Beza Lamesgin Derseh, Berhanu Assaye Alaba, Y. G. Wondifraw
{"title":"pms代数pms -理想的t-直觉模糊结构","authors":"Beza Lamesgin Derseh, Berhanu Assaye Alaba, Y. G. Wondifraw","doi":"10.1155/2022/5101293","DOIUrl":null,"url":null,"abstract":"<jats:p>In this article, we apply the concept of a <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy set to PMS-ideals in PMS-algebras. The notion of the <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal of PMS-algebra is introduced, and several related properties are studied. The relationships between a <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal and a <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, as well as the relationships between an intuitionistic fuzzy PMS-ideal and a <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal are discussed in detail. A condition for an intuitionistic fuzzy set to be a <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal is provided. The <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideals of PMS-algebra are described using their <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>α</mi>\n <mo>,</mo>\n <mi>β</mi>\n </mrow>\n </mfenced>\n </math>\n </jats:inline-formula> level cuts. The homomorphism of a <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal of a PMS-algebra is studied, and its homomorphic image and inverse image are explored. The Cartesian product of any two <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M10\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideals is discussed, and some related results are derived. The Cartesian product of the <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M11\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideals is also characterized using its <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M12\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>α</mi>\n <mo>,</mo>\n <mi>β</mi>\n </mrow>\n </mfenced>\n </math>\n </jats:inline-formula> level cuts. The strongest <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M13\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-relation in a PMS-algebra is defined. Finally, the relationships between the strongest <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M14\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-relation and <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M15\">\n <mi>t</mi>\n </math>\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal are studied.</jats:p>","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"t-Intuitionistic Fuzzy Structures on PMS-Ideals of a PMS-Algebra\",\"authors\":\"Beza Lamesgin Derseh, Berhanu Assaye Alaba, Y. G. Wondifraw\",\"doi\":\"10.1155/2022/5101293\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<jats:p>In this article, we apply the concept of a <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy set to PMS-ideals in PMS-algebras. The notion of the <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M2\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal of PMS-algebra is introduced, and several related properties are studied. The relationships between a <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M3\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal and a <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M4\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, as well as the relationships between an intuitionistic fuzzy PMS-ideal and a <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M5\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal are discussed in detail. A condition for an intuitionistic fuzzy set to be a <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M6\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal is provided. The <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M7\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideals of PMS-algebra are described using their <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M8\\\">\\n <mfenced open=\\\"(\\\" close=\\\")\\\" separators=\\\"|\\\">\\n <mrow>\\n <mi>α</mi>\\n <mo>,</mo>\\n <mi>β</mi>\\n </mrow>\\n </mfenced>\\n </math>\\n </jats:inline-formula> level cuts. The homomorphism of a <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M9\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal of a PMS-algebra is studied, and its homomorphic image and inverse image are explored. The Cartesian product of any two <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M10\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideals is discussed, and some related results are derived. The Cartesian product of the <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M11\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideals is also characterized using its <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M12\\\">\\n <mfenced open=\\\"(\\\" close=\\\")\\\" separators=\\\"|\\\">\\n <mrow>\\n <mi>α</mi>\\n <mo>,</mo>\\n <mi>β</mi>\\n </mrow>\\n </mfenced>\\n </math>\\n </jats:inline-formula> level cuts. The strongest <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M13\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-relation in a PMS-algebra is defined. Finally, the relationships between the strongest <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M14\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-relation and <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M15\\\">\\n <mi>t</mi>\\n </math>\\n </jats:inline-formula>-intuitionistic fuzzy PMS-ideal are studied.</jats:p>\",\"PeriodicalId\":301406,\"journal\":{\"name\":\"Int. J. Math. Math. Sci.\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Int. J. Math. Math. Sci.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2022/5101293\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Math. Math. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2022/5101293","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
t-Intuitionistic Fuzzy Structures on PMS-Ideals of a PMS-Algebra
In this article, we apply the concept of a -intuitionistic fuzzy set to PMS-ideals in PMS-algebras. The notion of the -intuitionistic fuzzy PMS-ideal of PMS-algebra is introduced, and several related properties are studied. The relationships between a -intuitionistic fuzzy PMS-ideal and a -intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, as well as the relationships between an intuitionistic fuzzy PMS-ideal and a -intuitionistic fuzzy PMS-ideal are discussed in detail. A condition for an intuitionistic fuzzy set to be a -intuitionistic fuzzy PMS-ideal is provided. The -intuitionistic fuzzy PMS-ideals of PMS-algebra are described using their level cuts. The homomorphism of a -intuitionistic fuzzy PMS-ideal of a PMS-algebra is studied, and its homomorphic image and inverse image are explored. The Cartesian product of any two -intuitionistic fuzzy PMS-ideals is discussed, and some related results are derived. The Cartesian product of the -intuitionistic fuzzy PMS-ideals is also characterized using its level cuts. The strongest -intuitionistic fuzzy PMS-relation in a PMS-algebra is defined. Finally, the relationships between the strongest -intuitionistic fuzzy PMS-relation and -intuitionistic fuzzy PMS-ideal are studied.
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