{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T04:30:54Z","timestamp":1781065854554,"version":"3.54.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Fuzzy Syst."],"published-print":{"date-parts":[[2025,11]]},"DOI":"10.1007\/s40815-024-01905-x","type":"journal-article","created":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T14:19:31Z","timestamp":1736259571000},"page":"2467-2494","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Innovative Multi-Criteria Group Decision Making with\u00a0Interval-Valued p,\u00a0q,\u00a0r-Spherical Fuzzy Sets: A Case Study on Optimal Solar Energy Investment Location"],"prefix":"10.1007","volume":"27","author":[{"given":"Muhammad","family":"Rahim","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sanaa Ahmed","family":"Bajri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Salma","family":"Khan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haifa","family":"Alqahtani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hamiden Abd El-Wahed","family":"Khalifa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,1,7]]},"reference":[{"issue":"3","key":"1905_CR1","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338\u2013353 (1965)","journal-title":"Inf. Control"},{"key":"1905_CR2","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"KT Atanassov","year":"1986","unstructured":"Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87\u201396 (1986)","journal-title":"Fuzzy Sets Syst."},{"key":"1905_CR3","doi-asserted-by":"crossref","unstructured":"Yager, R.R.: Pythagorean fuzzy subsets. In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA\/NAFIPS), pp. 57\u201361. IEEE (2013)","DOI":"10.1109\/IFSA-NAFIPS.2013.6608375"},{"key":"1905_CR4","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1007\/s12652-019-01377-0","volume":"11","author":"T Senapati","year":"2020","unstructured":"Senapati, T., Yager, R.R.: Fermatean fuzzy sets. J. Ambient Intell. Human. Comput. 11, 663\u2013674 (2020)","journal-title":"J. Ambient Intell. Human. Comput."},{"issue":"5","key":"1905_CR5","doi-asserted-by":"publisher","first-page":"1222","DOI":"10.1109\/TFUZZ.2016.2604005","volume":"25","author":"RR Yager","year":"2016","unstructured":"Yager, R.R.: Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25(5), 1222\u20131230 (2016)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1905_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2022.105299","volume":"115","author":"MR Seikh","year":"2022","unstructured":"Seikh, M.R., Mandal, U.: Multiple attribute group decision making based on quasirung orthopair fuzzy sets: application to electric vehicle charging station site selection problem. Eng. Appl. Artif. Intell. 115, 105299 (2022)","journal-title":"Eng. Appl. Artif. Intell."},{"key":"1905_CR7","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2023.3274494","author":"J Ali","year":"2023","unstructured":"Ali, J., Naeem, M.: Analysis and application of p, q-quasirung orthopair fuzzy Aczel\u2013Alsina aggregation operators in multiple criteria decision-making. IEEE Access (2023). https:\/\/doi.org\/10.1109\/ACCESS.2023.3274494","journal-title":"IEEE Access"},{"key":"1905_CR8","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1016\/j.aej.2023.07.051","volume":"78","author":"M Rahim","year":"2023","unstructured":"Rahim, M., Garg, H., Khan, S., Alqahtani, H., Khalifa, H.A.E.-W.: Group decision-making algorithm with sine trigonometric p, q-quasirung orthopair aggregation operators and their applications. Alex. Eng. J. 78, 530\u2013542 (2023)","journal-title":"Alex. Eng. J."},{"key":"1905_CR9","volume":"10","author":"M Rahim","year":"2023","unstructured":"Rahim, M., Shah, K., Abdeljawad, T., Aphane, M., Alburaikan, A., Khalifa, H.A.E.-W.: Confidence levels-based p, q-quasirung orthopair fuzzy operators and its applications to criteria group decision making problems. IEEE Access 10, e24726 (2023)","journal-title":"IEEE Access"},{"issue":"1","key":"1905_CR10","first-page":"53","volume":"46","author":"M Rahim","year":"2024","unstructured":"Rahim, M., Eldin, E.M., Khan, S., Ghamry, N.A., Alanzi, A.M., Khalifa, H.A.E.-W.: Multi-criteria group decision-making based on dombi aggregation operators under p, q-quasirung orthopair fuzzy sets. J. Intell. Fuzzy Syst. 46(1), 53\u201374 (2024)","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"4","key":"1905_CR11","first-page":"409","volume":"30","author":"BC Cuong","year":"2014","unstructured":"Cuong, B.C., Kreinovich, V.: Picture fuzzy sets. Journal of computer science and cybernetics 30(4), 409\u2013420 (2014)","journal-title":"Journal of computer science and cybernetics"},{"key":"1905_CR12","doi-asserted-by":"publisher","first-page":"7041","DOI":"10.1007\/s00521-018-3521-2","volume":"31","author":"T Mahmood","year":"2019","unstructured":"Mahmood, T., Ullah, K., Khan, Q., Jan, N.: An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput. Appl. 31, 7041\u20137053 (2019)","journal-title":"Neural Comput. Appl."