New Information Fusion and Information Aggregation Methods for Handling Multicriteria Fuzzy Decision-Making Problems

• Main Authors: Shi-Jay Chen, 陳士杰
• Other Authors: Shyi-Ming Chen
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/17522712212544897498

博士 === 國立臺灣科技大學 === 資訊工程系 === 93 === 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.