{"title":"Klein-4组的直觉水平亚组","authors":"S. D. M. Daise, S. Tresa, Shery Fernandez","doi":"10.37193/cmi.2021.02.06","DOIUrl":null,"url":null,"abstract":"A BSTRACT . In this paper we check the status of the already known result “level subgroups of any fuzzy subgroup of a finite group forms a chain” in Intuitionistic Fuzzy environment. The tool we use for this is the Klein-4 group V , which is a non-cyclic group. We prove that V has 64 distinct Intuitionistic Fuzzy Subgroups (IFSGs) upto isomorphism. The Intuitionistic Level Subgroups (ILSGs) of only 40 among them form chains and so the result is not true in intuitionistic fuzzy case. To strengthen our findings we provide a python program to construct the geometric representations of all the 64 IFSGs and its output.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Intuitionistic level subgroups in the Klein-4 group\",\"authors\":\"S. D. M. Daise, S. Tresa, Shery Fernandez\",\"doi\":\"10.37193/cmi.2021.02.06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A BSTRACT . In this paper we check the status of the already known result “level subgroups of any fuzzy subgroup of a finite group forms a chain” in Intuitionistic Fuzzy environment. The tool we use for this is the Klein-4 group V , which is a non-cyclic group. We prove that V has 64 distinct Intuitionistic Fuzzy Subgroups (IFSGs) upto isomorphism. The Intuitionistic Level Subgroups (ILSGs) of only 40 among them form chains and so the result is not true in intuitionistic fuzzy case. To strengthen our findings we provide a python program to construct the geometric representations of all the 64 IFSGs and its output.\",\"PeriodicalId\":112946,\"journal\":{\"name\":\"Creative Mathematics and Informatics\",\"volume\":\"27 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Creative Mathematics and Informatics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37193/cmi.2021.02.06\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Creative Mathematics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37193/cmi.2021.02.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Intuitionistic level subgroups in the Klein-4 group
A BSTRACT . In this paper we check the status of the already known result “level subgroups of any fuzzy subgroup of a finite group forms a chain” in Intuitionistic Fuzzy environment. The tool we use for this is the Klein-4 group V , which is a non-cyclic group. We prove that V has 64 distinct Intuitionistic Fuzzy Subgroups (IFSGs) upto isomorphism. The Intuitionistic Level Subgroups (ILSGs) of only 40 among them form chains and so the result is not true in intuitionistic fuzzy case. To strengthen our findings we provide a python program to construct the geometric representations of all the 64 IFSGs and its output.
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