},{"issue":"3","key":"1905_CR13","first-page":"1","volume":"46","author":"M Rahim","year":"2023","unstructured":"Rahim, M., Amin, F., Tag Eldin, E.M., Khalifa, A.E.-W., Ahmad, S.: p, q-Spherical fuzzy sets and their aggregation operators with application to third-party logistic provider selection. J. Intell. Fuzzy Syst. 46(3), 1\u201324 (2023)","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"3","key":"1905_CR14","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/0165-0114(89)90205-4","volume":"31","author":"K Atanassov","year":"1989","unstructured":"Atanassov, K., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343\u2013349 (1989)","journal-title":"Fuzzy Sets Syst."},{"key":"1905_CR15","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1016\/j.ins.2015.10.012","volume":"330","author":"X Zhang","year":"2016","unstructured":"Zhang, X.: Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking methods. Inf. Sci. 330, 104\u2013124 (2016)","journal-title":"Inf. Sci."},{"key":"1905_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.115613","volume":"185","author":"S Jeevaraj","year":"2021","unstructured":"Jeevaraj, S.: Ordering of interval-valued Fermatean fuzzy sets and its applications. Expert Syst. Appl. 185, 115613 (2021)","journal-title":"Expert Syst. Appl."},{"issue":"10","key":"1905_CR17","doi-asserted-by":"publisher","first-page":"8051","DOI":"10.1007\/s00521-021-06782-1","volume":"34","author":"P Rani","year":"2022","unstructured":"Rani, P., Mishra, A.R.: Interval-valued Fermatean fuzzy sets with multi-criteria weighted aggregated sum product assessment-based decision analysis framework. Neural Comput. Appl. 34(10), 8051\u20138067 (2022)","journal-title":"Neural Comput. Appl."},{"issue":"5","key":"1905_CR18","first-page":"5225","volume":"35","author":"BP Joshi","year":"2018","unstructured":"Joshi, B.P., Singh, A., Bhatt, P.K., Vaisla, K.S.: Interval valued q-rung orthopair fuzzy sets and their properties. J. Intell. Fuzzy Syst. 35(5), 5225\u20135230 (2018)","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"1","key":"1905_CR19","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1002\/int.22308","volume":"36","author":"H Garg","year":"2021","unstructured":"Garg, H.: A new possibility degree measure for interval-valued q-rung orthopair fuzzy sets in decision-making. Int. J. Intell. Syst. 36(1), 526\u2013557 (2021)","journal-title":"Int. J. Intell. Syst."},{"issue":"1","key":"1905_CR20","doi-asserted-by":"publisher","DOI":"10.1111\/exsy.12609","volume":"38","author":"H Garg","year":"2021","unstructured":"Garg, H., Ali, Z., Mahmood, T.: Algorithms for complex interval-valued q-rung orthopair fuzzy sets in decision making based on aggregation operators, AHP, and TOPSIS. Expert Syst. 38(1), e12609 (2021)","journal-title":"Expert Syst."},{"key":"1905_CR21","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/j.engappai.2019.06.003","volume":"85","author":"FK G\u00fcndo\u011fdu","year":"2019","unstructured":"G\u00fcndo\u011fdu, F.K., Kahraman, C.: A novel fuzzy TOPSIS method using emerging interval-valued spherical fuzzy sets. Eng. Appl. Artif. Intell. 85, 307\u2013323 (2019)","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"3","key":"1905_CR22","doi-asserted-by":"publisher","first-page":"357","DOI":"10.3390\/sym11030357","volume":"11","author":"K Ullah","year":"2019","unstructured":"Ullah, K., Hassan, N., Mahmood, T., Jan, N., Hassan, M.: Evaluation of investment policy based on multi-attribute decision-making using interval valued T-spherical fuzzy aggregation operators. Symmetry 11(3), 357 (2019)","journal-title":"Symmetry"},{"issue":"1","key":"1905_CR23","doi-asserted-by":"publisher","first-page":"292","DOI":"10.3390\/en15010292","volume":"15","author":"M Akram","year":"2022","unstructured":"Akram, M., Ullah, K., Pamucar, D.: Performance evaluation of solar energy cells using the interval-valued T-spherical fuzzy Bonferroni mean operators. Energies 15(1), 292 (2022)","journal-title":"Energies"},{"key":"1905_CR24","doi-asserted-by":"crossref","unstructured":"Waqar, M., Ullah, K., Pamucar, D., Jovanov, G., Vranje\u0161, \u0110.: An approach for the analysis of energy resource selection based on attributes by using Dombi T-norm based aggregation operators. Energies 15(11), 3939 (2022)","DOI":"10.3390\/en15113939"},{"issue":"2","key":"1905_CR25","first-page":"1","volume":"2","author":"J Ahmmad","year":"2023","unstructured":"Ahmmad, J.: Classification of renewable energy trends by utilizing the novel entropy measures under the environment of q-rung orthopair fuzzy soft sets. J. Innov. Res. Math. Comput. Sci. 2(2), 1\u201317 (2023)","journal-title":"J. Innov. Res. Math. Comput. Sci."