【摘要】：語言變量(值域為語言短語)在刻畫模糊信息尤其是定性信息時具有便捷、合理等優(yōu)勢,基于語言變量的模糊多屬性決策得到了快速發(fā)展,并成為模糊多屬性決策的重要組成部分。二維語言變量同時使用I、II維語言變量能更準確地反映出決策者對某一事物的評價,因此受到了較多的關注。本文將基于二維語言變量,進一步提出梯形二維語言變量,并提出基于梯形二維語言的三類集成算子和相應的多屬性決策方法。論文的主要工作和成果如下:(1)基于二維語言變量,將其中的I維變量擴展成梯形模糊數(TFN),提出梯形二維語言變量(TTLV),并進一步提出梯形二維語言變量的運算法則、運算性質、距離測度以及期望和排序方法,并對其性質和距離公式進行了證明。(2)基于梯形二維語言變量,提出基于梯形二維語言變量的廣義聚合算子,包括廣義加權平均算子、廣義有序加權算子、廣義混合加權平均算子,研究了它們的性質,包括冪等性、單調性、有界性等,并給出了參數取值不同時的特例�；谔岢龅募伤阕�,給出解決梯形二維語言變量的多屬性決策方法的詳細步驟,并應用算例對比說明該方法的有效性,分析廣義參數對決策結果的影響。(3)針對屬性間存在關聯(lián)關系的決策情況,提出基于梯形二維語言變量的幾種Bonferroni Mean(BM)算子,包括基于梯形二維語言BM算子、加權BM算子、幾何BM算子、加權幾何BM算子。研究和證明了這些算子的性質,分析了在參數p,q取不同值的情況下的各種特例。基于提出的梯形二維語言的BM集成算子,給出了相應的多屬性決策方法,通過一家投資公司投資選擇案例證明了該方法是行之有效的,并進一步分析參數p,q不同取值對最終決策結果的影響。(4)針對屬性間存在優(yōu)先等級的多屬性決策問題,提出了梯形二維語言優(yōu)先有序加權集成算子(TTFLPOWA),研究相關性質。進一步提出基于TTFLPOWA算子的多屬性決策方法,給出詳細的決策步驟,并通過某工業(yè)區(qū)的環(huán)境監(jiān)測案例進行說明和分析該決策方法,并將該方法同灰色關聯(lián)方法進行對比分析,證明了該方法的有效性。
[Abstract]:Language variables (range is language phrases) have the advantages of convenience and reasonableness in depicting fuzzy information, especially qualitative information. Fuzzy multi-attribute decision making based on language variables has developed rapidly. And it becomes an important part of fuzzy multi-attribute decision-making. Two-dimensional language variables can reflect the evaluation of a certain thing more accurately by using IHI-dimensional language variables simultaneously, so it has attracted more attention. In this paper, the trapezoid two-dimensional language variables are further proposed based on the two-dimensional language variables, and three kinds of integration operators based on the trapezoidal two-dimensional language and the corresponding multi-attribute decision-making method are proposed. The main work and achievements are as follows: (1) based on the two-dimensional linguistic variables, the I-dimensional variables are extended to trapezoidal fuzzy number (TFN), and the trapezoidal two-dimensional language variable (TTLV), is proposed. Furthermore, the algorithm, operation properties, distance measure, expectation and sorting methods of trapezoidal two-dimensional language variables are proposed, and their properties and distance formulas are proved. (2) based on trapezoidal two-dimensional language variables, A generalized aggregation operator based on trapezoidal two-dimensional linguistic variables is proposed, including generalized weighted average operator, generalized ordered weighted operator and generalized mixed weighted average operator. Their properties are studied, including idempotent, monotonicity, boundedness, etc. The special cases with different parameter values are given. Based on the proposed integration operator, the detailed steps of multi-attribute decision making method for trapezoid two-dimensional linguistic variables are given, and the effectiveness of the method is illustrated by a numerical example. This paper analyzes the influence of generalized parameters on the decision results. (3) in view of the decision making in which there is a correlation between attributes, several Bonferroni Mean (BM) operators based on trapezoidal two-dimensional language variables are proposed, including BM operators based on trapezoidal two-dimensional language. Weighted BM operator, geometric BM operator, weighted geometric BM operator. The properties of these operators are studied and proved, and various special cases with different values of parameter pQ are analyzed. Based on the BM integration operator of trapezoidal two-dimensional language, the corresponding multi-attribute decision making method is given. The method is proved to be effective by an investment selection case of an investment company, and the parameter p, is further analyzed. The influence of Q values on the final decision results. (4) aiming at the multi-attribute decision making problem with priority level among attributes, a trapezoidal two-dimensional language priority weighted integration operator (TTFLPOWA),) is proposed to study the related properties. Furthermore, the multi-attribute decision making method based on TTFLPOWA operator is put forward, and the detailed decision steps are given. The decision method is explained and analyzed by an environmental monitoring case in an industrial area, and the method is compared with the grey correlation method. The effectiveness of the method is proved.
【學位授予單位】：山東財經大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：O225

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