{"title":"NPN微积分:由三个严格q -代数组成的一族","authors":"Wen-Ran Zhang","doi":"10.1109/ISMVL.1991.130739","DOIUrl":null,"url":null,"abstract":"NPN (negative-positive-neutral) calculi, a family of three mathematical structures are introduced for qualitative reasoning. NPN crisp logic extends the usual 4-valued model (+, -, 0, ?) to a 6-valued model (1, 0, +1, (-1, 0), (0, +1), (-1, +1)) and adds one more level of specification to the usual model. NPN fuzzy logic extends the NPN model to the space ( For all (x,y) mod x, y epsilon (-1, 1) and x<or=y) and adds infinite levels of specifications to the usual model. NPN algebra generalizes the NPN model to include algebraic operations on NPN variables defined in the space of (- infinity , infinity ). Based on the three models, NPN relations and NPN matrices are proposed. It is proved that the three models provide three strict qualitative algebras after the usual 4-valued model. Properties of different models are discussed. Potential applications of NPN calculi in qualitative reasoning are outlined.<<ETX>>","PeriodicalId":127974,"journal":{"name":"[1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic","volume":"22 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"NPN calculi: a family of three strict Q-algebras\",\"authors\":\"Wen-Ran Zhang\",\"doi\":\"10.1109/ISMVL.1991.130739\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"NPN (negative-positive-neutral) calculi, a family of three mathematical structures are introduced for qualitative reasoning. NPN crisp logic extends the usual 4-valued model (+, -, 0, ?) to a 6-valued model (1, 0, +1, (-1, 0), (0, +1), (-1, +1)) and adds one more level of specification to the usual model. NPN fuzzy logic extends the NPN model to the space ( For all (x,y) mod x, y epsilon (-1, 1) and x<or=y) and adds infinite levels of specifications to the usual model. NPN algebra generalizes the NPN model to include algebraic operations on NPN variables defined in the space of (- infinity , infinity ). Based on the three models, NPN relations and NPN matrices are proposed. It is proved that the three models provide three strict qualitative algebras after the usual 4-valued model. Properties of different models are discussed. Potential applications of NPN calculi in qualitative reasoning are outlined.<<ETX>>\",\"PeriodicalId\":127974,\"journal\":{\"name\":\"[1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic\",\"volume\":\"22 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-05-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.1991.130739\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.1991.130739","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
摘要
NPN(负-正-中性)微积分,一个由三种数学结构组成的家族被引入定性推理。NPN清晰逻辑将通常的4值模型(+,-,0,?)扩展为6值模型(1,0,+1,(-1,0),(0,+1),(-1,+1)),并在通常的模型上增加了一个规格级别。NPN模糊逻辑将NPN模型扩展到空间(For all (x,y) mod x,y epsilon(- 1,1)和x>
NPN (negative-positive-neutral) calculi, a family of three mathematical structures are introduced for qualitative reasoning. NPN crisp logic extends the usual 4-valued model (+, -, 0, ?) to a 6-valued model (1, 0, +1, (-1, 0), (0, +1), (-1, +1)) and adds one more level of specification to the usual model. NPN fuzzy logic extends the NPN model to the space ( For all (x,y) mod x, y epsilon (-1, 1) and x>