本文選題：對偶猶豫模糊集 + 對偶猶豫模糊概率��； 參考：《南昌大學》2017年碩士論文

【摘要】：作為模糊集的擴展,對偶猶豫模糊集允許其隸屬函數(shù)與非隸屬函數(shù)為0與1之間的一些可能值的集合,以此來滿足不同專家對相同方案的不同意見.近年來,對偶猶豫模糊集受到越來越多學者的關注,一些學者獲得了一些比較好的結果.這些成果在諸如聚類分析,近似推理,圖像處理,醫(yī)療診斷,決策和信息集成等方面都有著十分重要的應用.因此研究對偶猶豫模糊集的多屬性決策及應用具有十分重要的理論意義和實踐意義.本文主要研究對象是對偶猶豫模糊集,主要研究內(nèi)容和創(chuàng)新性工作包括:第一章引論部分.本部分主要介紹了對偶猶豫模糊集理論與應用的歷史背景、現(xiàn)狀、對偶猶豫模糊集的有關概念.第二章凸對偶猶豫模糊集的集成.本部分首先在對偶猶豫模糊集的基礎上引入凸的概念,并研究其相關性質,然后,通過集成函數(shù)對凸對偶猶豫模糊元和凸對偶猶豫模糊集進行集成來研究對偶猶豫模糊集的保凸性.第三章對偶猶豫模糊概率.本部分基于直覺模糊數(shù)的概念,提出對偶猶豫模糊數(shù),并在此基礎上介紹了對偶猶豫模糊概率,并給出對偶猶豫模糊概率的相關性質以及在色盲問題上的應用.第四章對偶擴展猶豫模糊集.本部分基于對偶猶豫模糊集提出對偶擴展猶豫模糊集的概念,并給出了對偶擴展猶豫模糊元的基本運算和性質.最后,本章給出了對偶擴展猶豫模糊集的相關系數(shù),并運用于投資問題.第五章高階對偶猶豫模糊集的距離測度.本部分分析了對偶猶豫模糊集的已有相關距離測度的缺點,并提出新的測度;在此基礎上,提出高階對偶猶豫模糊集,并給出高階對偶猶豫模糊距離測度,并運用于信息系統(tǒng)方案評估問題.第六章結論和展望.本部分總結了文章的主要工作和創(chuàng)新點,并討論了今后研究工作展望.
[Abstract]:As the extension of the fuzzy set, the dual hesitant fuzzy set allows its membership function and the non subordinate function to be a set of possible values between 0 and 1, in order to meet the different opinions of the different experts on the same scheme. In recent years, more and more scholars have paid more attention to the dual hesitant fuzzy set, and some scholars have obtained some better results. Some achievements have very important applications in such aspects as clustering analysis, approximate reasoning, image processing, medical diagnosis, decision making and information integration. Therefore, it is of great theoretical and practical significance to study the multi attribute decision making and application of dual hesitant fuzzy sets. The content and innovative work include: the introduction of the first chapter. This part mainly introduces the historical background of the dual hesitant fuzzy set theory and application, the present situation, the related concepts of the dual hesitant fuzzy set. The second chapter is the integration of the convex dual hesitant fuzzy sets. And then, the convexity of dual hesitant fuzzy sets is integrated through integrated functions to study the convexity of dual hesitant fuzzy sets. The third chapter is dual hesitant fuzzy probability. Based on the concept of intuitionistic fuzzy numbers, the dual hesitant fuzzy number is proposed, and the dual hesitation fuzzy number is introduced on this basis. The correlation property of dual hesitant fuzzy probability and its application on color blindness are given. The fourth chapter is a dual extended hesitant fuzzy set. Based on the dual hesitant fuzzy set, the concept of dual extended hesitant fuzzy sets is proposed, and the basic operations and properties of the dual extended hesitant fuzzy element are given. Finally, the duality is given in this chapter. We extend the correlation coefficient of the hesitant fuzzy set and apply it to the investment problem. The fifth chapter is the distance measure of the high order dual hesitant fuzzy set. This part analyzes the shortcomings of the relative distance measure of the dual hesitant fuzzy set and proposes a new measure. On this basis, the high order duality hesitant fuzzy set is proposed and the high order dual hesitant fuzzy distance is given. In the sixth chapter, the main work and innovation of the article are summarized, and the future research work is also discussed.
【學位授予單位】：南昌大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O159;O225

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本文編號：2072794