},{"issue":"6","key":"1905_CR26","doi-asserted-by":"publisher","first-page":"2816","DOI":"10.3390\/en16062816","volume":"16","author":"M Akram","year":"2023","unstructured":"Akram, M., Ullah, K., \u0106irovi\u0107, G., Pamucar, D.: Algorithm for energy resource selection using priority degree-based aggregation operators with generalized orthopair fuzzy information and Aczel\u2013Alsina aggregation operators. Energies 16(6), 2816 (2023)","journal-title":"Energies"},{"issue":"2","key":"1905_CR27","first-page":"52","volume":"2","author":"M Hussain","year":"2023","unstructured":"Hussain, M., Hussain, A., Yin, S., Abid, M.N.: T-spherical fuzzy information and Shweizer\u2013Sklar operations based Maclaurin symmetric mean operator and their applications. J. Innov. Res. Math. Comput. Sci. 2(2), 52\u201364 (2023)","journal-title":"J. Innov. Res. Math. Comput. Sci."},{"key":"1905_CR28","doi-asserted-by":"publisher","first-page":"57863","DOI":"10.1109\/ACCESS.2024.3389296","volume":"12","author":"M Rahim","year":"2024","unstructured":"Rahim, M., Ahmad, S., Bajri, S.A., Alharbi, R., Khalifa, H.A.E.-W.: Confidence levels-based p, q, r-spherical fuzzy aggregation operators and their application in selection of solar panels. IEEE Access 12, 57863\u201357878 (2024)","journal-title":"IEEE Access"},{"key":"1905_CR29","doi-asserted-by":"publisher","first-page":"1293623","DOI":"10.3389\/fenrg.2023.1293623","volume":"11","author":"Y Wang","year":"2024","unstructured":"Wang, Y., Hussain, A., Yin, S., Ullah, K., Bo\u017eani\u0107, D.: Decision-making for solar panel selection using Sugeno\u2013Weber triangular norm-based on q-rung orthopair fuzzy information. Front. Energy Res. 11, 1293623 (2024)","journal-title":"Front. Energy Res."},{"issue":"1","key":"1905_CR30","first-page":"46","volume":"2","author":"H Bibi","year":"2023","unstructured":"Bibi, H., Ali, Z.: Ambiguities in the X-ray analysis of crystal structure based on neutrosophic fuzzy rough Aczel\u2013Alsina aggregation operators and their application in decision-making. J. Innov. Res. Math. Comput. Sci. 2(1), 46\u201375 (2023)","journal-title":"J. Innov. Res. Math. Comput. Sci."},{"issue":"1","key":"1905_CR31","first-page":"337","volume":"36","author":"F Kutlu G\u00fcndo\u011fdu","year":"2019","unstructured":"Kutlu G\u00fcndo\u011fdu, F., Kahraman, C.: Spherical fuzzy sets and spherical fuzzy TOPSIS method. J. Intell. Fuzzy Syst. 36(1), 337\u2013352 (2019)","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"12","key":"1905_CR32","doi-asserted-by":"publisher","first-page":"5275","DOI":"10.1007\/s13369-017-2625-9","volume":"42","author":"H Garg","year":"2017","unstructured":"Garg, H.: Some picture fuzzy aggregation operators and their applications to multicriteria decision-making. Arab. J. Sci. Eng. 42(12), 5275\u20135290 (2017)","journal-title":"Arab. J. Sci. Eng."},{"key":"1905_CR33","doi-asserted-by":"crossref","unstructured":"Lathamaheswari, M., Nagarajan, D., Garg, H., Kavikumar, J.: Interval valued spherical fuzzy aggregation operators and their application in decision making problem. In: Decision Making with Spherical Fuzzy Sets: Theory and Applications, pp. 27\u201351 (2021)","DOI":"10.1007\/978-3-030-45461-6_2"},{"issue":"3","key":"1905_CR34","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379\u2013423 (1948)","journal-title":"Bell Syst. Tech. J."},{"issue":"16","key":"1905_CR35","doi-asserted-by":"publisher","first-page":"1881","DOI":"10.3390\/math9161881","volume":"9","author":"G Haseli","year":"2021","unstructured":"Haseli, G., Sheikh, R., Wang, J., Tomaskova, H., Tirkolaee, E.B.: A novel approach for group decision making based on the best-worst method (G-bwm): application to supply chain management. Mathematics 9(16), 1881 (2021)","journal-title":"Mathematics"},{"key":"1905_CR36","doi-asserted-by":"publisher","DOI":"10.59400\/jam.v2i2.79","author":"MS Nazeer","year":"2023","unstructured":"Nazeer, M.S., Ullah, K., Hussain, A.: A novel decision-making approach based on interval-valued T-spherical fuzzy information with applications. J. Appl. Math. (2023). https:\/\/doi.org\/10.59400\/jam.v2i2.79","journal-title":"J. Appl. Math."