{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:44:34Z","timestamp":1740149074771,"version":"3.37.3"},"reference-count":12,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2018]]},"abstract":"<jats:p>We introduce a new type of functions from a soft set to a soft set and study their properties under soft real number setting. Firstly, we investigate some properties of soft real sets. Considering the partial order relation of soft real numbers, we introduce concept of soft intervals. Boundedness of soft real sets is defined, and the celebrated theorems like nested intervals theorem and Bolzano-Weierstrass theorem are extended in this setting. Next, we introduce the concepts of limit, continuity, and differentiability of functions of soft sets. It has been possible for us to study some fundamental results of continuity of functions of soft sets such as Bolzano\u2019s theorem, intermediate value property, and fixed point theorem. Because the soft real numbers are not linearly ordered, several twists in the arguments are required for proving those results. In the context of differentiability of functions, some basic theorems like Rolle\u2019s theorem and Lagrange\u2019s mean value theorem are also extended in soft setting.<\/jats:p>","DOI":"10.1155\/2018\/6429572","type":"journal-article","created":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T18:34:04Z","timestamp":1519929244000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["A Study on Some Fundamental Properties of Continuity and Differentiability of Functions of Soft Real Numbers"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7882-2245","authenticated-orcid":true,"given":"Ramkrishna","family":"Thakur","sequence":"first","affiliation":[{"name":"Department of Mathematics, Bidhannagar College, Salt Lake, Sector I, Kolkata, West Bengal 700064, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. K.","family":"Samanta","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Visva Bharati, Santiniketan, West Bengal 731235, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(99)00056-5"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(03)00016-6"},{"issue":"3","key":"4","first-page":"589","volume":"9","year":"2001","journal-title":"Journal of Fuzzy Mathematics"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.02.006"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.12.008"},{"key":"7","first-page":"151","volume":"5","year":"2010","journal-title":"Kochi Journal of Mathematics"},{"issue":"3","key":"8","first-page":"707","volume":"21","year":"2013","journal-title":"Journal of Fuzzy Mathematics"},{"issue":"1","key":"9","first-page":"91","volume":"9","year":"2015","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"issue":"3","key":"10","first-page":"551","volume":"20","year":"2012","journal-title":"Journal of Fuzzy Mathematics"},{"issue":"1","key":"11","first-page":"1207","volume":"8","year":"2016","journal-title":"Journal of Progressive Research in Mathematics"},{"issue":"3","key":"12","first-page":"397","volume":"10","year":"2015","journal-title":"Annals of Fuzzy Mathematics and Informatics"}],"container-title":["Advances in Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/6429572.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/6429572.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/6429572.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T18:34:05Z","timestamp":1519929245000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/afs\/2018\/6429572\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"references-count":12,"alternative-id":["6429572","6429572"],"URL":"https:\/\/doi.org\/10.1155\/2018\/6429572","relation":{},"ISSN":["1687-7101","1687-711X"],"issn-type":[{"type":"print","value":"1687-7101"},{"type":"electronic","value":"1687-711X"}],"subject":[],"published":{"date-parts":[[2018]]}}}