一类拟凹积分的等价定义
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摘要
本文引入了一个泛函关于泛加和泛乘运算的拟凹性和拟正齐性的概念并讨论了它们的基本性质。利用一族具有单调性、拟凹性和正齐性的泛函给出了一类拟凹积分的等价表述,讨论了一个容度(或称单调测度)关于拟凹积分的完全均衡性。基于算术加法和乘法运算的凹积分的相关结果得到了进一步推广。
In this note,the concepts of pseudo-concavity and positive pseudo-homogeneity( for pseudo-addition and pseudo-multiplication) of a functional is introduced and some properties are discussed.The equivalence definition of the pseudo-concave integrals is presented by means of functionals with monotonicity,pseudo-concavity and positive homogeneity. The totally balance of a monotone measure for pseudo-concave integral is also discussed. Some previous results on concave integrals are generalized.
In this note,the concepts of pseudo-concavity and positive pseudo-homogeneity( for pseudo-addition and pseudo-multiplication) of a functional is introduced and some properties are discussed.The equivalence definition of the pseudo-concave integrals is presented by means of functionals with monotonicity,pseudo-concavity and positive homogeneity. The totally balance of a monotone measure for pseudo-concave integral is also discussed. Some previous results on concave integrals are generalized.
引文
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[11]J Li,R Mesiar,P Stuck. Pseudo-optimal measures[J]. Information Science,2010(180):4015-4021.
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[13]M Sugeno,T Murofushi. Pseudo-additive measures and integrals[M]. J Math Anal Appl,1987(122):197-222.
[14]E Pap. Null-additive Set Functions[M]. Kluwer,Dordrecht,1995.
[15]E Pap. Handbook of Measure Theory[M]. Elsevier,Amsterdam,2002.
[16]J Li,Y Ouyang,M Yu. Pan-Integrals Based on Optimal Measures[C]. MDAI2017,LNAI 10571,40-50.
[2]E Lehrer,R Teper. The concave integral over large spaces[J]. Fuzzy Sets and Systems,2008(159):2130-2144.
[3]R Teper. On the continuity of the concave integral[J]. Fuzzy Sets and Systems,2009(160):1318-1326.
[4]Y Even,E Lehrer. Decomposition-integral:unifying Choquet and the concave integrals[J]. Economic Theory,2014(56):33-58.
[5]G Choquet. Theory of capacities[J]. Ann inst Fourier(Grenoble),1954(5):131-295.
[6]杨庆季.模糊测度空间上的泛积分[J].模糊数学,1985(3):107-114.
[7]Z Wang,G J Klir. Generalized Measure Theory[M]. Springer,2009.
[8]R Mesiar,J Li,E Pap. Discrete pseudo-integrals[J]. Int J Approx Reasoning,2013(54):357-364.
[9]R Mesiar,A Stupnanova. Decomposition Integrals[J]. Int J Approx Reasoning,2013(54):1252-1259.
[10]R Mesiar,J Li,E Pap. Pseudo-concave integrals[J]. NLMUA’2011,Adv Intell Syst Comput,SpringerVerlag,Berlin Heidelberg,2011(100):43-49.
[11]J Li,R Mesiar,P Stuck. Pseudo-optimal measures[J]. Information Science,2010(180):4015-4021.
[12]D Denneberg. Non-additive Measure and Integral[M]. Kluwer Academic Publishers,Dordrecht,1994.
[13]M Sugeno,T Murofushi. Pseudo-additive measures and integrals[M]. J Math Anal Appl,1987(122):197-222.
[14]E Pap. Null-additive Set Functions[M]. Kluwer,Dordrecht,1995.
[15]E Pap. Handbook of Measure Theory[M]. Elsevier,Amsterdam,2002.
[16]J Li,Y Ouyang,M Yu. Pan-Integrals Based on Optimal Measures[C]. MDAI2017,LNAI 10571,40-50.