{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T12:56:29Z","timestamp":1769950589565,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T00:00:00Z","timestamp":1672099200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2021M700920"],"award-info":[{"award-number":["2021M700920"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and q-rung orthopair fuzzy sets (q-ROFS) are among those concepts which are widely used in real-world applications. However, these theories have their own limitations in terms of membership and non-membership functions, as they cannot be obtained from the whole unit plane. To overcome these restrictions, we developed the concept of a complex linear Diophantine fuzzy set (CLDFS) by generalizing the notion of a linear Diophantine fuzzy set (LDFS). This concept can be applied to real-world decision-making problems involving complex uncertain information. The main motivation behind this paper is to study the applications of CLDFS in a non-associative algebraic structure (AG-groupoid), which has received less attention as compared to associative structures. We characterize a strongly regular AG-groupoid in terms of newly developed CLDF-score left (right) ideals and CLDF-score (0,2)-ideals. Finally, we construct a novel approach to decision-making problems based on the proposed CLDF-score ideals, and some practical examples from civil engineering are considered to demonstrate the flexibility and clarity of the initiated CLDF-score ideals.<\/jats:p>","DOI":"10.3390\/sym15010074","type":"journal-article","created":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T08:42:22Z","timestamp":1672216942000},"page":"74","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Complex Linear Diophantine Fuzzy Sets over AG-Groupoids with Applications in Civil Engineering"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7859-5409","authenticated-orcid":false,"given":"Hao","family":"Guan","sequence":"first","affiliation":[{"name":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China"},{"name":"School of Computer Science of Information Technology, Qiannan Normal University for Nationalities, Duyun 558000, China"}]},{"given":"Faisal","family":"Yousafzai","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Humanities, National University of Sciences and Technology (NUST), Islamabad 24090, Pakistan"}]},{"given":"Muhammad Danish","family":"Zia","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Humanities, National University of Sciences and Technology (NUST), Islamabad 24090, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0055-9077","authenticated-orcid":false,"given":"Murad-ul-Islam","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Haripur, Haripur 22620, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6511-9892","authenticated-orcid":false,"given":"Muhammad","family":"Irfan","sequence":"additional","affiliation":[{"name":"School of Civil and Environmental Engineering, National University of Sciences and Technology, Islamabad 24090, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6425-2619","authenticated-orcid":false,"given":"Kostaq","family":"Hila","sequence":"additional","affiliation":[{"name":"Department of Mathematical Engineering, Polytechnic University of Tirana, 1001 Tirana, Albania"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zadeh, L.A. (1996). Fuzzy sets. Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi A Zadeh, World Scientific.","DOI":"10.1142\/9789814261302_0001"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Krassimir","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1109\/TFUZZ.2013.2278989","article-title":"Pythagorean membership grades in multicriteria decision making","volume":"22","author":"Yager","year":"2013","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_4","unstructured":"Atanassov, K.T. (2022, November 01). Geometrical Interpretation of the Elements of the Intuitionistic Fuzzy Objects. Preprint IM-MFAIS-1-89, Sofia, Available online: http:\/\/www.biomed.bas.bg\/bioautomation\/2016\/vol_20.s1\/files\/20.s1_05.pdf."