臺灣博碩士論文加值系統

資訊融合和資訊聚合在許多研究中是重要的主題，例如模糊邏輯系統，多屬性決策，群體決策以及資訊擷取等等。在本論文中，我們首先提出一個新的一般性模糊數相似度測量方法。首先，我們提出簡單重心法以計算一般性模糊數的重心點。然後，我們使用SCGM以提出一種新的測量方法以計算一般性模糊數之間的相似程度。我們所提出的相似度測量方法主要是先計算出梯形或者三角形的一般化模糊數之重心點，然後再計算在模糊數之間的相似程度。我們也證明我們所提出的相似度測量方法符合一些特性，並且利用一個例子將所提出的方法與現有的模糊數相似度測量方法做比較。我們所提出的方法能夠克服現有方法的缺點。同時，我們也利用所提出的相似度測量，發展出一個新的處理模糊風險分析問題之方法。我們所提出的模糊風險分析方法能考量到決策者表達意見時的信任程度。我們更進一步修改所提出的相似度量測方法以簡化一般性模糊數相似度的計算過程。我們也提出一個方法來計算區間值模糊數的相似程度。
在本論文中，我們亦提出一個新的排序方法來處理一般性模糊數之排序問題。我們也基於所提出之新的排序方法，發展出一個新的演算法來解決風險分析問題。所提出的排序方法主要是考慮一般化模糊數的重心點和標準差。我們也使用一個例子把所提出的方法與現有的以重心為基礎之排序方法做比較。我們所提出的排序方法能克服現有的以重心為基礎之排序方法的缺點。而我們所提出的以模糊數排序法為基礎之模糊風險分析演算法能克服我們在前面所提出的模糊風險分析方法之缺點。
在本論文中，我們使用模糊數來擴展傳統的IOWA運算子並提出以模糊數為基礎的FN-IOWA運算子。模糊數主要是用來描述FN-IOWA運算子的評估值和權重值，並且透過模糊數算術運算來求得資訊聚合結果。我們並且以FN-IOWA運算子提出一個新的演算法來處理多準則模糊決策問題。而我們所提出的演算法能更聰明且更靈活地處理多準則模糊決策問題。我們更進一步地利用FN-IOWA運算子和語義量詞提出一個新的資訊融合演算法應用於異質群體決策環境中。我們所提出的資訊融合演算法有下列優點︰(1)它使用以FN-IOWA運算子為基礎的語義量詞來彈性地決定每一位專家Ei的意見之權重值，以聚合每一位專家的意見。(2) 每一位專家所定的意見評估值不一定要有交集的區域。(3)可以不需要使用德爾菲法來調整專家所給的模糊數之語義意見。
在本論文中，我們亦擴展由Yager所提出之優先運算子以提出一個以一般性模糊數相似度測量為基礎的優先資訊融合演算法。所提出的優先資訊融合演算法有下列優點︰(1)由於它允許每一個準則的評估值可以是一般性模糊數，或是介於0和1之間的實數值，因此能以更靈活的方式來處理模糊決策問題，(2)它能夠處理以一般化模糊數為基礎之資訊過濾問題。此外，我們另外提出新的優先資訊融合演算法來處理以區間值模糊數為基礎之資訊過濾問題。而且，我們利用所提出的優先資訊融合演算法來處理多層次資訊過濾問題。所提出的優先資訊融合演算法不僅能處理以區間值模糊數的資訊過濾問題，也能以更靈活的方式處理多層資訊過濾問題。
最後，我們指出一些現存且應用於處理資訊檢索之 “AND” 與 “OR” 查詢的平均運算子 (即：P-Norm 運算子，Infinite-One 運算子及 Waller-Kraft 運算子) 之缺點。此外，我們也提出一個以幾何平均數為基礎之GMA運算子來解決這些現存平均運算子的缺點。我們利用一些範例將所提出的GMA運算子與先前所提之三個平均運算子做比較。同時，我們也證明所提出之GMA運算子的一些特性。我們所提出的GMA 運算子能克服現存平均運算子的缺點，並且能容易地決定出合適的值給參數a以處理模糊資訊檢索的 “AND” 與 “OR” 查詢問題。在此，參數a不是0就是1。而且，我們也將所提出的GMA運算子擴展為以一般性模糊數為基礎的GMA運算子。我們也使用GFNGMA運算子處理以區間值模糊數為基礎的查詢問題。我們所提出的GFNGMA 運算子能以更靈活和更聰明的方式處理模糊數的查詢問題。

Fusion and aggregation of information are important topics in many researches, such as fuzzy logic systems, multi-attribute decision-making, group decision-making, and information retrieval,…, etc. In this dissertation, we firstly present a new similarity measure of generalized fuzzy numbers. First, we present a method called the Simple Center of Gravity Method (SCGM) to calculate the center-of-gravity (COG) points of generalized fuzzy numbers. Then, we use the SCGM to propose a new method to measure the degree of similarity between generalized fuzzy numbers. The proposed similarity measure uses the SCGM to calculate the COG points of trapezoidal or triangular generalized fuzzy numbers and then to calculate the degree of similarity between generalized fuzzy numbers. We also prove some properties of the proposed similarity measure and use an example to compare the proposed method with the existing similarity measures. The proposed similarity measure can overcome the drawbacks of the existing methods. We also apply the proposed similarity measure to develop a new method to deal with fuzzy risk analysis problems. The proposed fuzzy risk analysis method is more flexible and more intelligent then the existing methods due to the fact that it considers the degrees of confidence of decision-makers’ opinions. Furthermore, we modify the proposed similarity measure to simplify the calculation process to measure the degree of similarity between generalized fuzzy numbers. We also present a method to measure the degree of similarity between interval-valued fuzzy numbers.
