computational complexity. To overcome this limitation and achieve a unified element quantity in hesitant multiplicative numbers, researchers have proposed a standardization method for hesitant multiplicative numbers.
在該小節，作者首先介紹了标準猶豫乘性數的定義，如下圖所示。
In this subsection, the author initially presents the definition of standard hesitant multiplicative numbers, as shown in the figure below.
基于偏好系數建構的标準猶豫乘性數，作者給出了不同标準猶豫乘性數之間的距離測度并且根據其定義證明了距離測度滿足的性質。
The author then provides the distance measures between different standard hesitant multiplicative numbers based on preference coefficients and proves the properties of these distance measures according to their definitions.
同樣地，由猶豫乘性數組成的HMPR也需要标準化操作以減少資訊集結過程運算的複雜程度，得到的NHMPR的定義如下。
Similarly, HMPR composed of hesitant multiplicative numbers also requires a standardization operation to reduce the computational complexity during the information aggregation process. The definition of NHMPR obtained is as follows.
由于在後續的研究中，本章在最終的備選方案選擇階段采取将NHMPR轉化為一個乘性偏好關系（MPR）的方式以确定備選方案的排序，是以将引入标準猶豫乘性數的改進記分函數的概念并且得到了相關的命題，如下圖所示。
Considering that in subsequent research, this chapter adopts the approach of transforming NHMPR into a multiplicative preference relation (MPR) during the final stage of selecting alternative solutions, the concept of an improved scoring function using standard hesitant multiplicative numbers is introduced and related propositions are derived, as shown in the figure below.
根據定義6.2可以得到不同NHMPR之間的距離測度的計算方法，并得到了該距離測度的簡化計算式。
Based on Definition 6.2, the calculation method for the distance measures between different NHMPR is obtained, along with a simplified formula for this distance measure.
四、知識補充——猶豫乘性數（ Supplementary Knowledge - Hesitant Multiplicative Numbers）
猶豫乘性數是一種用于處理模糊性和不确定性的數學工具，常用于多準則決策問題中。它是對傳統的模糊數進行了擴充，考慮了決策者在做決策時的猶豫和不确定性因素。與傳統的模糊數相比，猶豫乘性數具有更強的表達能力和更靈活的模組化能力，能夠更好地反映決策者的主觀偏好和不确定性程度。在決策過程中，猶豫乘性數可以用來表示決策者對不同決策方案的偏好程度，進而用于計算權重或進行排序，進而輔助決策者做出更合理的決策。
Hesitant multiplicative numbers are mathematical tools used to handle ambiguity and uncertainty, commonly employed in multi-criteria decision-making problems. They extend traditional fuzzy numbers by considering the hesitation and uncertainty factors that decision-makers encounter when making decisions. Compared to traditional fuzzy numbers, hesitant multiplicative numbers possess stronger expressive power and more flexible modeling capabilities, allowing them to better reflect decision-makers' subjective preferences and the degree of uncertainty. In the decision-making process, hesitant multiplicative numbers can be used to represent decision-makers' preferences for different decision alternatives, enabling the calculation of weights or rankings to assist decision-makers in making more informed decisions.
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參考資料：ChatGPT、百度百科
參考文獻：
王睿. 廣義乘性偏好資訊下考慮專家共識的多屬性群決策方法 [D]. 四川: 西南交通大學, 2022.
本文由LearningYard學苑整理并發出，如有侵權請在背景留言！
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