基于梯形二维语言变量的信息集成算子研究
发布时间：2018-12-10 19:27
【摘要】：语言变量(值域为语言短语)在刻画模糊信息尤其是定性信息时具有便捷、合理等优势,基于语言变量的模糊多属性决策得到了快速发展,并成为模糊多属性决策的重要组成部分。二维语言变量同时使用I、II维语言变量能更准确地反映出决策者对某一事物的评价,因此受到了较多的关注。本文将基于二维语言变量,进一步提出梯形二维语言变量,并提出基于梯形二维语言的三类集成算子和相应的多属性决策方法。论文的主要工作和成果如下:(1)基于二维语言变量,将其中的I维变量扩展成梯形模糊数(TFN),提出梯形二维语言变量(TTLV),并进一步提出梯形二维语言变量的运算法则、运算性质、距离测度以及期望和排序方法,并对其性质和距离公式进行了证明。(2)基于梯形二维语言变量,提出基于梯形二维语言变量的广义聚合算子,包括广义加权平均算子、广义有序加权算子、广义混合加权平均算子,研究了它们的性质,包括幂等性、单调性、有界性等,并给出了参数取值不同时的特例。基于提出的集成算子,给出解决梯形二维语言变量的多属性决策方法的详细步骤,并应用算例对比说明该方法的有效性,分析广义参数对决策结果的影响。(3)针对属性间存在关联关系的决策情况,提出基于梯形二维语言变量的几种Bonferroni Mean(BM)算子,包括基于梯形二维语言BM算子、加权BM算子、几何BM算子、加权几何BM算子。研究和证明了这些算子的性质,分析了在参数p,q取不同值的情况下的各种特例。基于提出的梯形二维语言的BM集成算子,给出了相应的多属性决策方法,通过一家投资公司投资选择案例证明了该方法是行之有效的,并进一步分析参数p,q不同取值对最终决策结果的影响。(4)针对属性间存在优先等级的多属性决策问题,提出了梯形二维语言优先有序加权集成算子(TTFLPOWA),研究相关性质。进一步提出基于TTFLPOWA算子的多属性决策方法,给出详细的决策步骤,并通过某工业区的环境监测案例进行说明和分析该决策方法,并将该方法同灰色关联方法进行对比分析,证明了该方法的有效性。
[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.
【学位授予单位】：山东财经大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O225
本文编号：2371082
[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.
【学位授予单位】：山东财经大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O225
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