{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:45:22Z","timestamp":1740149122763,"version":"3.37.3"},"reference-count":58,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T00:00:00Z","timestamp":1651190400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T00:00:00Z","timestamp":1651190400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100006261","name":"Taif University","doi-asserted-by":"publisher","award":["TURSP-2020\/160"],"award-info":[{"award-number":["TURSP-2020\/160"]}],"id":[{"id":"10.13039\/501100006261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Comput Intell Syst"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The framework of fuzzy-interval-valued functions (FIVFs) is a generalization of interval-valued functions (IVF) and single-valued functions. To discuss convexity with these kinds of functions, in this article, we introduce and investigate the harmonically<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf{h}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>h<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-convexity for FIVFs through fuzzy-order relation (FOR). Using this class of harmonically<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf{h}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>h<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-convex FIVFs (<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal{H}-\\mathsf{h}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>H<\/mml:mi><mml:mo>-<\/mml:mo><mml:mi>h<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-convex FIVFs), we prove some Hermite\u2013Hadamard (<jats:italic>H<\/jats:italic>\u22c5<jats:italic>H<\/jats:italic>) and Hermite\u2013Hadamard\u2013Fej\u00e9r (<jats:italic>H<\/jats:italic>\u22c5<jats:italic>H<\/jats:italic>Fej\u00e9r) type inequalities via fuzzy interval Riemann\u2013Liouville fractional integral (FI Riemann\u2013Liouville fractional integral). The concepts and techniques of this paper are refinements and generalizations of many results which are proved in the literature.<\/jats:p>","DOI":"10.1007\/s44196-022-00081-w","type":"journal-article","created":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T18:03:35Z","timestamp":1651255415000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Riemann\u2013Liouville Fractional Integral Inequalities for Generalized Harmonically Convex Fuzzy-Interval-Valued Functions"],"prefix":"10.1007","volume":"15","author":[{"given":"Muhammad Bilal","family":"Khan","sequence":"first","affiliation":[]},{"given":"Hatim Ghazi","family":"Zaini","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6609-5493","authenticated-orcid":false,"given":"Gustavo","family":"Santos-Garc\u00eda","sequence":"additional","affiliation":[]},{"given":"Pshtiwan Othman","family":"Mohammed","sequence":"additional","affiliation":[]},{"given":"Mohamed S.","family":"Soliman","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,4,29]]},"reference":[{"key":"81_CR1","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1186\/s13660-020-02419-4","volume":"2020","author":"PO Mohammed","year":"2020","unstructured":"Mohammed, P.O., Abdeljawad, T.: Opial integral inequalities for generalized fractional operators with nonsingular kernel. J. Inequal. Appl. 2020, 148 (2020)","journal-title":"J. Inequal. Appl."},{"key":"81_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.30538\/oms2021.0139","volume":"5","author":"G Farid","year":"2021","unstructured":"Farid, G., Rehman, A.U., Bibi, S., Chu, Y.M.: Refinements of two fractional versions of Hadamard inequalities for Caputo fractional derivatives and related results. Open J. Math. Sci. 5, 1\u201310 (2021)","journal-title":"Open J. Math. Sci."