基于多粒度二元语义信息的几类信息集结算子及其在多属性群决策中的应用
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摘要
由于受客观事物自身的复杂性、不确定性以及人类思维的模糊性等因素的影响,实际的决策信息往往难以量化,而一般较好的选择是采用定性的语言形式来表示。在群决策中,由于不同的决策者对同一决策问题会依据其个人偏好提出不同语言短语数目(简称粒度)的语言评价集给出各自的语言评价信息,因此如何利用信息集结算子将决策者提供的多粒度语言评价信息进行有效集结,进而更好的做出决策有着较高的实际应用价值。
本文将GOWA算子、IGOWA算子、PG算子、POWG算子和C-OWH算子拓展到二元语义(区间二元语义)信息下,提出了一系列新的算子,研究了它们的性质,并将其应用到多属性群决策中,主要工作概括如下：
第一章,首先介绍基于多粒度二元语义信息的集结算子的研究背景和国内外研究现状,最后给出本文的主要研究工作。
第二章,针对具有语言评价信息的多属性决策问题,提出了一种基于二元语义信息算子的决策方法。首先把GOWA算子和IGOWA算子拓展到二元语义环境中,提出了二元语义广义有序加权平均(T-GOWA)算子和二元语义诱导广义有序加权平均(T-IGOWA)算子,并探讨了这些算子的一些性质和特例,最后基于这些算子,分别在单人决策和群决策这两种情形下,提出了属性权重已知且属性值为语言信息形式给出的多属性决策方法。
第三章,研究了多粒度语言信息的集成问题,首先利用转换函数将多粒度语言信息一致化为二元语义信息形式,考虑集成信息之间相互支持程度的影响,再将幂几何(PG)平均算子、加权幂几何(WPG)平均算子、幂有序加权几何(POWG)平均算子拓展到二元语义环境中,提出了二元语义幂几何(T-PG)平均算子、二元语义加权幂几何(T-WPG)平均算子、二元语义幂有序加权几何(T-POWG)平均算子,探讨了它们的一些性质。最后基于这些算子,给出了属性值为二元语义信息形式的多属性群决策方法。
第四章,研究了多粒度区间语言信息的集成问题,首先利用转换函数将多粒度区间语言信息一致化为区间二元语义信息形式,再将连续的有序加权调和(C-OWH)平均算子拓展到多粒度区间语言环境中,提出了连续区间二元语义有序加权调和OWH (ITC-OWH)平均算子,并在此基础上提出了加权调和的ITC-OWH (WHITC-OWH)算子,有序加权调和的ITC-OWH (OWHITC-OWH)算子以及组合的ITC-OWH (CITC-OWH)算子,探讨了它们的一些性质。最后基于这些算子,给出了属性权重已知且属性值为区间二元语义信息形式的不确定语言型多属性群决策方法。
第五章,通过三个例题对前三章中的基于相关集结算子的多属性群决策方法进行了实例分析。实例分析说明了这些方法是有效的和可行的。
第六章,对全文进行了总结,并对进一步的研究前景作了展望。
Practical decision information is hard to quantificate, because many factors such as complexity、uncertainty of objects and the ambiguity of human thoughts always place restrictions on it. Using a specified language to express it is a favorable choice. In group decision making course, treating with the same decision making problem, different decision makers are likely to use different linguistic terms of granularity to describe the object of decision-making based on his or her habit. Hence it is of high value in the practical application of the research on how to make use of aggregating operator to aggregate multi-granularity linguistic assessment information that the decision maker provides and then make better decision.
In this dissertation, generalized ordered weighted averaging (GOWA) operator, induced generalized ordered weighted averaging (IGOWA) operator, power geometric averaging (PG) operator, power ordered weighted geometric averaging (POWG) operator and continuous ordered weighted harmonic averaging (C-OWH) operator are extended to accommodate two-tuple linguistic or interval two-tuple linguistic environment. A series of new operators are given, and their properties are studied. Finally, based on these operators, multi-attribute group decision-making is developed. Main jobs are as follows:
In Chapter One, first of all, the author introduces the background and the current research situation of aggregating operators with multi-granularity two-tuple linguistic information. At last, the author points out the main research tasks of the article.
In Chapter Two, with respect to multi-attribute decision making problems with linguistic assessment information, an approach is proposed based on two-tuple linguistic information operators. Firstly, some new aggregation operators are proposed, which are the two-tuple linguistic generalized ordered weighted averaging (T-GOWA) operator and the two-tuple linguistic induced generalized ordered weighted averaging (T-IGOWA) operator, and the properties of the operators are analyzed. Then two methods of two-tuple linguistic information multi-attribute (group) decision making based on the T-GOWA and T-IGOWA operators, by which the attribute weight information is known and the attribute information is two-tuple linguistic information, are presented.