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/TFUZZ.2016.2604005","article-title":"Generalized orthopair fuzzy sets","volume":"25","author":"Yager","year":"2016","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1002\/int.21927","article-title":"Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making","volume":"33","author":"Liu","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2139","DOI":"10.1002\/int.22007","article-title":"Another view on q-rung orthopair fuzzy sets","volume":"33","author":"Ali","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1109\/91.995119","article-title":"Complex fuzzy sets","volume":"10","author":"Ramot","year":"2002","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1063\/1.4757515","article-title":"Complex intuitionistic fuzzy sets","volume":"Volume 1482","author":"Alkouri","year":"2012","journal-title":"AIP Conference Proceedings"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s40747-019-0103-6","article-title":"On some distance measures of complex pythagorean fuzzy sets and their applications in pattern recognition","volume":"6","author":"Ullah","year":"2020","journal-title":"Complex Intell. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.2991\/ijcis.d.191030.002","article-title":"A method to multi-attribute group decision-making problem with complex q-rung orthopair linguistic information based on heronian mean operators","volume":"12","author":"Liu","year":"2019","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5417","DOI":"10.3233\/JIFS-190550","article-title":"Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems","volume":"37","author":"Riaz","year":"2019","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1687","DOI":"10.1007\/s12652-021-03130-y","article-title":"A new approach to q-linear diophantine fuzzy emergency decision support system for COVID-19","volume":"13","author":"Almagrabi","year":"2022","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sertic, P., Alahmar, A., Akilan, T., Javorac, M., and Gupta, Y. (2022). Intelligent Real-Time Face-Mask Detection System with Hardware Acceleration for COVID-19 Mitigation. Healthcare, 10.","DOI":"10.3390\/healthcare10050873"},{"key":"ref_15","unstructured":"Refonaa, J., Huy, D.T.N., Trung, N.D., Van Thuc, H., Raj, R., Haq, M.A., and Kumar, A. (2022). Probabilistic methods and neural networks in structural engineering. Int. J. Adv. Manuf. Technol., 1\u20139."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"459","DOI":"10.3846\/tede.2020.13181","article-title":"Identifying key factors for adopting artificial intelligence-enabled auditing techniques by joint utilization of fuzzy-rough set theory and MRDM technique","volume":"27","author":"Hu","year":"2021","journal-title":"Technol. Econ. Dev. Econ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"402","DOI":"10.3846\/tede.2021.14433","article-title":"An overview of fuzzy techniques in supply chain management: Bibliometrics, methodologies, applications and future directions","volume":"27","author":"Lu","year":"2021","journal-title":"Technol. Econ. Dev. Econ."},{"key":"ref_18","first-page":"27","article-title":"Symmetric implicational algorithm derived from intuitionistic fuzzy entropy","volume":"19","author":"Tang","year":"2022","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"147","DOI":"10.36548\/jismac.2019.3.002","article-title":"A comprehensive survey on the computational intelligence techniques and its applications","volume":"1","author":"Raj","year":"2019","journal-title":"J. ISMAC"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"196075","DOI":"10.1109\/ACCESS.2020.3034626","article-title":"A novel applications of complex intuitionistic fuzzy sets in group theory","volume":"8","author":"Gulzar","year":"2020","journal-title":"IEEE Access."},{"key":"ref_21","first-page":"1","article-title":"On almost semigroups","volume":"2","author":"Kazim","year":"1972","journal-title":"Alig. Bull. Math."},{"key":"ref_22","first-page":"175","article-title":"Composition of Abel-Grassmann\u2019s 3-bands","volume":"34","year":"2004","journal-title":"Novi Sad J. Math."},{"key":"ref_23","first-page":"65","article-title":"On LA-semigroups","volume":"8","author":"Mushtaq","year":"1978","journal-title":"Alig. Bull. Math."},{"key":"ref_24","unstructured":"Kamran, M.S. (1987). Structural Properties of LA-Semigroups. [Master\u2019s Thesis, Quaid-i-Azam University]."},{"key":"ref_25","first-page":"57","article-title":"On locally associative left almost semigroups","volume":"19","author":"Mushtaq","year":"1979","journal-title":"J. Nat. Sci. Math."},{"key":"ref_26","first-page":"371","article-title":"AG-test and some general properties of Abel-Grassmann\u2019s groupoids","volume":"6","year":"1995","journal-title":"Pure Math. Appl."