In this dissertation, we also present a new method for ranking generalized fuzzy numbers. Based on the proposed method, we also present an algorithm to deal with fuzzy risk analysis problems. The proposed method considers the centroid points and the standard deviations of generalized fuzzy numbers for ranking generalized fuzzy numbers. We also use an example to compare the proposed method with the existing centroid-index ranking methods. The proposed ranking method can overcome the drawbacks of the existing centroid-index ranking methods. The proposed fuzzy risk analysis algorithm can overcome the drawbacks of the one we presented in the above.
In this dissertation, we also use fuzzy numbers to extend the traditional Induced OWA (IOWA) operator to present the fuzzy-number IOWA (FN-IOWA) operator, where fuzzy numbers are used to describe the argument values and the weights of the FN-IOWA operator, and the aggregation results are obtained by using fuzzy number arithmetic operations. Based on the proposed FN-IOWA operator and the proposed ranking method of fuzzy numbers, we present a new algorithm to deal with multi-criteria fuzzy decision-making problems. The proposed algorithm can deal with multi-criteria fuzzy decision-making problems in a more intelligent and more flexible manner. Furthermore, we use the FN-IOWA operator and linguistic quantifiers to present a new information fusion algorithm for fusing fuzzy opinions in heterogeneous group decision-making environment. The proposed information fusion algorithm has the following advantages: (1) It uses linguistic quantifiers based on the FN-IOWA operator to flexibly determine the weight wi of the opinion of each expert Ei for aggregating the experts’ fuzzy opinions. (2) The experts’ opinions do not necessarily need to have a common intersection. (3) It does not need to use the Delphi method to adjust fuzzy numbers given by experts.
In this dissertation, we extend the prioritized operator presented by Yager and to present a prioritized information fusion algorithm based on the similarity measure of generalized fuzzy numbers. The proposed prioritized information fusion algorithm has the following advantages: (1) It can handle prioritized multi-criteria fuzzy decision-making problems in a more flexible manner due to the fact that it allows the evaluating values of criteria to be represented by generalized fuzzy numbers or crisp values between zero and one, and (2) it can deal with prioritized information filtering problems based on generalized fuzzy numbers. Furthermore, we present a new prioritized information fusion algorithm for handling information filtering problems based on interval-valued fuzzy numbers. Furthermore, we use the proposed fusion algorithm for handling multi-level information filtering problems. The proposed prioritized information fusion algorithm can deal with information filtering problems in a more flexible manner due to the fact that it not only can deal with information filtering problems based on interval-valued fuzzy numbers, but also can deal with multi-level information filtering problems.
Finally, we point out that there are some drawbacks in the existing averaging operators (i.e., P-Norm operators, Infinite-One operators, and Waller-Kraft operators) to deal with AND and OR operations of fuzzy information retrieval. Furthermore, we present new averaging operators based on geometric-mean averaging (GMA) operators to deal with these drawbacks. We use some examples to compare the proposed GMA operators with the existing averaging operators. We also prove some properties of the proposed GMA operators. The proposed GMA operators can overcome the drawbacks of the existing averaging operators and easily determine an appropriate value of the parameter α, where α is either 0 or 1, for handling AND and OR operations of fuzzy information retrieval. Furthermore, we present generalized fuzzy number geometric-mean averaging operators (GFNGMA operators) for dealing with queries based on generalized fuzzy numbers. Furthermore, we use GFNGMA operators to deal with queries represented by interval-valued fuzzy numbers. The proposed GFNGMA operators can deal with fuzzy-number queries in a more flexible and more intelligent manner.

