{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:38:06Z","timestamp":1777703886255,"version":"3.51.4"},"reference-count":28,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2017,5,11]],"date-time":"2017-05-11T00:00:00Z","timestamp":1494460800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2017,7]]},"abstract":"<jats:p>\n                    Let 0\u00a0\u2260\u00a0\n                    <jats:italic>p<\/jats:italic>\n                    \u00a0(\n                    <jats:italic>x<\/jats:italic>\n                    ) be a nondecreasing real valued function on [0, \u221e) such that\n                    <jats:italic>p<\/jats:italic>\n                    \u00a0(0)\u00a0=0 and\n                    <jats:disp-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:munder>\n                          <mml:mrow>\n                            <mml:mo>lim<\/mml:mo>\n                            <mml:mo>inf<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>\u2192<\/mml:mo>\n                            <mml:mo>\u221e<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:munder>\n                        <mml:mfrac>\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mi>\u03bb<\/mml:mi>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:mfrac>\n                        <mml:mo>&gt;<\/mml:mo>\n                        <mml:mn>1<\/mml:mn>\n                        <mml:mspace width=\"2em\"\/>\n                        <mml:mrow>\n                          <mml:mi mathvariant=\"normal\">for<\/mml:mi>\n                          <mml:mi mathvariant=\"normal\">every<\/mml:mi>\n                        <\/mml:mrow>\n                        <mml:mspace width=\"1em\"\/>\n                        <mml:mi>\u03bb<\/mml:mi>\n                        <mml:mo>&gt;<\/mml:mo>\n                        <mml:mn>1<\/mml:mn>\n                        <mml:mo>.<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:disp-formula>\n                  <\/jats:p>\n                  <jats:p>\n                    Given a fuzzy-number-valued continuous function\n                    <jats:italic>f<\/jats:italic>\n                    \u00a0(\n                    <jats:italic>x<\/jats:italic>\n                    ) on [0, \u221e), we define\n                    <jats:disp-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi>s<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>x<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mo>:<\/mml:mo>\n                        <mml:mo>=<\/mml:mo>\n                        <mml:msubsup>\n                          <mml:mo>\u222b<\/mml:mo>\n                          <mml:mn>0<\/mml:mn>\n                          <mml:mi>x<\/mml:mi>\n                        <\/mml:msubsup>\n                        <mml:mi>f<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>t<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mi mathvariant=\"italic\">dt<\/mml:mi>\n                        <mml:mspace width=\"2em\"\/>\n                        <mml:mi mathvariant=\"normal\">and<\/mml:mi>\n                        <mml:mspace width=\"1em\"\/>\n                        <mml:mi>\u03c3<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>x<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mo>:<\/mml:mo>\n                        <mml:mo>=<\/mml:mo>\n                        <mml:mfrac>\n                          <mml:mn>1<\/mml:mn>\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:mfrac>\n                        <mml:msubsup>\n                          <mml:mo>\u222b<\/mml:mo>\n                          <mml:mn>0<\/mml:mn>\n                          <mml:mi>x<\/mml:mi>\n                        <\/mml:msubsup>\n                        <mml:mi>s<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>t<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mi mathvariant=\"italic\">dp<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>t<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:mspace width=\"1em\"\/>\n                        <mml:mi>x<\/mml:mi>\n                        <mml:mo>&gt;<\/mml:mo>\n                        <mml:mn>0<\/mml:mn>\n                        <mml:mo>.<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:disp-formula>\n                  <\/jats:p>\n                  <jats:p>\n                    It is known that the limit\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:munder>\n                          <mml:mo>lim<\/mml:mo>\n                          <mml:mrow>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>\u2192<\/mml:mo>\n                            <mml:mo>\u221e<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:munder>\n                        <mml:mi>s<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>x<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mo>=<\/mml:mo>\n                        <mml:mi>\u03bc<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    exists, then the limit\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:munder>\n                          <mml:mo>lim<\/mml:mo>\n                          <mml:mrow>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>\u2192<\/mml:mo>\n                            <mml:mo>\u221e<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:munder>\n                        <mml:mi>\u03c3<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>x<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mo>=<\/mml:mo>\n                        <mml:mi>\u03bc<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    also exists. But the converse of this implication need not be satisfied in general.