A Chebyshev type inequality for fuzzy integrals

Flores-Franulič, A.; Román-Flores, Heriberto

doi:10.1016/j.amc.2007.02.143

Cited by 101 publications

(42 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The inequality of the Chebyshev type has been studied in [1,12,13,29,30,32]. The generalizations of different classical integral inequalities in the frame of the pseudo-analysis, such as Minkowski, Hölder, Berwald, Jensen and Cauchy-Schwarz inequalities were studied in [2][3][4]8,13].…”

Section: Introductionmentioning

confidence: 99%

Inequalities of the Chebyshev type based on pseudo-integrals

Grbic

Medic

Perović

et al. 2016

Fuzzy Sets and Systems

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

Inequalities of the Chebyshev type based on pseudo-integrals

Grbic

Medic

Perović

et al. 2016

Fuzzy Sets and Systems

View full text Add to dashboard Cite

“…Fuzzy integrals (also known as Sugeno integrals) have very interesting properties from a mathematical point of view which have been studied by many authors, including Pap (1995), Ralescu and Adams (1980), Flores-Franulič and Román-Flores (2007), Chalco-Cano (2006, 2007), Román-Flores et al (2007a, b, 2008 and Wang and Klir (1992) among others. Ralescu and Adams (1980) studied several equivalent definitions of fuzzy integrals, while Pap (1995) and Wang and Klir (1992) provided an overview of fuzzy measures theory.…”

Section: Introductionmentioning

confidence: 99%

A general inequality of Chebyshev type for semi(co)normed fuzzy integrals

Agahi

Eslami

2010

Soft Comput

View full text Add to dashboard Cite

Generalization of the Chebyshev inequality for semi(co)normed fuzzy integrals on an abstract fuzzy measure space based on a binary operation is given. Also, Minkowski's and Hölder's inequalities for semi(co)normed fuzzy integrals are studied in a rather general form. The main results of this paper generalize some previous results. Finally, a conclusion is drawn and an open problem for further investigations is given.

show abstract

“…The study of inequalities for Sugeno integral was initiated by Román-Flores et al [10,25], and then followed by some authors [1,[3][4][5]16,[19][20][21]. Recently, the authors generalized several classical inequalities, including Minkowski's and Chebyshev's inequalities, to the frame of Sugeno integral [1,4,20].…”

Section: Introductionmentioning

confidence: 99%

On Non-additive Probabilistic Inequalities of Hölder-type

et al. 2011

View full text Add to dashboard Cite

Non-additive measure is a generalization of additive probability measure. Integral inequalities play important roles in classical probability and measure theory. Some well-known inequalities such as the Minkowski inequality and the Hölder inequality play important roles not only in the theoretical area but also in application. Non-additive integrals are useful tools in several theoretical and applied statistics which have been built on non-additive measure. For instance, in decision theory and applied statistics, the use of the non-additive integrals can be envisaged from two points of view: decision under uncertainty and multi-criteria decision-making. In fact, the non-additive integrals provide useful tools in many problems in engineering and social choice where the aggregation of data is required. In this paper, Hölder and Minkowski type inequalities for semi(co)normed non-additive integrals are discussed. The main results of this paper generalize some previous results obtained by the authors. Mathematics Subject Classification (2000). Primary 99Z99; Secondary 00A00.

show abstract

A Chebyshev type inequality for fuzzy integrals

Cited by 101 publications

References 7 publications

Inequalities of the Chebyshev type based on pseudo-integrals

Inequalities of the Chebyshev type based on pseudo-integrals

A general inequality of Chebyshev type for semi(co)normed fuzzy integrals

On Non-additive Probabilistic Inequalities of Hölder-type

Contact Info

Product

Resources

About