Abstract in Chinese……………………………………………………i
Abstract in English…………………………………………………iii
Acknowledgements………………………………………………………v
Contents…………………………………………………………………vi
List of Figures………………………………………………………ix
List of Tables…………………………………………………………xii
Chapter 1 Introduction………………………………………………1
1.1 Motivation………………………………………………………1
1.2 Organization of This Dissertation…………………………5
Chapter 2 Literatures Review………………………………………7
2.1 Fuzzy Sets Theory………………………………………………7
2.2 Fuzzy Numbers and Their Arithmetic Operations…………8
2.3 Generalized Fuzzy Numbers and Their Arithmetic
Operations………………………………………………………9
2.4 Triangular Norm and Triangular Conorm…………………12
2.5 Interval-Valued Fuzzy Sets, Interval-Valued Fuzzy
Numbers and Their Arithmetic Operations………………13
2.6 Traditional Centroid Method………………………………16
2.7 Summary…………………………………………………………16
Chapter 3 New Methods to Calculate the Degree of Similarity
between Fuzzy Numbers…………………………………17
3.1 Traditional Center of Gravity Method……………………18
3.2 Some Existing Similarity Measures Between Fuzzy
Numbers…………………………………………………………19
3.3 A New Simple Center of Gravity Method (SCGM)…………21
3.4 A New Similarity Measure Between Generalized Fuzzy
Numbers…………………………………………………………28
3.5 Fuzzy Risk Analysis Based on the Proposed Similarity
Measure of Generalized Fuzzy Numbers……………………35
3.6 Modify the Proposed Similarity Measure…………………42
3.7 A New Methods to Calculate the Degree of Similarity
between Interval-Valued Fuzzy Numbers……………………45
3.8 Summary……………………………………………………………55
Chapter 4 Fuzzy Risk Analysis Based on the Ranking of
Generalized Fuzzy Numbers………………………………56
4.1 Some Centroid-Index Ranking Methods of Fuzzy Numbers…56
4.2 A New Ranking Method for Generalized Fuzzy Numbers……59
4.3 Handling Fuzzy Risk Analysis Problems Based on the
Proposed Method of Generalized Fuzzy Numbers……………69
4.4 Summary……………………………………………………………80
Chapter 5 New Information Fusion and Aggregation Methods for
Handling Fuzzy Decision-Making Problems……………81
5.1 Preliminary ………………………………………………………83
5.1.1 IOWA Operator………………………………………………83
5.1.2 Fuzzy Linguistic Quantifiers……………………………84
5.1.3 Non-Monotonic/Prioritized Intersection Operator…86
5.2 A New FN-IOWA Operator to Deal with Multi-Criteria Fuzzy
Decision-Making Problems………………………………………87
5.3 Using FN-IOWA Operator for Handling Human Selection
Problems……………………………………………………………96
5.4 A New Information Fusion Algorithm for Aggregating
Fuzzy Opinions…………………………………………………102
5.5 Using the Proposed Information Fusion Algorithm for
Handling Heterogeneous Group Fuzzy Decision-Making
Problems…………………………………………………………107
5.6 A New Prioritized Fuzzy Information Fusion Algorithm
……………………………………………………………………116
5.7 Using the Prioritized Fuzzy Information Fusion
Algorithm for Handling Multi-Criteria Fuzzy Decision-
Making Problems…………………………………………………122
5.8 A New Prioritized Information Fusion Algorithm Based on
Interval- Valued Fuzzy Numbers……………………………128
5.9 Using the Proposed Information Fusion Algorithm for
Handling Multi-Level Information Filtering
Problems…………………………………………………………139
5.10 Summary…………………………………………………………145
Chapter 6 New Averaging Operators for Aggregating Fuzzy Query
Terms of Fuzzy Information Retrieval………………147
6.1 Preliminary ……………………………………………………148
6.1.1 Geometric Mean……………………………………………148
6.1.2 Information Retrieval Based on the Conventional
Fuzzy Set Set Model………………………………………148
6.1.3 Some Averaging Operators for AND and OR Operations ………………………………………………………………149
6.1.4 Operator Graphs of the T-Operators and the
Averaging Operators………………………………………151
6.1.5 Some Analytic Results of the T-Operators and the
Averaging Operators………………………………………152
6.2 Analysis of the Existing Averaging Operators…………156
6.3 New Geometric-Mean Averaging Operators for Fuzzy
Information Retrieval…………………………………………160
6.4 Weighted Fuzzy Query Based on the Extended Geometric-
Mean Averaging Operators……………………………………169
6.5 New GFNGMA Operators for Dealing with Fuzzy-Number
Queries……………………………………………………………171
6.6 Using GFNGMA Operators to Deal with Queries Represented
by Interval-Valued Fuzzy Numbers…………………………181
6.7 Summary……………………………………………………………192
Chapter 7 Conclusions…………………………………………………194
7.1 Contributions of This Dissertation………………………194
7.2 Future Research…………………………………………………196
References…………………………………………………………………197

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