},{"key":"81_CR3","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1186\/s13660-018-1664-4","volume":"2018","author":"MA Khan","year":"2018","unstructured":"Khan, M.A., Begum, S., Khurshid, Y., Chu, Y.M.: Ostrowski type inequalities involving conformable fractional integrals. J. Inequal. Appl. 2018, 70 (2018)","journal-title":"J. Inequal. Appl."},{"issue":"2","key":"81_CR4","first-page":"443","volume":"10","author":"MZ Sarikaya","year":"2020","unstructured":"Sarikaya, M.Z., Bili\u015fik, C.C., Tun\u00e7, T.: On Hardy type inequalities via k-fractional integrals. TWMS J. Appl. Eng. Math. 10(2), 443\u2013451 (2020)","journal-title":"TWMS J. Appl. Eng. Math."},{"issue":"3","key":"81_CR5","first-page":"93","volume":"2","author":"Z Dahmani","year":"2010","unstructured":"Dahmani, Z., Tabharit, L., Taf, S.: New generalizations of Gr\u00fcss inequality using Riemann-Liouville fractional integrals. Bull. Math. Anal. Appl. 2(3), 93\u201399 (2010)","journal-title":"Bull. Math. Anal. Appl."},{"issue":"3","key":"81_CR6","first-page":"402","volume":"19","author":"E Set","year":"2020","unstructured":"Set, E., Akdemir, A.O., Ozata, F.: Gr\u00fcss type inequalities for fractional integral operator involving the extended generalized Mittag-Leffler function. Appl. Comput. Math. 19(3), 402\u2013414 (2020)","journal-title":"Appl. Comput. Math."},{"issue":"6","key":"81_CR7","first-page":"935","volume":"43","author":"I Iscan","year":"2014","unstructured":"Iscan, I.: Hermite-Hadamard type inequalities for harmonically convex functions. Hacet. J. Math. Stat. 43(6), 935\u2013942 (2014)","journal-title":"Hacet. J. Math. Stat."},{"key":"81_CR8","doi-asserted-by":"publisher","first-page":"386806","DOI":"10.1155\/2014\/386806","volume":"2014","author":"F Chen","year":"2014","unstructured":"Chen, F., Wu, S.: Fej\u00e9r and Hermite-Hadamard type inequalities for harmonically convex functions. J. Appl. Math. 2014, 386806 (2014)","journal-title":"J. Appl. Math."},{"key":"81_CR9","first-page":"121","volume":"268","author":"F Chen","year":"2015","unstructured":"Chen, F.: Extensions of the Hermite-Hadamard inequality for harmonically convex functions via fractional integrals. Appl. Math. Comput. 268, 121\u2013128 (2015)","journal-title":"Appl. Math. Comput."},{"key":"81_CR10","first-page":"297","volume":"16","author":"T Allahviranloo","year":"2012","unstructured":"Allahviranloo, T., Salahshour, S., Abbasbandy, S.: Explicit solutions of fractional differential equations with uncertainty. Soft Comput. Fus. Found. Meth. Appl. 16, 297\u2013302 (2012)","journal-title":"Soft Comput. Fus. Found. Meth. Appl."},{"key":"81_CR11","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.fss.2017.02.001","volume":"327","author":"TM Costa","year":"2017","unstructured":"Costa, T.M.: Jensen\u2019s inequality type integral for fuzzy-interval-valued functions. Fuzzy Sets Syst. 327, 31\u201347 (2017)","journal-title":"Fuzzy Sets Syst."},{"key":"81_CR12","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.ins.2017.08.055","volume":"420","author":"TM Costa","year":"2017","unstructured":"Costa, T.M., Roman-Flores, H.: Some integral inequalities for fuzzy-interval-valued functions. Inform. Sci. 420, 110\u2013125 (2017)","journal-title":"Inform. Sci."