In Chapter Three, the problem of multi-granularity linguistic information aggregation is investigated. Firstly, a transformation function is given to uniform the multi-granularity linguistic information into the form of two-tuple linguistic information in basic linguistic term set. Based on the affecting from the support between the aggregation information, power geometric averaging (PG) operator, weights power geometric averaging (WPG) operator and power ordered weighted geometric averaging (POWG) operator are extended to two-tuple linguistic information environment, and two-tuple linguistic power geometric averaging (T-PG) operator, two-tuple linguistic weights power geometric averaging (T-WPG) operator and two-tuple linguistic power ordered weighted geometric averaging (T-POWG) operator are proposed. Some properties of these operators are discussed. Finally, a method of applying these relative operators to the multi-attribute group decision making, by which the attribute information is two-tuple linguistic information, is presented.
In Chapter Four, the problem of multi-granularity interval linguistic information aggregation is investigated. Firstly, a transformation function is given to uniform the multi-granularity interval linguistic information into the form of interval two-tuple linguistic information in basic linguistic term set. The continuous ordered weighted harmonic (C-OWH) averaging operator is extended to accommodate multi-granularity interval linguistic environment, thus continuous interval two-tuple OWH (ITC-OWH) operator is proposed. Based on ITC-OWH operator, some new operators, such as weighted harmonic ITC-OWH (WHITC-OWH) operator, ordered weighted harmonic ITC-OWH (OWHITC-OWH) operator, combined ITC-OWH (CITC-OWH) operator, are proposed, and some properties of these operators are discussed. Finally, an approach is developed to apply these relative operators to the multi-granularity interval linguistic multi-attribute group decision making, by which the attribute weight information is known and the attribute information is interval two-tuple linguistic information,.
In Chapter Five, the example analysis of methods for multi-attribute group decision making based on the relative operators, which are put forward in the last three chapters, is given to demonstrate the feasibility and practicability of the proposed methods.
In Chapter Six, full text job is summed up, and the prospect of the research on multiple attribute group decision making based on multi-granularity two-tuple linguistic information is looking into the distance.
本文将GOWA算子、IGOWA算子、PG算子、POWG算子和C-OWH算子拓展到二元语义(区间二元语义)信息下,提出了一系列新的算子,研究了它们的性质,并将其应用到多属性群决策中,主要工作概括如下：
第一章,首先介绍基于多粒度二元语义信息的集结算子的研究背景和国内外研究现状,最后给出本文的主要研究工作。
第二章,针对具有语言评价信息的多属性决策问题,提出了一种基于二元语义信息算子的决策方法。首先把GOWA算子和IGOWA算子拓展到二元语义环境中,提出了二元语义广义有序加权平均(T-GOWA)算子和二元语义诱导广义有序加权平均(T-IGOWA)算子,并探讨了这些算子的一些性质和特例,最后基于这些算子,分别在单人决策和群决策这两种情形下,提出了属性权重已知且属性值为语言信息形式给出的多属性决策方法。
第三章,研究了多粒度语言信息的集成问题,首先利用转换函数将多粒度语言信息一致化为二元语义信息形式,考虑集成信息之间相互支持程度的影响,再将幂几何(PG)平均算子、加权幂几何(WPG)平均算子、幂有序加权几何(POWG)平均算子拓展到二元语义环境中,提出了二元语义幂几何(T-PG)平均算子、二元语义加权幂几何(T-WPG)平均算子、二元语义幂有序加权几何(T-POWG)平均算子,探讨了它们的一些性质。最后基于这些算子,给出了属性值为二元语义信息形式的多属性群决策方法。
第四章,研究了多粒度区间语言信息的集成问题,首先利用转换函数将多粒度区间语言信息一致化为区间二元语义信息形式,再将连续的有序加权调和(C-OWH)平均算子拓展到多粒度区间语言环境中,提出了连续区间二元语义有序加权调和OWH (ITC-OWH)平均算子,并在此基础上提出了加权调和的ITC-OWH (WHITC-OWH)算子,有序加权调和的ITC-OWH (OWHITC-OWH)算子以及组合的ITC-OWH (CITC-OWH)算子,探讨了它们的一些性质。最后基于这些算子,给出了属性权重已知且属性值为区间二元语义信息形式的不确定语言型多属性群决策方法。
第五章,通过三个例题对前三章中的基于相关集结算子的多属性群决策方法进行了实例分析。实例分析说明了这些方法是有效的和可行的。
第六章,对全文进行了总结,并对进一步的研究前景作了展望。
Practical decision information is hard to quantificate, because many factors such as complexity、uncertainty of objects and the ambiguity of human thoughts always place restrictions on it. Using a specified language to express it is a favorable choice. In group decision making course, treating with the same decision making problem, different decision makers are likely to use different linguistic terms of granularity to describe the object of decision-making based on his or her habit. Hence it is of high value in the practical application of the research on how to make use of aggregating operator to aggregate multi-granularity linguistic assessment information that the decision maker provides and then make better decision.
