{"title":"Norma(标准与标准)上的直觉模糊子群性质","authors":"Rizka 'Abid Fadhiilah, Budi Surodjo","doi":"10.24198/jmi.v18.n2.40461.141-155","DOIUrl":null,"url":null,"abstract":"Fuzzy subgroups can be generalized into intuitionistic fuzzy subgroups and fuzzy subgroups over t -norm. Furthermore, intuitionistic fuzzy subgroups and fuzzy subgroups over t -norm can be generalized into intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm). The property of product under norms ( t -norm and s -norm) of two intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) and the property of image of intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) under group homomorphism were dis-cussed by Rasuli [8] . However, by giving counterexamples, it can be shown that both properties are not true. In this article, we reinvestigate the property of product under norms ( t -norm and s -norm) of two intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) and the property of image of intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) under group homomorphism. We use the literature study method in this research. The results show that the property of product under norms ( t -norm and s -norm) of two intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) and the property of image of intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) under group homomorphism in [8] can be valid if t -norm and s -norm are continuous.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Sifat-Sifat Subgrup Fuzzy Intuitionistik atas Norm (t-Norm dan s-Norm)\",\"authors\":\"Rizka 'Abid Fadhiilah, Budi Surodjo\",\"doi\":\"10.24198/jmi.v18.n2.40461.141-155\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Fuzzy subgroups can be generalized into intuitionistic fuzzy subgroups and fuzzy subgroups over t -norm. Furthermore, intuitionistic fuzzy subgroups and fuzzy subgroups over t -norm can be generalized into intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm). The property of product under norms ( t -norm and s -norm) of two intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) and the property of image of intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) under group homomorphism were dis-cussed by Rasuli [8] . However, by giving counterexamples, it can be shown that both properties are not true. In this article, we reinvestigate the property of product under norms ( t -norm and s -norm) of two intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) and the property of image of intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) under group homomorphism. We use the literature study method in this research. The results show that the property of product under norms ( t -norm and s -norm) of two intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) and the property of image of intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) under group homomorphism in [8] can be valid if t -norm and s -norm are continuous.\",\"PeriodicalId\":53096,\"journal\":{\"name\":\"Jurnal Matematika Integratif\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Jurnal Matematika Integratif\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24198/jmi.v18.n2.40461.141-155\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Jurnal Matematika Integratif","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24198/jmi.v18.n2.40461.141-155","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Sifat-Sifat Subgrup Fuzzy Intuitionistik atas Norm (t-Norm dan s-Norm)
Fuzzy subgroups can be generalized into intuitionistic fuzzy subgroups and fuzzy subgroups over t -norm. Furthermore, intuitionistic fuzzy subgroups and fuzzy subgroups over t -norm can be generalized into intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm). The property of product under norms ( t -norm and s -norm) of two intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) and the property of image of intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) under group homomorphism were dis-cussed by Rasuli [8] . However, by giving counterexamples, it can be shown that both properties are not true. In this article, we reinvestigate the property of product under norms ( t -norm and s -norm) of two intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) and the property of image of intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) under group homomorphism. We use the literature study method in this research. The results show that the property of product under norms ( t -norm and s -norm) of two intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) and the property of image of intuitionistic fuzzy subgroups with respect to norms ( t -norm and s -norm) under group homomorphism in [8] can be valid if t -norm and s -norm are continuous.