模糊集相似性測度之比較性研究

A Comparative Study on Similarity Measures for Fuzzy Sets

林高正(Kao-Cheng Lin) ； 曾文宏(Wen-Hung Tseng) ； 林川煥(Chuan-Huan Lin)

《管理資訊計算》 7卷特刊2 (2018/08) Pp. 107-116

https://doi.org/10.6285/MIC.201808_7(S2).0012

摘要

〝相似性＂在評估兩個事物間相同的程度，它既是日常生活中經常用到的概念與辭彙，也是科學研究最基礎而重要的概念與工具之一。隨著模糊數與語意變數應用的日趨普遍，模糊集的相似性測度也變得日益重要，因而有許多學者開始探討模糊集相似性測度的建立方法與相關測度的理論性質。本文即針對以下列三種方法所建立的各種模糊集相似性測度之性質作進一步的討論與整理：（1）以幾何距離為基礎的相似性測度；（2）以集合運算為基礎的相似性測度；以及（3）以適配函數為基礎的相似性測度。這類討論可用以釐清測度的適用性，並有助於相關結果之推論。

關鍵字

相似性測度 ； 模糊集 ； 幾何距離 ； 集合運算 ； 適配函數

並列摘要

＂Similarity＂ is an evaluation of the degree that two objects are equal. It is one of the most widely used daily life concepts and vocabulary; and also one of the most fundamental and important concepts and tools in sciences. With the applications of the fuzzy number and the linguistic variable becoming more and more common, similarity measures of fuzzy sets become more and more important, so many scholars begin to discuss the methods for constructing similarity measures and the theoretical property of relative measures. In this comparative study, we give a survey and discussion on the similarity measures constructed based on the geometric distance, the set operations and the matching function. Such discussions can be used to clarify the applicability of measures and to derive more related results.

並列關鍵字

Similarity measures ； Fuzzy sets ； Geometric distance ； Set operations ； Matching function

參考文獻

Bellman, R., Kalaba, R., Zadeh, L. A. (1966), Abstraction and pattern classification, Journal of Mathematical Analysis and Applications 13, 1-7. doi: 10.1016/0022-247X(66)90071-0

Chen, S.-M. (1988), A new approach to handling fuzzy decision making problems, IEEE Trans. Systems, Man, Cybernetics 18 (6), 1012-1016. doi: 10.1109/21.23100

Chen, S.-M., Yeh, M.-S. and Hsiao, P.-Y. (1995), A comparison of similarity measures of fuzzy values, Fuzzy Sets and Systems 72 (1), 79-89. doi: 10.1016/0165-0114(94)00284-E

Dubois, D. and Prade, H. (1997), The three semantics of fuzzy sets, Fuzzy Sets and Systems 90 (2), 141-150. doi: 10.1016/S0165-0114(97)00080-8

Fan, J. and Xie, W. (1999a), Some notes on similarity measure and proximity measure, Fuzzy Sets and Systems 101 (3), 403-412. doi: 10.1016/S0165-0114(97)00108-5