\n                  <\/jats:p>\n                  <jats:p>\n                    In this paper, our goal is to find a condition under which the existence of\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:munder>\n                          <mml:mo>lim<\/mml:mo>\n                          <mml:mrow>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>\u2192<\/mml:mo>\n                            <mml:mo>\u221e<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:munder>\n                        <mml:mi>\u03c3<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>x<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mo>=<\/mml:mo>\n                        <mml:mi>\u03bc<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    follows from that of\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:munder>\n                          <mml:mo>lim<\/mml:mo>\n                          <mml:mrow>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>\u2192<\/mml:mo>\n                            <mml:mo>\u221e<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:munder>\n                        <mml:mi>s<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>x<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mo>=<\/mml:mo>\n                        <mml:mi>\u03bc<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>\n                  <jats:p>As special cases, we obtain some Tauberian conditions of slowly decreasing type and Landau type for the Ces\u00e0ro summability method of improper integrals of fuzzy-number-valued functions.<\/jats:p>","DOI":"10.3233\/jifs-161596","type":"journal-article","created":{"date-parts":[[2017,5,12]],"date-time":"2017-05-12T11:43:09Z","timestamp":1494589389000},"page":"293-303","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["A Tauberian theorem for the weighted mean\u00a0method of improper integrals of\u00a0fuzzy-number-valued functions"],"prefix":"10.1177","volume":"33","author":[{"given":"Zerrin","family":"\u00d6nder","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ege University, \u0130zmir, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u0130brahim","family":"\u00c7anak","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ege University, \u0130zmir, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,5,11]]},"reference":[{"issue":"3","key":"e_1_3_2_2_2","first-page":"755","article-title":"Rate of convergence of fuzzy neural network operators, univariate case","volume":"10","author":"Anastassiou G.A.","year":"2002","unstructured":"AnastassiouG.A., Rate of convergence of fuzzy neural network operators, univariate case, J Fuzzy Math10(3) (2002), 755\u2013780.","journal-title":"J Fuzzy Math"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-11220-1"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.10.014"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35221-8"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-131053"},{"issue":"4","key":"e_1_3_2_7_2","first-page":"87","article-title":"H\u00f6lder summability method of fuzzy numbers and a Tauberian theorem","volume":"11","author":"\u00c7anak \u0130.","year":"2014","unstructured":"\u00c7anak\u0130., H\u00f6lder summability method of fuzzy numbers and a Tauberian theorem, Iran J Fuzzy Syst11(4) (2014), 87\u201393.","journal-title":"Iran J Fuzzy Syst"},{"issue":"4","key":"e_1_3_2_8_2","first-page":"15","article-title":"Some conditions under which slow oscillation of a sequence of fuzzy numbers follows from Ces\u00e0ro summability of its generator sequence","volume":"11","author":"\u00c7anak \u0130.","year":"2014","unstructured":"\u00c7anak\u0130., Some conditions under which slow oscillation of a sequence of fuzzy numbers follows from Ces\u00e0ro summability of its generator sequence, Iran J Fuzzy Syst11(4) (2014), 15\u201322.","journal-title":"Iran J Fuzzy Syst"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130938"},{"issue":"6","key":"e_1_3_2_10_2","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1080\/00207727808941724","article-title":"Operations on fuzzy numbers","volume":"9","author":"Dubois D.","year":"1978","unstructured":"DuboisD. and PradeH., Operations on fuzzy numbers, Internat J Systems Sci9(6) (1978), 613\u2013626.","journal-title":"Internat J Systems Sci"},{"key":"e_1_3_2_11_2","volume-title":"Fuzzy sets and systems","author":"Dubois D.","year":"1980","unstructured":"DuboisD., PradeH., Fuzzy sets and systems, Academic Press, New York-London, 1980."