},{"issue":"3","key":"1905_CR37","doi-asserted-by":"publisher","first-page":"145","DOI":"10.3390\/axioms10030145","volume":"10","author":"Y Jin","year":"2021","unstructured":"Jin, Y., Kousar, Z., Ullah, K., Mahmood, T., Yapici Pehlivan, N., Ali, Z.: Approach to multi-attribute decision-making methods for performance evaluation process using interval-valued T-spherical fuzzy Hamacher aggregation information. Axioms 10(3), 145 (2021)","journal-title":"Axioms"},{"issue":"6","key":"1905_CR38","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.3390\/sym13061053","volume":"13","author":"K Ullah","year":"2021","unstructured":"Ullah, K., Garg, H., Gul, Z., Mahmood, T., Khan, Q., Ali, Z.: Interval valued T-spherical fuzzy information aggregation based on Dombi t-norm and Dombi t-conorm for multi-attribute decision making problems. Symmetry 13(6), 1053 (2021)","journal-title":"Symmetry"},{"issue":"11","key":"1905_CR39","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0294596","volume":"18","author":"Q Ma","year":"2023","unstructured":"Ma, Q., Sun, H., Chen, Z., Tan, Y.: A novel MCDM approach for design concept evaluation based on interval-valued picture fuzzy sets. PLoS ONE 18(11), e0294596 (2023)","journal-title":"PLoS ONE"},{"issue":"4","key":"1905_CR40","doi-asserted-by":"publisher","first-page":"661","DOI":"10.15388\/21-INFOR451","volume":"32","author":"S Duleba","year":"2021","unstructured":"Duleba, S., Kutlu G\u00fcndo\u011fdu, F., Moslem, S.: Interval-valued spherical fuzzy analytic hierarchy process method to evaluate public transportation development. Informatica 32(4), 661\u2013686 (2021)","journal-title":"Informatica"},{"key":"1905_CR41","doi-asserted-by":"crossref","unstructured":"Monika, Sangwan, O. P.: A framework for evaluating cloud computing services using AHP and TOPSIS approaches with interval valued spherical fuzzy sets. Clust. Comput. 25(6), 4383\u20134396 (2022)","DOI":"10.1007\/s10586-022-03679-z"},{"issue":"12","key":"1905_CR42","doi-asserted-by":"publisher","first-page":"5361","DOI":"10.1109\/TFUZZ.2022.3176686","volume":"30","author":"J Wang","year":"2022","unstructured":"Wang, J., Ma, X., Xu, Z., Zhan, J.: Regret theory-based three-way decision model in hesitant fuzzy environments and its application to medical decision. IEEE Trans. Fuzzy Syst. 30(12), 5361\u20135375 (2022)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"12","key":"1905_CR43","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1002\/int.21676","volume":"29","author":"X Zhang","year":"2014","unstructured":"Zhang, X., Xu, Z.: Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int. J. Intell. Syst. 29(12), 1061\u20131078 (2014)","journal-title":"Int. J. Intell. Syst."},{"key":"1905_CR44","doi-asserted-by":"publisher","first-page":"733","DOI":"10.1016\/j.jclepro.2019.03.049","volume":"222","author":"TS Aung","year":"2019","unstructured":"Aung, T.S., Luan, S., Xu, Q.: Application of multi-criteria-decision approach for the analysis of medical waste management systems in Myanmar. J. Clean. Prod. 222, 733\u2013745 (2019)","journal-title":"J. Clean. Prod."},{"key":"1905_CR45","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2022.108435","volume":"117","author":"L Wang","year":"2022","unstructured":"Wang, L., Wang, H.: An integrated qualitative group decision-making method for assessing health-care waste treatment technologies based on linguistic terms with weakened hedges. Appl. Soft Comput. 117, 108435 (2022)","journal-title":"Appl. Soft Comput."}],"container-title":["International Journal of Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-024-01905-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40815-024-01905-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-024-01905-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T15:34:05Z","timestamp":1764084845000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40815-024-01905-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,7]]},"references-count":45,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["1905"],"URL":"https:\/\/doi.org\/10.1007\/s40815-024-01905-x","relation":{},"ISSN":["1562-2479","2199-3211"],"issn-type":[{"value":"1562-2479","type":"print"},{"value":"2199-3211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,7]]},"assertion":[{"value":"28 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 October 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 October 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 January 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}