},{"key":"81_CR13","doi-asserted-by":"publisher","first-page":"1306","DOI":"10.1007\/s40314-016-0396-7","volume":"37","author":"H Rom\u00e1n-Flores","year":"2018","unstructured":"Rom\u00e1n-Flores, H., Chalco-Cano, Y., Lodwick, W.A.: Some integral inequalities for interval-valued functions. Comput. Appl. Math. 37, 1306\u20131318 (2018)","journal-title":"Comput. Appl. Math."},{"key":"81_CR14","doi-asserted-by":"crossref","unstructured":"H. Roman-Flores, Y. Chalco-Cano, G.N. Silva, A note on Gronwall type inequality for interval-valued functions, in 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA\/NAFIPS), 35 (2013), 1455\u20131458.","DOI":"10.1109\/IFSA-NAFIPS.2013.6608616"},{"key":"81_CR15","first-page":"457","volume":"31","author":"Y Chalco-Cano","year":"2012","unstructured":"Chalco-Cano, Y., Flores-Franuli\u010d, A., Rom\u00e1n-Flores, H.: Ostrowski type inequalities for interval-valued functions using generalized Hukuhara derivative. Comput. Appl. Math. 31, 457\u2013472 (2012)","journal-title":"Comput. Appl. Math."},{"key":"81_CR16","doi-asserted-by":"publisher","first-page":"3293","DOI":"10.1007\/s00500-014-1483-6","volume":"19","author":"Y Chalco-Cano","year":"2015","unstructured":"Chalco-Cano, Y., Lodwick, W.A., Condori-Equice, W.: Ostrowski type inequalities and applications in numerical integration for interval-valued functions. Soft Comput. 19, 3293\u20133300 (2015)","journal-title":"Soft Comput."},{"key":"81_CR17","first-page":"979","volume":"4","author":"K Nikodem","year":"2014","unstructured":"Nikodem, K., S\u00e1nchez, J.L., S\u00e1nchez, L.: Jensen and Hermite-Hadamard inequalities for strongly convex set-valued maps. Math. Aeterna 4, 979\u2013987 (2014)","journal-title":"Math. Aeterna"},{"key":"81_CR18","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1007\/BF03323058","volume":"26","author":"J Matkowski","year":"1994","unstructured":"Matkowski, J., Nikodem, K.: An integral Jensen inequality for convex multifunctions. Results Math. 26, 348\u2013353 (1994)","journal-title":"Results Math."},{"key":"81_CR19","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.fss.2019.10.006","volume":"396","author":"D Zhao","year":"2020","unstructured":"Zhao, D., An, T., Ye, G., Liu, W.: Chebyshev type inequalities for interval-valued functions. Fuzzy Sets Syst. 396, 82\u2013101 (2020)","journal-title":"Fuzzy Sets Syst."},{"key":"81_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13660-018-1896-3","volume":"2018","author":"DF Zhao","year":"2018","unstructured":"Zhao, D.F., An, T.Q., Ye, G.J., Liu, W.: New Jensen and Hermite-Hadamard type inequalities for h-convex interval-valued functions. J. Inequal. Appl. 2018, 1\u201314 (2018)","journal-title":"J. Inequal. Appl."},{"key":"81_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.fss.2019.06.002","volume":"2020","author":"D Zhang","year":"2020","unstructured":"Zhang, D., Guo, C., Chen, D., Wang, G.: Jensen\u2019s inequalities for set-valued and fuzzy set-valued functions. Fuzzy Sets Syst. 2020, 1\u201327 (2020)","journal-title":"Fuzzy Sets Syst."},{"key":"81_CR22","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1090\/proc\/14741","volume":"148","author":"H Budak","year":"2019","unstructured":"Budak, H., Tun\u00e7, T., Sarikaya, M.Z.: Fractional Hermite-Hadamard type inequalities for interval-valued functions. Proc. Am. Math. Soc. 148, 705\u2013718 (2019)","journal-title":"Proc. Am. Math. Soc."