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This article examines the impact of carbon emissions on non-instantaneously degrading commodities with price-dependent demand and advertisements since many nations are implementing emission reduction policies. The paper also focuses on the effects of inflation, where shortages are partially backlogged and partially lost in sales. This paper develops a new concept of non-linear triangular dense neutrosophic numbers with its basic properties. Further, the classifications of symmetry and asymmetry are introduced, and thereafter De-neutrosophication technique is applied for crispification. Since the effect of some parameters like carbon emissions, advertising, and inflation are uncertain, we have considered it in this new form described above to grab the uncertain characters of the underlying parameters. The classification of the uncertain parameter based on the symmetric and asymmetric nature and linear-nonlinear nature of triangular dense neutrosophic numbers have also been investigated here. Additionally, the effect of the model is examined under different situations for both linear and non-linear triangular dense fuzzy, dense intuitionistic, and dense neutrosophic. Finally, a numerical example is considered to illustrate the model, and it is observed that the model is optimum when the parameters are considered in Asymmetric Convex Non-Linear numbers for a shorter replenishment cycle. Also, a comparative study has been done by performing sensitivity analysis through the case study and provides managerial insight into this outcome.<\/jats:p>","DOI":"10.1051\/ro\/2024078","type":"journal-article","created":{"date-parts":[[2024,4,4]],"date-time":"2024-04-04T08:23:52Z","timestamp":1712219032000},"page":"193-218","source":"Crossref","is-referenced-by-count":2,"title":["A case study of the impact of carbon emissions and inflation on nonlinear dense neutrosophic fuzzy inventory system of varying demand with delayed deterioration"],"prefix":"10.1051","volume":"59","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6899-2315","authenticated-orcid":false,"given":"Shilpi","family":"Pal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Avishek","family":"Chakraborty","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5225-0445","authenticated-orcid":false,"given":"Ghanshaym Singha","family":"Mahapatra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2025,1,16]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.asoc.2019.01.035","volume":"77","author":"Abdel-Basset","year":"2019","journal-title":"Appl. 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