{"title":"图像模糊集的几个方面","authors":"Palash Dutta, Silpashree Ganju","doi":"10.1016/j.trmi.2017.10.006","DOIUrl":null,"url":null,"abstract":"<div><p>Picture fuzzy set (PFS) is a recently developed tool to deal with uncertainty which is a direct extension of intuitionistic fuzzy set (IFS) that can model uncertainty in such situations involving more answers of these types: yes, abstain, no. In this paper, (<span><math><mi>α</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>β</mi></math></span>)-cut and strong (<span><math><mi>α</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>β</mi></math></span>)-cut of PFS have been defined and decomposition theorems of PFS are proved. Later on extension principle for PFS has been defined and studied some of its properties. Finally, picture fuzzy arithmetic based on extension principle has been performed with examples.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 2","pages":"Pages 164-175"},"PeriodicalIF":0.3000,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.10.006","citationCount":"44","resultStr":"{\"title\":\"Some aspects of picture fuzzy set\",\"authors\":\"Palash Dutta, Silpashree Ganju\",\"doi\":\"10.1016/j.trmi.2017.10.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Picture fuzzy set (PFS) is a recently developed tool to deal with uncertainty which is a direct extension of intuitionistic fuzzy set (IFS) that can model uncertainty in such situations involving more answers of these types: yes, abstain, no. In this paper, (<span><math><mi>α</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>β</mi></math></span>)-cut and strong (<span><math><mi>α</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>β</mi></math></span>)-cut of PFS have been defined and decomposition theorems of PFS are proved. Later on extension principle for PFS has been defined and studied some of its properties. Finally, picture fuzzy arithmetic based on extension principle has been performed with examples.</p></div>\",\"PeriodicalId\":43623,\"journal\":{\"name\":\"Transactions of A Razmadze Mathematical Institute\",\"volume\":\"172 2\",\"pages\":\"Pages 164-175\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2018-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.trmi.2017.10.006\",\"citationCount\":\"44\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of A Razmadze Mathematical Institute\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2346809217300028\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of A Razmadze Mathematical Institute","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2346809217300028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Picture fuzzy set (PFS) is a recently developed tool to deal with uncertainty which is a direct extension of intuitionistic fuzzy set (IFS) that can model uncertainty in such situations involving more answers of these types: yes, abstain, no. In this paper, ()-cut and strong ()-cut of PFS have been defined and decomposition theorems of PFS are proved. Later on extension principle for PFS has been defined and studied some of its properties. Finally, picture fuzzy arithmetic based on extension principle has been performed with examples.
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