In this dissertation, generalized ordered weighted averaging (GOWA) operator, induced generalized ordered weighted averaging (IGOWA) operator, power geometric averaging (PG) operator, power ordered weighted geometric averaging (POWG) operator and continuous ordered weighted harmonic averaging (C-OWH) operator are extended to accommodate two-tuple linguistic or interval two-tuple linguistic environment. A series of new operators are given, and their properties are studied. Finally, based on these operators, multi-attribute group decision-making is developed. Main jobs are as follows:
In Chapter One, first of all, the author introduces the background and the current research situation of aggregating operators with multi-granularity two-tuple linguistic information. At last, the author points out the main research tasks of the article.
In Chapter Two, with respect to multi-attribute decision making problems with linguistic assessment information, an approach is proposed based on two-tuple linguistic information operators. Firstly, some new aggregation operators are proposed, which are the two-tuple linguistic generalized ordered weighted averaging (T-GOWA) operator and the two-tuple linguistic induced generalized ordered weighted averaging (T-IGOWA) operator, and the properties of the operators are analyzed. Then two methods of two-tuple linguistic information multi-attribute (group) decision making based on the T-GOWA and T-IGOWA operators, by which the attribute weight information is known and the attribute information is two-tuple linguistic information, are presented.
In Chapter Three, the problem of multi-granularity linguistic information aggregation is investigated. Firstly, a transformation function is given to uniform the multi-granularity linguistic information into the form of two-tuple linguistic information in basic linguistic term set. Based on the affecting from the support between the aggregation information, power geometric averaging (PG) operator, weights power geometric averaging (WPG) operator and power ordered weighted geometric averaging (POWG) operator are extended to two-tuple linguistic information environment, and two-tuple linguistic power geometric averaging (T-PG) operator, two-tuple linguistic weights power geometric averaging (T-WPG) operator and two-tuple linguistic power ordered weighted geometric averaging (T-POWG) operator are proposed. Some properties of these operators are discussed. Finally, a method of applying these relative operators to the multi-attribute group decision making, by which the attribute information is two-tuple linguistic information, is presented.
In Chapter Four, the problem of multi-granularity interval linguistic information aggregation is investigated. Firstly, a transformation function is given to uniform the multi-granularity interval linguistic information into the form of interval two-tuple linguistic information in basic linguistic term set. The continuous ordered weighted harmonic (C-OWH) averaging operator is extended to accommodate multi-granularity interval linguistic environment, thus continuous interval two-tuple OWH (ITC-OWH) operator is proposed. Based on ITC-OWH operator, some new operators, such as weighted harmonic ITC-OWH (WHITC-OWH) operator, ordered weighted harmonic ITC-OWH (OWHITC-OWH) operator, combined ITC-OWH (CITC-OWH) operator, are proposed, and some properties of these operators are discussed. Finally, an approach is developed to apply these relative operators to the multi-granularity interval linguistic multi-attribute group decision making, by which the attribute weight information is known and the attribute information is interval two-tuple linguistic information,.
In Chapter Five, the example analysis of methods for multi-attribute group decision making based on the relative operators, which are put forward in the last three chapters, is given to demonstrate the feasibility and practicability of the proposed methods.
In Chapter Six, full text job is summed up, and the prospect of the research on multiple attribute group decision making based on multi-granularity two-tuple linguistic information is looking into the distance.
引文
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[3]Yager R.R, Families of OWA operators[J]. Fuzzy Sets and Systems,1993, 59:125-148.
[4]Yager R.R, Fuzzy aggregation of modular neural networks with ordered weighted averaging operators [J]. International Journal of Approximate Reasoning, 1995,13:359-375.
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[6]Mitchell H.B., Estrakh D.D. A modified OWA operator and its use in lossless DPCM image compression[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,1997,5:429-436.
[7]Xu Z.S., Da Q.L.The ordered weighted geometric averaging operators[J], International Journal of Intelligent Systems,2002,17:709-716.
[8]樊治平,姜艳萍,基于0WG算子的不同形式偏好信息的群决策方法[J].管理科学学报,2003,6(1)：32-36.
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