},{"key":"81_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13662-019-2438-0","volume":"2020","author":"D Zhao","year":"2020","unstructured":"Zhao, D., Ali, M.A., Murtaza, G., Zhang, Z.: On the Hermite-Hadamard inequalities for interval-valued coordinated convex functions. Adv. Differ. Equations 2020, 1\u201314 (2020)","journal-title":"Adv. Differ. Equations"},{"key":"81_CR24","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1002\/mma.6712","volume":"44","author":"H Kara","year":"2021","unstructured":"Kara, H., Ali, M.A., Budak, H.: Hermite-Hadamard-type inequalities for interval-valued coordinated convex functions involving generalized fractional integrals. Math. Methods Appl. Sci. 44, 104\u2013123 (2021)","journal-title":"Math. Methods Appl. Sci."},{"key":"81_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13662-020-03200-z","volume":"2021","author":"F Shi","year":"2021","unstructured":"Shi, F., Ye, G., Zhao, D., Liu, W.: Some fractional Hermite-Hadamard-type inequalities for interval-valued coordinated functions. Adv. Differ. Equations 2021, 1\u201317 (2021)","journal-title":"Adv. Differ. Equations"},{"key":"81_CR26","first-page":"775","volume":"2001","author":"SS Dragomir","year":"2001","unstructured":"Dragomir, S.S.: On the Hadamard\u2019s inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwan. J. Math. 2001, 775\u2013788 (2001)","journal-title":"Taiwan. J. Math."},{"issue":"1","key":"81_CR27","doi-asserted-by":"publisher","first-page":"812","DOI":"10.3934\/mbe.2022037","volume":"19","author":"MB Khan","year":"2022","unstructured":"Khan, M.B., Srivastava, H.M., Mohammed, P.O., Guirao, J.L., Jawa, T.M.: Fuzzy-interval inequalities for generalized preinvex fuzzy interval valued functions. Math. Bio. Eng. 19(1), 812\u2013835 (2022)","journal-title":"Math. Bio. Eng."},{"key":"81_CR28","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1186\/s13662-021-03245-8","volume":"2021","author":"MB Khan","year":"2021","unstructured":"Khan, M.B., Noor, M.A., Noor, K.I., Chu, Y.M.: New Hermite-Hadamard type inequalities for (h1, h2)-convex fuzzy-interval-valued functions. Adv. Differ. Equ. 2021, 6\u201320 (2021)","journal-title":"Adv. Differ. Equ."},{"key":"81_CR29","doi-asserted-by":"publisher","first-page":"673","DOI":"10.3390\/sym13040673","volume":"13","author":"MB Khan","year":"2021","unstructured":"Khan, M.B., Mohammed, P.O., Noor, M.A., Hamed, Y.S.: New Hermite-Hadamard inequalities in fuzzy-interval fractional calculus and related inequalities. Symmetry 13, 673 (2021)","journal-title":"Symmetry"},{"key":"81_CR30","doi-asserted-by":"publisher","first-page":"10964","DOI":"10.3934\/math.2021637","volume":"6","author":"MB Khan","year":"2021","unstructured":"Khan, M.B., Mohammed, P.O., Noor, M.A., Alsharif, A.M., Noor, K.I.: New fuzzy-interval inequalities in fuzzy-interval fractional calculus by means of fuzzy order relation. AIMS Math. 6, 10964\u201310988 (2021)","journal-title":"AIMS Math."},{"key":"81_CR31","doi-asserted-by":"publisher","first-page":"1403","DOI":"10.2991\/ijcis.d.210409.001","volume":"14","author":"MB Khan","year":"2021","unstructured":"Khan, M.B., Noor, M.A., Abdullah, L., Chu, Y.M.: Some new classes of preinvex fuzzy-interval-valued functions and inequalities. Int. J. Comput. Intell. Syst. 14, 1403\u20131418 (2021)","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"81_CR32","first-page":"1","volume":"2021","author":"P Liu","year":"2021","unstructured":"Liu, P., Khan, M.B., Noor, M.A., Noor, K.I.: New Hermite-Hadamard and Jensen inequalities for log-s-convex fuzzy-interval-valued functions in the second sense. Complex Intell. Syst. 2021, 1\u201315 (2021)","journal-title":"Complex Intell. Syst."