{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T01:56:05Z","timestamp":1777600565819,"version":"3.51.4"},"reference-count":63,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T00:00:00Z","timestamp":1707091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>As digital technologies continue to reshape economic landscapes, the comprehensive evaluation of digital economy (DE) development in provincial regions becomes a critical endeavor. This article proposes a novel approach, integrating the linear programming method, fuzzy logic, and the alternative ranking order method accounting for two-step normalization (AROMAN), to assess the multifaceted facets of DE growth. The primary contribution of the AROMAN is the coupling of vector and linear normalization techniques in order to produce accurate data structures that are subsequently utilized in calculations. The proposed methodology accommodates the inherent uncertainties and complexities associated with the evaluation process, offering a robust framework for decision-makers. The linear programming aspect optimizes the weightings assigned to different evaluation criteria, ensuring a dynamic and context-specific assessment. By incorporating fuzzy logic, the model captures the vagueness and imprecision inherent in qualitative assessments, providing a more realistic representation of the DE\u2019s multifaceted nature. The AROMAN further refines the ranking process, considering the interdependencies among the criteria and enhancing the accuracy of the evaluation. In order to ascertain the efficacy of the suggested methodology, a case study is undertaken pertaining to provincial areas, showcasing its implementation in the evaluation and a comparison of DE progress in various geographical settings. The outcomes illustrate the capacity of the model to produce perceptive and implementable insights for policymakers, thereby enabling them to make well-informed decisions and implement focused interventions that promote the expansion of the DE. Moreover, managerial implications, theoretical limitations, and a comparative analysis are also given of the proposed method.<\/jats:p>","DOI":"10.3390\/axioms13020109","type":"journal-article","created":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T08:41:43Z","timestamp":1707122503000},"page":"109","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Linear Programming-Based Fuzzy Alternative Ranking Order Method Accounting for Two-Step Normalization for Comprehensive Evaluation of Digital Economy Development in Provincial Regions"],"prefix":"10.3390","volume":"13","author":[{"given":"Huiling","family":"Xiang","sequence":"first","affiliation":[{"name":"College of Business, Quzhou University, Quzhou 324000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8318-0750","authenticated-orcid":false,"given":"Hafiz Muhammad Athar","family":"Farid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8115-9168","authenticated-orcid":false,"given":"Muhammad","family":"Riaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mao, Y., Zhu, Y., Tang, Z., and Chen, Z. 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