{"title":"q-Rung正交模糊导数和不定积分的一些性质","authors":"Junle Zhuo","doi":"10.22457/jmi.139av16a5","DOIUrl":null,"url":null,"abstract":"Abstract. In this paper, we first present the chain rule and the form invariance of differential for q-rung orthopair fuzzy functions (q-ROFFs). In addi tion, we obtain the general formula of indefinite integrals of q-ROFFs by ordinary differential equations. Next, we give the substitution rule of indefinite i ntegrals for q-ROFFs. Meanwhile, we give some examples to verify above-mentioned formul a, such as the chain rule and the substitution rule.","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"70 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Some Properties of q-Rung Orthopair Fuzzy Derivatives and Indefinite Integrals\",\"authors\":\"Junle Zhuo\",\"doi\":\"10.22457/jmi.139av16a5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. In this paper, we first present the chain rule and the form invariance of differential for q-rung orthopair fuzzy functions (q-ROFFs). In addi tion, we obtain the general formula of indefinite integrals of q-ROFFs by ordinary differential equations. Next, we give the substitution rule of indefinite i ntegrals for q-ROFFs. Meanwhile, we give some examples to verify above-mentioned formul a, such as the chain rule and the substitution rule.\",\"PeriodicalId\":43016,\"journal\":{\"name\":\"Journal of Applied Mathematics Statistics and Informatics\",\"volume\":\"70 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2019-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mathematics Statistics and Informatics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22457/jmi.139av16a5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics Statistics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22457/jmi.139av16a5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Some Properties of q-Rung Orthopair Fuzzy Derivatives and Indefinite Integrals
Abstract. In this paper, we first present the chain rule and the form invariance of differential for q-rung orthopair fuzzy functions (q-ROFFs). In addi tion, we obtain the general formula of indefinite integrals of q-ROFFs by ordinary differential equations. Next, we give the substitution rule of indefinite i ntegrals for q-ROFFs. Meanwhile, we give some examples to verify above-mentioned formul a, such as the chain rule and the substitution rule.