},{"key":"81_CR33","doi-asserted-by":"publisher","first-page":"1809","DOI":"10.2991\/ijcis.d.210620.001","volume":"14","author":"G Sana","year":"2021","unstructured":"Sana, G., Khan, M.B., Noor, M.A., Mohammed, P.O., Chu, Y.M.: Harmonically convex fuzzy-interval-valued functions and fuzzy-interval Riemann-Liouville fractional integral inequalities. Int. J. Comput. Intell. Syst. 14, 1809\u20131822 (2021)","journal-title":"Int. J. Comput. Intell. Syst."},{"issue":"5","key":"81_CR34","doi-asserted-by":"publisher","first-page":"6552","DOI":"10.3934\/mbe.2021325","volume":"18","author":"MB Khan","year":"2021","unstructured":"Khan, M.B., Mohammed, P.O., Noor, M.A., Abualnaja, K.M.: Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions. Math. Biosci. Eng. 18(5), 6552\u20136580 (2021)","journal-title":"Math. Biosci. Eng."},{"key":"81_CR35","volume-title":"Computer Arithmetic in Theory and Practice","author":"U Kulish","year":"2014","unstructured":"Kulish, U., Miranker, W.: Computer Arithmetic in Theory and Practice. Academic Press, New York (2014)"},{"key":"81_CR36","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/0165-0114(87)90029-7","volume":"24","author":"O Kaleva","year":"1987","unstructured":"Kaleva, O.: Fuzzy differential equations. Fuzzy Sets Syst. 24, 301\u2013317 (1987)","journal-title":"Fuzzy Sets Syst."},{"key":"81_CR37","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/0165-0114(92)90256-4","volume":"48","author":"N Nanda","year":"1992","unstructured":"Nanda, N., Kar, K.: Convex fuzzy mappings. Fuzzy Sets Syst. 48, 129\u2013132 (1992)","journal-title":"Fuzzy Sets Syst."},{"key":"81_CR38","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/0165-0114(94)90011-6","volume":"64","author":"MA Noor","year":"1994","unstructured":"Noor, M.A.: Fuzzy preinvex functions. Fuzzy Sets Syst. 64, 95\u2013104 (1994)","journal-title":"Fuzzy Sets Syst."},{"key":"81_CR39","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1186\/1029-242X-2014-45","volume":"2014","author":"Z-B Fang","year":"2014","unstructured":"Fang, Z.-B., R-J, Shi,: On the (p, h)-convex function and some integral inequalities. J. Inequal. Appl. 2014, 45 (2014)","journal-title":"J. Inequal. Appl."},{"issue":"2","key":"81_CR40","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.ajmsc.2016.11.001","volume":"23","author":"M Kunt","year":"2017","unstructured":"Kunt, M., \u0130\u015fcan, \u0130: Hermite\u2013Hadamard\u2013Fej\u00e9r type inequalities for p-convex functions. Arab. J. Math. Sci. 23(2), 215\u2013230 (2017)","journal-title":"Arab. J. Math. Sci."},{"key":"81_CR41","first-page":"369","volume":"24","author":"L Fej\u00e9r","year":"1906","unstructured":"Fej\u00e9r, L.: Uberdie Fourierreihen II. Math. Naturwise. Anz Ungar. Akad. Wiss 24, 369\u2013390 (1906)","journal-title":"Math. Naturwise. Anz Ungar. Akad. Wiss"},{"key":"81_CR42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3390\/sym13061023","volume":"13","author":"HM Srivastava","year":"2021","unstructured":"Srivastava, H.M., El-Deeb, S.M.: Fuzzy differential subordinations based upon the Mittag-Leffler type Borel distribution. Symmetry 13, 1\u201315 (2021)","journal-title":"Symmetry"},{"issue":"1","key":"81_CR43","first-page":"5","volume":"77","author":"MA Noor","year":"2015","unstructured":"Noor, M.A., Noor, K.I., Awan, M.U., Costache, S.: Some integral inequalities for harmonically h-convex functions. Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys 77(1), 5\u201316 (2015)","journal-title":"Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys"},{"issue":"1","key":"81_CR44","doi-asserted-by":"publisher","first-page":"6","DOI":"10.3390\/fractalfract6010006","volume":"6","author":"MB Khan","year":"2022","unstructured":"Khan, M.B., Trean\u021b\u01ce, S., Soliman, M.S., Nonlaopon, K., Zaini, H.G.: Some Hadamard-Fej\u00e9r type inequalities for LR-convex interval-valued functions. Fract. Fract. 6(1), 6 (2022)","journal-title":"Fract. Fract."},{"issue":"3","key":"81_CR45","doi-asserted-by":"publisher","first-page":"4338","DOI":"10.3934\/math.2022241","volume":"7","author":"MB Khan","year":"2022","unstructured":"Khan, M.B., Srivastava, H.M., Mohammed, P.O., Nonlaopon, K., Hamed, Y.S.: Some new Jensen, Schur and Hermite-Hadamard inequalities for log convex fuzzy interval-valued functions. AIMS Math. 7(3), 4338\u20134358 (2022)","journal-title":"AIMS Math."},{"issue":"3","key":"81_CR46","doi-asserted-by":"publisher","first-page":"4266","DOI":"10.3934\/math.2022236","volume":"7","author":"JE Mac\u00edas-D\u00edaz","year":"2022","unstructured":"Mac\u00edas-D\u00edaz, J.E., Khan, M.B., Noor, M.A., Abd Allah, A.M., Alghamdi, S.M.: Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus. AIMS Math. 7(3), 4266\u20134292 (2022)","journal-title":"AIMS Math."},{"issue":"12","key":"81_CR47","doi-asserted-by":"publisher","first-page":"2352","DOI":"10.3390\/sym13122352","volume":"13","author":"MB Khan","year":"2021","unstructured":"Khan, M.B., Mohammed, P.O., Machado, J.A.T., Guirao, J.L.: Integral inequalities for generalized harmonically convex functions in fuzzy-interval-valued settings. Symmetry 13(12), 2352 (2021)","journal-title":"Symmetry"},{"issue":"4","key":"81_CR48","doi-asserted-by":"publisher","first-page":"243","DOI":"10.3390\/fractalfract5040243","volume":"5","author":"MB Khan","year":"2021","unstructured":"Khan, M.B., Noor, M.A., Abdeljawad, T., Mousa, A.A.A., Abdalla, B., Alghamdi, S.M.: LR-Preinvex interval-valued functions and Riemann-Liouville fractional integral inequalities. Fract. Fract. 5(4), 243 (2021)","journal-title":"Fract. Fract."},{"key":"81_CR49","doi-asserted-by":"publisher","first-page":"204","DOI":"10.3390\/math10020204","volume":"10","author":"MB Khan","year":"2022","unstructured":"Khan, M.B., Zaini, H.G., Trean\u021b\u01ce, S., Soliman, M.S., Nonlaopon, K.: Riemann-Liouville fractional integral inequalities for generalized pre-invex functions of interval-valued settings based upon pseudoorder relation. Mathematics 10, 204 (2022)","journal-title":"Mathematics"},{"issue":"1","key":"81_CR50","doi-asserted-by":"publisher","first-page":"349","DOI":"10.3934\/math.2022024","volume":"7","author":"MB Khan","year":"2022","unstructured":"Khan, M.B., Noor, M.A., Abdeljawad, T., Abdalla, B., Althobaiti, A.: Some fuzzy-interval integral inequalities for harmonically convex fuzzy-interval-valued functions. AIMS Math. 7(1), 349\u2013370 (2022)","journal-title":"AIMS Math."},{"issue":"12","key":"81_CR51","doi-asserted-by":"publisher","first-page":"3220","DOI":"10.1002\/int.22191","volume":"34","author":"C Jana","year":"2019","unstructured":"Jana, C., Muhiuddin, G., Pal, M.: Some Dombi aggregation of Q-rung orthopair fuzzy numbers in multiple-attribute decision making. Int. J. Intell. Syst. 34(12), 3220\u20133240 (2019)","journal-title":"Int. J. Intell. Syst."},{"issue":"5","key":"81_CR52","doi-asserted-by":"publisher","first-page":"3631","DOI":"10.1007\/s00500-019-04130-z","volume":"24","author":"C Jana","year":"2020","unstructured":"Jana, C., Pal, M., Wang, J.Q.: Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making. Soft. Comput. 