{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:22:01Z","timestamp":1760149321424,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T00:00:00Z","timestamp":1690502400000},"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>This work is concerned with the branch of complex analysis known as geometric function theory, which has been modified for use in the study of fuzzy sets. We develop a novel operator L\u03b1,\u03bbm:An\u2192An in the open unit disc \u0394 using the Noor integral operator and the generalized S\u0103l\u0103gean differential operator. First, we develop fuzzy differential subordination for the operator L\u03b1,\u03bbm and then, taking into account this operator, we define a particular fuzzy class of analytic functions in the open unit disc \u0394, represented by R\u03dd\u03bb(m,\u03b1,\u03b4). Using the idea of fuzzy differential subordination, several new results are discovered that are relevant to this class. The fundamental theorems and corollaries are presented, and then examples are provided to illustrate their practical use.<\/jats:p>","DOI":"10.3390\/axioms12080745","type":"journal-article","created":{"date-parts":[[2023,7,31]],"date-time":"2023-07-31T03:30:02Z","timestamp":1690774202000},"page":"745","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Applications of Fuzzy Differential Subordination for a New Subclass of Analytic Functions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0361-4887","authenticated-orcid":false,"given":"Shahid","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4429-9393","authenticated-orcid":false,"given":"Jong-Suk","family":"Ro","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea"},{"name":"Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7855-508X","authenticated-orcid":false,"given":"Fairouz","family":"Tchier","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1123-8578","authenticated-orcid":false,"given":"Nazar","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2751","DOI":"10.1016\/j.ins.2008.02.012","article-title":"Is there a need for fuzzy logic","volume":"178","author":"Zadeh","year":"2008","journal-title":"Inf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1080\/01969727208542910","article-title":"Fuzzy-set-theoretic interpretation of linguistic hedges","volume":"2","author":"Zadeh","year":"1972","journal-title":"J. Cybern."},{"key":"ref_3","first-page":"421","article-title":"Concepts of probabilistic sets, Fuzzy event","volume":"23","author":"Hirota","year":"1981","journal-title":"J. Math. Anna. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1080\/03081078608934952","article-title":"On the theory of bags","volume":"13","author":"Yager","year":"1986","journal-title":"Int. J. Gener. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"748","DOI":"10.15837\/ijccc.2017.6.3111","article-title":"Fuzzy logic is not fuzzy. world-renowned computer scientist Lotfi A. Zadeh","volume":"12","author":"Dzitac","year":"2017","journal-title":"Int. J. Comp. Commun. Control"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Dzitac, S., and N\u0103d\u0103ban, S. (2021). Soft computing for decision-making in fuzzy environments: A tribute to Professor Ioan Dzitac. Mathematics, 9.","DOI":"10.3390\/math9141701"},{"key":"ref_8","unstructured":"Zadeh, L.A., Tufis, D., Filip, F.G., and Dzitac, I. (2008). From Natural Language to Soft Computing: New Paradigms in Artificial Intelligence, Editing House of Romanian Academy."},{"key":"ref_9","first-page":"97","article-title":"The notion of subordination in fuzzy sets theory","volume":"19","author":"Oros","year":"2011","journal-title":"Gen. Math."},{"key":"ref_10","first-page":"55","article-title":"Fuzzy differential subordination","volume":"3","author":"Oros","year":"2012","journal-title":"Acta Univ. Apulensis"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/0022-247X(78)90181-6","article-title":"Second order-differential inequalities in the complex plane","volume":"65","author":"Miller","year":"1978","journal-title":"J. Math. Anal. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1307\/mmj\/1029002507","article-title":"Differential subordinations and univalent functions","volume":"28","author":"Miller","year":"1981","journal-title":"Michig. Math. J."},{"key":"ref_13","first-page":"1476","article-title":"A note on special fuzzy differential subordinations using generalized S\u0103l\u0103gean operator and Ruscheweyh derivative","volume":"15","author":"Lupas","year":"2013","journal-title":"J. Comput. Anal. Appl."},{"key":"ref_14","first-page":"119","article-title":"On special fuzzy differential subordinations using S\u0103l\u0103gean and Ruscheweyh operators","volume":"261","author":"Lupas","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_15","first-page":"167","article-title":"On special fuzzy differential subordination using Ruscheweyh operator","volume":"22","author":"Venter","year":"2015","journal-title":"Analele Univ. Oradea Fasc. Mat."},{"key":"ref_16","first-page":"133","article-title":"Fuzzy differential subordinations associated with an integral operator","volume":"27","author":"Lupas","year":"2020","journal-title":"An. Univ. Oradea Fasc. Mat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"397","DOI":"10.21136\/MB.2020.0159-19","article-title":"Fuzzy differential subordinations connected with the linear operator","volume":"146","author":"Oros","year":"2021","journal-title":"Math. Bohem."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"229","DOI":"10.31801\/cfsuasmas.784080","article-title":"New fuzzy differential subordinations","volume":"70","author":"Oros","year":"2021","journal-title":"Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Srivastava, H.M., and El-Deeb, S.M. (2021). Fuzzy differential subordinations based upon the Mittag-Leffler type Borel distribution. Symmetry, 13.","DOI":"10.3390\/sym13061023"},{"key":"ref_20","first-page":"781","article-title":"On special differential subordinations using S \u0103l\u0103gean and Ruscheweyh operators","volume":"12","year":"2009","journal-title":"Math. Inequal. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1070\/RM9740","article-title":"Perturbations of self-adjoint and normal operators with discrete spectrum","volume":"71","author":"Shkalikov","year":"2016","journal-title":"Russ. Math. Surv."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1461647","DOI":"10.1155\/2020\/1461647","article-title":"On One Method of Studying Spectral Properties of Non-selfadjoint Operators","volume":"2020","author":"Kukushkin","year":"2020","journal-title":"Abstr. Appl. Anal."},{"key":"ref_23","first-page":"67","article-title":"On a certain subclass of analytic functions defined by S\u0103l\u0103gean and Ruscheweyh operators","volume":"31","author":"Lupas","year":"2009","journal-title":"J. Math. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Lupa\u0327s, A.A., and Oros, G.I. (2021). New applications of S\u0103l\u0103 gean and Ruscheweyh operators for obtaining fuzzy differential subordinations. Mathematics, 9.","DOI":"10.3390\/math9162000"},{"key":"ref_25","first-page":"71","article-title":"On new classes of integral operators","volume":"16","author":"Noor","year":"1999","journal-title":"J. Natur. Geom."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1090\/S0002-9939-1975-0367176-1","article-title":"New criteria for univalent functions","volume":"49","author":"Ruscheweyh","year":"1975","journal-title":"Proc. Amer. Math. Soc."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Oros, G.I., and Dzitac, S. (2022). Applications of subordination chains and fractional integral in fuzzy differential subordinations. Mathematics, 10.","DOI":"10.3390\/math10101690"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Alb Lupas, A. (2021). Fuzzy differential sandwich theorems involving the fractional integral of confluent hypergeometric function. Symmetry, 13.","DOI":"10.3390\/sym13111992"},{"key":"ref_29","first-page":"1429","article-title":"On univalent functions defined by a generalized S\u0103l\u0103gean operator","volume":"27","year":"2004","journal-title":"Ind. J. Math. Math. Sci."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/8\/745\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:21:55Z","timestamp":1760127715000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/8\/745"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,28]]},"references-count":29,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["axioms12080745"],"URL":"https:\/\/doi.org\/10.3390\/axioms12080745","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,7,28]]}}}