{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T19:07:58Z","timestamp":1769713678744,"version":"3.49.0"},"reference-count":41,"publisher":"SAGE Publications","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,12,2]]},"abstract":"<jats:p>A T-spherical fuzzy set (TSFS) is an extended and logical algebraic representation to handle uncertainty, with the help of four functions describing four possible aspects of uncertain information. Aczel-Alsina triangular norm (TN) and conorm (TCN) are novel and proved to be more efficient than other existing TNs and TCNs. In our article, we establish the concept of a T-spherical fuzzy Aczel-Alsina graph (TSFAAG). We described the energy of TSFAAG along with the splitting and shadow energy of TSFAAG. Furthermore, we figured out the Randi\u0107 energy of TSFAAG and obtained some useful results. Moreover, we give the notion of the Aczel-Alsina digraph (TSFAADG). To see the significance of the proposed TSFAADGs, we employed the energy and Randi\u0107 energy of TSFAADGs for solving the problem of selecting the best investing company by using a decision-making algorithm. The sensitivity analysis of the variable parameters is also discussed and where the effect on ranking results is studied. To see the effectiveness of the proposed work, we did a comparative study and established some remarks.<\/jats:p>","DOI":"10.3233\/jifs-231086","type":"journal-article","created":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T12:04:37Z","timestamp":1689681877000},"page":"9363-9385","source":"Crossref","is-referenced-by-count":2,"title":["Energies of T-spherical fuzzy graph based on novel Aczel-Alsina T-norm and T-conorm with their applications in decision making"],"prefix":"10.1177","volume":"45","author":[{"given":"Mah","family":"Noor","sequence":"first","affiliation":[{"name":"Department of Mathematics, Riphah International University Lahore, Pakistan"}]},{"given":"Muhammad Kamran","family":"Jamil","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riphah International University Lahore, Pakistan"}]},{"given":"Kifayat","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riphah International University Lahore, Pakistan"}]},{"given":"Muhammad","family":"Azeem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riphah International University Lahore, Pakistan"}]},{"given":"Dragan","family":"Pamucar","sequence":"additional","affiliation":[{"name":"Faculty of Organizational Sciences, University of Belgrade, Belgrade, Serbia"},{"name":"College of Engineering, Yuan Ze University, Taiwan"},{"name":"Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon"}]},{"given":"Bandar","family":"Almohsen","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-231086_ref1","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/BF02189626","article-title":"Characterizations of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements","volume":"25","author":"Acz\u00e9l","year":"1982","journal-title":"Aequationes Mathematicae"},{"issue":"1","key":"10.3233\/JIFS-231086_ref2","doi-asserted-by":"crossref","first-page":"8","DOI":"10.3390\/mca25010008","article-title":"Spherical fuzzy graphs with application to decision-making","volume":"25","author":"Akram","year":"2020","journal-title":"Mathematical and Computational Applications"},{"issue":"1","key":"10.3233\/JIFS-231086_ref3","doi-asserted-by":"crossref","first-page":"301","DOI":"10.31181\/rme20020042022a","article-title":"Intervalvalued picture fuzzy maclaurin symmetric mean operator with application in multiple attribute decision-making","volume":"3","author":"Ashraf","year":"2022","journal-title":"Reports in Mechanical Engineering"},{"key":"10.3233\/JIFS-231086_ref4","doi-asserted-by":"crossref","unstructured":"Asif K. , Jamil M.K. , Karamti H. , Azeem M. and Ullah K. , Randic energies for t-spherical fuzzy hamacher graphs and their applications in decision making for business plans, Computational and Applied Mathematics 42(3) (2023).","DOI":"10.1007\/s40314-023-02243-8"},{"key":"10.3233\/JIFS-231086_ref5","first-page":"1","article-title":"Intuitionistic fuzzy sets","author":"Atanassov","year":"1999","journal-title":"Intuitionistic Fuzzy Sets"},{"issue":"2","key":"10.3233\/JIFS-231086_ref6","doi-asserted-by":"crossref","first-page":"101779","DOI":"10.1016\/j.jksus.2021.101779","article-title":"Sharp bounds on partition dimension of hexagonal m\u00f6bius ladder","volume":"34","author":"Azeem","year":"2022","journal-title":"Journal of King Saud University - Science"},{"issue":"4","key":"10.3233\/JIFS-231086_ref7","doi-asserted-by":"crossref","first-page":"844","DOI":"10.3390\/math11040844","article-title":"Notes on the localization of generalized hexagonal cellular networks","volume":"11","author":"Azeem","year":"2023","journal-title":"Mathematics"},{"key":"10.3233\/JIFS-231086_ref8","doi-asserted-by":"crossref","unstructured":"Cuong B.C. and Kreinovich V. , Picture fuzzy sets - a new concept for computational intelligence problems. 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