{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:50:06Z","timestamp":1777704606608,"version":"3.51.4"},"reference-count":59,"publisher":"SAGE Publications","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,4,22]]},"abstract":"<jats:p>T-spherical fuzzy numbers (FNs), which add an abstinence degree based on membership and non-membership degrees, can express neutral information conveniently and have a considerable large range of information expression. The normal FNs (NFNs) are very available to characterize normal distribution phenomenon widely existing in social life. In this paper, we first define the normal T-SFNs (NT-SFNs) which can combine the advantages of T-SFNs and NFNs. Then, we define their operational laws, score value, and accuracy value. By considering the interrelationship among multi-input parameters, we propose the Maclaurin symmetric mean operator with NT-SFNs (NT-SFMSM) and its weighted form (NT-SFWMSM). Furthermore, we study some characteristics and special cases of them. Based on the NT-SFWMSM operator, we put forward a novel multi-attribute decision-making (MADM) approach. Finally, some numerical examples are conducted to prove that the proposed approach is valid and superior to some other existing methods.<\/jats:p>","DOI":"10.3233\/jifs-202000","type":"journal-article","created":{"date-parts":[[2021,2,2]],"date-time":"2021-02-02T18:20:32Z","timestamp":1612290032000},"page":"9543-9565","source":"Crossref","is-referenced-by-count":16,"title":["Multi-attribute decision-making method based on normal T-spherical fuzzy aggregation operator"],"prefix":"10.1177","volume":"40","author":[{"given":"Peide","family":"Liu","sequence":"first","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan Shandong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongyang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan Shandong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Zhang","sequence":"additional","affiliation":[{"name":"Inspur Group Ltd, Jinan Shandong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Yan","sequence":"additional","affiliation":[{"name":"Inspur Group Ltd, Jinan Shandong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Li","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan Shandong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lili","family":"Rong","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan Shandong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"1","key":"10.3233\/JIFS-202000_ref1","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets System"},{"issue":"1","key":"10.3233\/JIFS-202000_ref2","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0165-0114(89)90215-7","article-title":"More on intuitionistic fuzzy sets","volume":"33","author":"Atanassov","year":"1989","journal-title":"Fuzzy Sets System"},{"issue":"4","key":"10.3233\/JIFS-202000_ref3","first-page":"409","article-title":"Picture fuzzy sets","volume":"30","author":"Cuong","year":"2014","journal-title":"Journal of Computer Science Cybernetics"},{"key":"10.3233\/JIFS-202000_ref4","doi-asserted-by":"crossref","unstructured":"Cuong B.C. , Kreinovich V. , Picture Fuzzy Sets \u2013 a new concept for computational intelligence problems, 2013 Third World Congress on Information and Communication Technologies. 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