【摘要】：在決策分析問題中,精確給出方案間重要程度的判斷數(shù)值往往比較困難,決策者通常只能給出判斷值的大致范圍,如以區(qū)間數(shù)、區(qū)間粗糙數(shù)等形式給出.用大致范圍給出重要程度間的判斷值,更能反映客觀事物間的模糊不確定性,也更符合人類的思維習(xí)慣.本文針對判斷矩陣值為區(qū)間數(shù)和區(qū)間粗糙數(shù)的層次分析法,從以下幾個(gè)方面進(jìn)行研究:1、提出一種區(qū)間粗糙數(shù)間大小比較的新方法.現(xiàn)有文獻(xiàn)對區(qū)間數(shù)大小比較的研究已獲得豐碩的成果,但對區(qū)間粗糙數(shù)大小比較的研究相對欠缺,新的比較的方法充分吸收眾多區(qū)間數(shù)間大小比較方法中的互補(bǔ)性、傳遞性等優(yōu)點(diǎn),為后續(xù)研究區(qū)間粗糙數(shù)判斷矩陣的排序方法打基礎(chǔ).2、引入指數(shù)型區(qū)間數(shù)標(biāo)度和指數(shù)型區(qū)間粗糙數(shù)標(biāo)度.合理的標(biāo)度是構(gòu)建判斷矩陣的基礎(chǔ),也是影響最終排序的決定性因素.新的標(biāo)度不但充分克服了 1-9標(biāo)度與人們心理感覺判斷差距較大、評價(jià)結(jié)果與事實(shí)相反、一致性檢驗(yàn)與思維一致性不協(xié)調(diào)等缺點(diǎn),還融入指數(shù)標(biāo)度的傳遞性、平均相對誤差小于其他標(biāo)度等優(yōu)點(diǎn).為判斷矩陣的構(gòu)建及判斷矩陣一致性研究打下堅(jiān)實(shí)的基礎(chǔ).3、重新定義了區(qū)間數(shù)判斷矩陣及區(qū)間粗糙數(shù)判斷矩陣的一致性.單一準(zhǔn)則下,由所給定標(biāo)度構(gòu)建的判斷矩陣的一致性,直接影響該準(zhǔn)則下的排序向量,也間接決定了最終的排序向量,所以判斷矩陣一致性的判斷方法極為關(guān)鍵.新的一致性定義從直接與間接判斷區(qū)間重疊部分比例的角度,抓住“具有一致性的判斷矩陣在間接比較中,區(qū)間的占比較大”這一思想給出.新定義不但克服現(xiàn)有文獻(xiàn)中對區(qū)間數(shù)判斷矩陣及區(qū)間粗糙數(shù)判斷矩陣一致性定義過于嚴(yán)格或過于寬松的缺點(diǎn),還參照Saaty給出的一致性條件的方法,通過大量計(jì)算機(jī)的仿真實(shí)驗(yàn)給出判斷矩陣具有一致性時(shí)應(yīng)具有的數(shù)值條件.
[Abstract]:In the decision analysis problem, it is difficult to accurately give the judgment value of the importance degree between the schemes. The decision maker usually can only give the approximate range of the judgment value, such as interval number, interval rough number and so on. It can reflect the fuzzy uncertainty between the objective things and accord with the human thinking habits by giving the judgment value of the important degree in the general range. In this paper, a new method of comparing the size of interval rough numbers is proposed by using the Analytic hierarchy process (AHP), in which the judgment matrix values are interval numbers and interval rough numbers. The research on the comparison of interval numbers in the existing literature has been fruitful, but the study on the size comparison of interval rough numbers is relatively lacking. The new comparison method fully absorbs the complementarities of many interval number size comparison methods. Based on the transitivity, the paper introduces the exponential interval number scale and the exponential interval rough number scale for the further study of the ranking method of interval rough number judgment matrix. Reasonable scale is the basis of constructing judgment matrix and the decisive factor that affects the final ranking. The new scale not only overcomes the gap between 1-9 scale and people's psychological feeling judgment, but also integrates the transitivity of index scale. The average relative error is smaller than other scales. The consistency of interval number judgment matrix and interval rough number judgment matrix is redefined. Under the single criterion, the consistency of the judgment matrix constructed by the given scale directly affects the sorting vector under the criterion, and indirectly determines the final sorting vector, so the judgment method of the consistency of the judgment matrix is very important. The new definition of consistency, from the angle of directly and indirectly judging the proportion of overlapped parts of the interval, grasps the idea that the judgment matrix with consistency has a large proportion of the interval in the indirect comparison. The new definition not only overcomes the shortcomings of the consistency definition of interval number judgment matrix and interval rough number judgment matrix, but also refers to the method of consistency condition given by Saaty. Through a lot of computer simulation experiments, the numerical conditions for consistency of judgment matrix are given.
【學(xué)位授予單位】：廣西大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O151.21

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 陳靈毓;于憲偉;;一種新的互補(bǔ)判斷矩陣排序方法[J];數(shù)學(xué)的實(shí)踐與認(rèn)識;2016年24期

2 劉開第;龐彥軍;金斕;;對AHP單準(zhǔn)則排序方法的改進(jìn)[J];數(shù)學(xué)的實(shí)踐與認(rèn)識;2015年12期

3 袁杰;梁雪春;;層次分析法中判斷矩陣的一致性改進(jìn)[J];統(tǒng)計(jì)與決策;2014年12期

4 李建;李俊宏;;基于最大滿意度的互補(bǔ)判斷矩陣排序方法[J];模糊系統(tǒng)與數(shù)學(xué);2014年02期

5 周宏安;;基于最小偏差和優(yōu)勢度的區(qū)間數(shù)互補(bǔ)判斷矩陣排序法[J];運(yùn)籌與管理;2013年02期

6 靳鳳俠;黃天民;;區(qū)間數(shù)判斷矩陣滿意一致性的判定方法和方案的排序[J];控制與決策;2013年03期

7 李丁;韓偉一;汪云林;;關(guān)于層次分析法的數(shù)值試驗(yàn)[J];統(tǒng)計(jì)與信息論壇;2013年02期

8 邱滌珊;賀川;朱曉敏;;基于概率可信度的區(qū)間數(shù)排序方法[J];控制與決策;2012年12期

9 呂躍進(jìn);程宏濤;覃菊瑩;;基于判斷可信度的層次分析排序方法[J];控制與決策;2012年05期

10 劉勝;張玉廷;于大泳;;動態(tài)三角模糊數(shù)互反判斷矩陣一致性及修正[J];兵工學(xué)報(bào);2012年02期

相關(guān)碩士學(xué)位論文 前2條

1 何朝麗;基于區(qū)間粗糙數(shù)多屬性決策模型若干問題的研究[D];廣西大學(xué);2014年

2 靳宗偉;基于區(qū)間粗糙數(shù)的多屬性決策方法研究[D];廣西大學(xué);2013年

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