24(5), 3631\u20133646 (2020)","journal-title":"Soft. Comput."},{"issue":"6","key":"81_CR53","first-page":"1","volume":"16","author":"C Jana","year":"2019","unstructured":"Jana, C., Pal, M., Wang, J.: A robust aggregation operator for multi-criteria decision-making method with bipolar fuzzy soft environment. Iran. J. Fuzzy Syst. 16(6), 1\u201316 (2019)","journal-title":"Iran. J. Fuzzy Syst."},{"issue":"9","key":"81_CR54","doi-asserted-by":"publisher","first-page":"3717","DOI":"10.1007\/s12652-019-01568-9","volume":"11","author":"C Jana","year":"2020","unstructured":"Jana, C., Muhiuddin, G., Pal, M.: Multiple-attribute decision making problems based on SVTNH methods. J. Ambient. Intell. Humaniz. Comput. 11(9), 3717\u20133733 (2020)","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"issue":"7","key":"81_CR55","first-page":"5055","volume":"25","author":"C Jana","year":"2021","unstructured":"Jana, C., Pal, M.: Multi-criteria decision making process based on some single-valued neutrosophic Dombi power aggregation operators. Soft. Comput. 25(7), 5055\u20135072 (2021)","journal-title":"Soft. Comput."},{"issue":"4","key":"81_CR56","doi-asserted-by":"publisher","first-page":"534","DOI":"10.3390\/math10040534","volume":"10","author":"MB Khan","year":"2022","unstructured":"Khan, M.B., Santos-Garc\u00eda, G., Zaini, H.G., Trean\u021b\u01ce, S., Soliman, M.S.: Some new concepts related to integral operators and inequalities on coordinates in fuzzy fractional calculus. Mathematics 10(4), 534 (2022)","journal-title":"Mathematics"},{"issue":"2","key":"81_CR57","doi-asserted-by":"publisher","first-page":"83","DOI":"10.3390\/fractalfract6020083","volume":"6","author":"MB Khan","year":"2022","unstructured":"Khan, M.B., Noor, M.A., Shah, N.A., Abualnaja, K.M., Botmart, T.: Some new versions of Hermite-Hadamard integral inequalities in fuzzy fractional calculus for generalized pre-invex functions via fuzzy-interval-valued settings. Fract. Fract. 6(2), 83 (2022)","journal-title":"Fract. Fract."},{"issue":"2","key":"81_CR58","doi-asserted-by":"publisher","first-page":"341","DOI":"10.3390\/sym14020341","volume":"14","author":"MB Khan","year":"2022","unstructured":"Khan, M.B., Zaini, H.G., Trean\u021b\u01ce, S., Santos-Garc\u00eda, G., Mac\u00edas-D\u00edaz, J.E., Soliman, M.S.: Fractional calculus for convex functions in interval-valued settings and inequalities. Symmetry 14(2), 341 (2022)","journal-title":"Symmetry"}],"container-title":["International Journal of Computational Intelligence Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-022-00081-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44196-022-00081-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-022-00081-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T21:41:00Z","timestamp":1700516460000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44196-022-00081-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,29]]},"references-count":58,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["81"],"URL":"https:\/\/doi.org\/10.1007\/s44196-022-00081-w","relation":{},"ISSN":["1875-6883"],"issn-type":[{"type":"electronic","value":"1875-6883"}],"subject":[],"published":{"date-parts":[[2022,4,29]]},"assertion":[{"value":"1 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 March 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 April 2022","order":3,"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 competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"28"}}