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We investigate several fundamental properties of metric space in the contemporary of Type 2 interval setting. After significant findings in differential calculus using generalized Hukuhara difference of Type 2 interval numbers, a detailed and novel manifestation of integral calculus including Riemann and Lebesgue senses is also done in this paper. We also provide hints for possible mathematical modelings of real-world scenarios using Type 2 interval-ruled uncertain decision realm. <\/jats:p>","DOI":"10.1142\/s1752890924500181","type":"journal-article","created":{"date-parts":[[2024,7,17]],"date-time":"2024-07-17T14:47:56Z","timestamp":1721227676000},"source":"Crossref","is-referenced-by-count":2,"title":["Metric Space and Calculus of Type-2 Interval-Valued Functions"],"prefix":"10.1142","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5513-4095","authenticated-orcid":false,"given":"Mostafijur","family":"Rahaman","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India"},{"name":"Department of Mathematics, School of Liberal Arts and Sciences, Mohan Babu University, Tirupati, Andhra Pradesh 517102, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0544-3949","authenticated-orcid":false,"given":"Manojit","family":"Das","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India"},{"name":"School of Applied Science and Humanities, Haldia Institute of Technology, Haldia, West Bengal 721657, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8263-117X","authenticated-orcid":false,"given":"Shariful","family":"Alam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1390-3551","authenticated-orcid":false,"given":"Soheil","family":"Salahshour","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey"},{"name":"Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4690-2598","authenticated-orcid":false,"given":"Sankar Prasad","family":"Mondal","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata 741249, Nadia, West Bengal, India"}]}],"member":"219","published-online":{"date-parts":[[2024,9,4]]},"reference":[{"key":"S1752890924500181BIB001","doi-asserted-by":"publisher","DOI":"10.1177\/0954411919865389"},{"key":"S1752890924500181BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s13369-020-04583-7"},{"key":"S1752890924500181BIB003","first-page":"1","volume":"35","author":"Sen B.","year":"2023","journal-title":"Sustain. 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