},{"issue":"1","key":"e_1_3_2_12_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0165-0114(82)90025-2","article-title":"Towards fuzzy differential calculus","volume":"8","author":"Dubois D.","year":"1982","unstructured":"DuboisD. and PradeH., Towards fuzzy differential calculus, Fuzzy Sets and Systems8(1) (1982), 1\u201317.","journal-title":"Fuzzy Sets and Systems"},{"issue":"2","key":"e_1_3_2_13_2","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/0165-0114(82)90001-X","article-title":"Towards fuzzy differential calculus","volume":"8","author":"Dubois D.","year":"1982","unstructured":"DuboisD. and PradeH., Towards fuzzy differential calculus, Fuzzy Sets and Systems8(2) (1982), 105\u2013116.","journal-title":"Fuzzy Sets and Systems"},{"issue":"3","key":"e_1_3_2_14_2","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/S0165-0114(82)80001-8","article-title":"Towards fuzzy differential calculus","volume":"8","author":"Dubois D.","year":"1982","unstructured":"DuboisD. and PradeH., Towards fuzzy differential calculus, Fuzzy Sets and Systems8(3) (1982), 225\u2013233.","journal-title":"Fuzzy Sets and Systems"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(86)90026-6"},{"key":"e_1_3_2_16_2","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.ins.2011.11.024","article-title":"The Henstock-Stieltjes integral for fuzzy-number-valued functions","volume":"188","author":"Gong Z.","year":"2012","unstructured":"GongZ. and WangL., The Henstock-Stieltjes integral for fuzzy-number-valued functions, Inform Sci188 (2012), 276\u2013297.","journal-title":"Inform Sci"},{"issue":"1","key":"e_1_3_2_17_2","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1142\/S0218488598000045","article-title":"The fuzzy Riemann-Stieltjes integral","volume":"6","author":"Wu H.-C.","year":"1998","unstructured":"WuH.-C., The fuzzy Riemann-Stieltjes integral, Internat J Uncertain Fuzziness Knowledge-Based Systems6(1) (1998), 51\u201367.","journal-title":"Internat J Uncertain Fuzziness Knowledge-Based Systems"},{"key":"e_1_3_2_18_2","first-page":"28","article-title":"Sequences of fuzzy numbers","volume":"28","author":"Matloka M.","year":"1986","unstructured":"MatlokaM., Sequences of fuzzy numbers, Busefal28 (1986), 28\u201337.","journal-title":"Busefal"},{"issue":"1","key":"e_1_3_2_19_2","first-page":"87","article-title":"Necessary and sufficient Tauberian conditions in the case of weighted mean summable integrals over \u211d+","volume":"7","author":"M\u00f3ricz F.","year":"2004","unstructured":"M\u00f3riczF., Necessary and sufficient Tauberian conditions in the case of weighted mean summable integrals over \u211d+, Math Inequal Appl7(1) (2004), 87\u201393.","journal-title":"Math Inequal Appl"},{"issue":"4","key":"e_1_3_2_20_2","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1023\/B:AMHU.0000024678.80514.94","article-title":"Necessary and sufficient Tauberian conditions for certain weighted mean methods of summability II","volume":"102","author":"M\u00f3ricz F.","year":"2004","unstructured":"M\u00f3riczF. and RhoadesB.E., Necessary and sufficient Tauberian conditions for certain weighted mean methods of summability II, Acta Math Hungar102(4) (2004), 279\u2013285.","journal-title":"Acta Math Hungar"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90222-4"},{"issue":"1","key":"e_1_3_2_22_2","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0165-0114(89)90090-0","article-title":"On integration of fuzzy mappings","volume":"32","author":"Nanda S.","year":"1989","unstructured":"NandaS., On integration of fuzzy mappings, Fuzzy Sets and Systems32(1) (1989), 95\u2013101.","journal-title":"Fuzzy Sets and Systems"},{"issue":"6","key":"e_1_3_2_23_2","doi-asserted-by":"crossref","first-page":"2134","DOI":"10.1007\/s10773-013-1511-9","article-title":"The fuzzy Riemann-Stieltjes integral","volume":"52","author":"Ren X.","year":"2013","unstructured":"RenX. and WuC., The fuzzy Riemann-Stieltjes integral, Internat J Theoret Phys52(6) (2013), 2134\u20132151.","journal-title":"Internat J Theoret Phys"},{"key":"e_1_3_2_24_2","first-page":"159","article-title":"Ces\u00e0ro summability for fuzzy real numbers","volume":"7","author":"Subrahmanyam P.V.","year":"1999","unstructured":"SubrahmanyamP.V., Ces\u00e0ro summability for fuzzy real numbers, J Anal7 (1999), 159\u2013168.","journal-title":"J Anal"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2010.02.006"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2011.09.002"},{"key":"e_1_3_2_27_2","first-page":"7","article-title":"On the slowly decreasing sequences of fuzzy numbers","volume":"891986","author":"Talo \u00d6.","year":"2013","unstructured":"Talo\u00d6. and Ba\u015farF., On the slowly decreasing sequences of fuzzy numbers, Abstr Appl AnalArt. ID 891986 (2013), 7.","journal-title":"Abstr Appl Anal"},{"key":"e_1_3_2_28_2","unstructured":"YavuzE. Talo\u00d6. and Co\u015fkunH. Ces\u00e0ro summability of integrals of fuzzy-number-valued functions https:\/\/arXiv.1604.05338."},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-161596","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-161596","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-161596","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:52Z","timestamp":1777455592000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-161596"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,11]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["10.3233\/JIFS-161596"],"URL":"https:\/\/doi.org\/10.3233\/jifs-161596","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,11]]}}}