{"title":"用k-偏好积分法研究步长隶属函数模糊数的表示、排序、距离和相似度","authors":"Shan-Huo Chen, Chien-Chung Wang","doi":"10.1109/NAFIPS.2001.944706","DOIUrl":null,"url":null,"abstract":"The modified k-preference integration method is applied to treat the representation, ranking; distance and similarity of fuzzy numbers with step form membership function. First, the representation value is computed by using the modified k-preference integration method. Then two or more fuzzy numbers with step form membership function are ranked by comparing their representation values. The distance between two fuzzy numbers with step form membership function is the absolute value of the difference between their representation values, while the similarity between them can be derived from their distance. Finally, some properties regarding the representation, ranking, distance, and similarity have been proved.","PeriodicalId":227374,"journal":{"name":"Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569)","volume":"71 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Representation, ranking, distance, and similarity of fuzzy numbers with step form membership function using k-preference integration method\",\"authors\":\"Shan-Huo Chen, Chien-Chung Wang\",\"doi\":\"10.1109/NAFIPS.2001.944706\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The modified k-preference integration method is applied to treat the representation, ranking; distance and similarity of fuzzy numbers with step form membership function. First, the representation value is computed by using the modified k-preference integration method. Then two or more fuzzy numbers with step form membership function are ranked by comparing their representation values. The distance between two fuzzy numbers with step form membership function is the absolute value of the difference between their representation values, while the similarity between them can be derived from their distance. Finally, some properties regarding the representation, ranking, distance, and similarity have been proved.\",\"PeriodicalId\":227374,\"journal\":{\"name\":\"Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569)\",\"volume\":\"71 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/NAFIPS.2001.944706\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NAFIPS.2001.944706","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Representation, ranking, distance, and similarity of fuzzy numbers with step form membership function using k-preference integration method
The modified k-preference integration method is applied to treat the representation, ranking; distance and similarity of fuzzy numbers with step form membership function. First, the representation value is computed by using the modified k-preference integration method. Then two or more fuzzy numbers with step form membership function are ranked by comparing their representation values. The distance between two fuzzy numbers with step form membership function is the absolute value of the difference between their representation values, while the similarity between them can be derived from their distance. Finally, some properties regarding the representation, ranking, distance, and similarity have been proved.
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