Jensen-type inequalities for Sugeno integral
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- 作者：Sadegh Abbaszadeha ; abbaszadeh@semnan.ac.ir" class="auth_mail" title="E-mail the corresponding author ; Madjid Eshaghi Gordjia ; meshaghi@semnan.ac.ir" class="auth_mail" title="E-mail the corresponding author ; Endre Pap ; b ; c ; pape@eunet.rs" class="auth_mail" title="E-mail the corresponding author ; epap@singidunum.ac.rs" class="auth_mail" title="E-mail the corresponding author ; Anikó ; Szaká ; lc ; szakal@bmf.hu" class="auth_mail" title="E-mail the corresponding author
- 关键词：Sugeno integral ; The Jensen inequality ; Concave function ; Supergradient ; Superdifferential
- 刊名：Information Sciences
- 出版年：2017
- 出版时间：10 January 2017
- 年：2017
- 卷：376
- 期：Complete
- 页码：148-157
- 全文大小：387 K
文摘
In this paper, the classical Jensen inequalities for concave function φ, i.e.,
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are adapted for the Sugeno integral using the notion of the supergradient. Moreover, we give some modifications of previous results of Román-Flores et al. concerning Jensen-type inequalities for Sugeno integral. Some examples in the framework of the Lebesgue measure and counting measure to illustrate the results are presented.class="mathml">mmlsi1" class="mathmlsrc">class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0020025516311537&_mathId=si1.gif&_user=111111111&_pii=S0020025516311537&_rdoc=1&_issn=00200255&md5=a4367ff3a6486d25a4c96a42c7650173">mg class="imgLazyJSB inlineImage" height="56" width="527" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0020025516311537-si1.gif"> class="mathContainer hidden">class="mathCode"><math altimg="si1.gif" overflow="scroll"><mtable displaystyle="true"><mtr><mtd columnalign="right"><mrow><mi>φmi><mrow><mo stretchy="true">(mo><mo>∫mo><mi>fmi><mo>(mo><mi>xmi><mo>)mo><mspace width="0.16em">mspace><mrow><mi mathvariant="normal">dmi>mrow><mi>μmi><mo stretchy="true">)mo>mrow><mo>⩾mo><mo>∫mo><mi>φmi><mrow><mo>(mo><mi>fmi><mo>)mo>mrow><mspace width="0.16em">mspace><mrow><mi mathvariant="normal">dmi>mrow><mi>μmi><mspace width="14.22636pt">mspace><mtext>andmtext><mspace width="14.22636pt">mspace><mi>φmi><mrow><mo stretchy="true">(mo><munderover><mo>∑mo><mrow><mi>imi><mo>=mo><mn>1mn>mrow><mi>nmi>munderover><msub><mi>λmi><mi>imi>msub><msub><mi>xmi><mi>imi>msub><mo stretchy="true">)mo>mrow><mo>⩾mo><munderover><mo>∑mo><mrow><mi>imi><mo>=mo><mn>1mn>mrow><mi>nmi>munderover><msub><mi>λmi><mi>imi>msub><mi>φmi><mrow><mo>(mo><msub><mi>xmi><mi>imi>msub><mo>)mo>mrow><mo>,mo>mrow>mtd>mtr>mtable>math>mg class="temp" src="/sd/blank.gif">