},{"key":"ref_27","first-page":"879","article-title":"Some congruences on an AG**-groupoid","volume":"9","year":"1995","journal-title":"Filomat"},{"key":"ref_28","first-page":"283","article-title":"Congruences on an inverse AG**-groupoid via the natural partial order","volume":"17","year":"2009","journal-title":"Quasigroups Relat. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0165-0114(94)90084-1","article-title":"Handling multicriteria fuzzy decision-making problems based on vague set theory","volume":"67","author":"Chen","year":"1994","journal-title":"Fuzzy Sets Syst."},{"key":"ref_30","first-page":"203","article-title":"Congruences on completely inverse AG**-groupoid","volume":"20","author":"Dudek","year":"2012","journal-title":"Quasigroups Relat. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s00233-013-9465-z","article-title":"Completely inverse AG**-groupoid","volume":"87","author":"Dudek","year":"2013","journal-title":"Semigroup Forum"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s13370-011-0055-5","article-title":"Left almost semigroups characterized by their interval valued fuzzy ideals","volume":"24","author":"Yaqoob","year":"2013","journal-title":"Afr. Mat."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1007\/s13370-012-0081-y","article-title":"Left regular AG-groupoids in terms of fuzzy interior ideals","volume":"24","author":"Yousafzai","year":"2013","journal-title":"Afr. Mat."},{"key":"ref_34","first-page":"83","article-title":"Congruences induced by certain relations on AG**-groupoids","volume":"82","author":"Yousafzai","year":"2020","journal-title":"UPB Sci. Bull. Ser. A"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF00122574","article-title":"Advances in prospect theory: Cumulative representation of uncertainty","volume":"5","author":"Tversky","year":"1992","journal-title":"J. Risk Uncertain."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S0165-0114(98)00271-1","article-title":"Multicriteria fuzzy decision making problems based on vague set theory","volume":"114","author":"Hong","year":"2000","journal-title":"Fuzzy Sets Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1080\/03081070600574353","article-title":"Some geometric aggregation operators based on intuitionistic fuzzy sets","volume":"35","author":"Xu","year":"2006","journal-title":"Int. J. Gen. Syst."},{"key":"ref_38","first-page":"215","article-title":"Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making","volume":"22","author":"Xu","year":"2007","journal-title":"Control Decis."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Mordeson, J.N., Malik, D.S., and Kuroki, N. (2003). Fuzzy Semigroups, Springer. Studies in Fuzziness and Soft Computing 131.","DOI":"10.1007\/978-3-540-37125-0_5"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"109","DOI":"10.5373\/jarpm.670.121410","article-title":"On some classes of Abel-Grassmann\u2019s groupoids","volume":"3","author":"Khan","year":"2011","journal-title":"J. Adv. Res. Pure Math."},{"key":"ref_41","first-page":"277","article-title":"On generalized ideals of left almost semigroups","volume":"9","author":"Khan","year":"2016","journal-title":"Eur. J. Pure Appl. Math."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1917","DOI":"10.3233\/JIFS-161299","article-title":"Some studies in fuzzy non-associative semigroups","volume":"32","author":"Yousafzai","year":"2017","journal-title":"J. Of Intelligent Fuzzy Syst."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2038724","DOI":"10.1155\/2020\/2038724","article-title":"On Structural Properties of \u03be-Complex Fuzzy Sets and Their Applications","volume":"2020","author":"Imtiaz","year":"2020","journal-title":"Complexity"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Huy, D.T.N., Nhan, V.K., Bich, N.T.N., Hong, N.T.P., Chung, N.T., and Huy, P.Q. (2021). Impacts of internal and external macroeconomic factors on firm stock price in an expansion econometric model\u2014A case in the Vietnam real estate industry. Data Science for Financial Econometrics, Springer.","DOI":"10.1007\/978-3-030-48853-6_14"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/1\/74\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:52:44Z","timestamp":1760147564000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/1\/74"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,27]]},"references-count":44,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["sym15010074"],"URL":"https:\/\/doi.org\/10.3390\/sym15010074","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,27]]}}}