Yao Ouyang

General Chebyshev type inequalities for Sugeno integrals

Chebyshev type inequalities for the Sugeno integral on abstract spaces are studied in a rather general form, thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation.

General Minkowski type inequalities for Sugeno integrals

Minkowski type inequalities for the Sugeno integral on abstract spaces are studied in a rather general form, thus closing the series of papers on the topic dealing with special cases restricted to the (pseudo-)additive operation.

An inequality related to Minkowski type for Sugeno integrals

An inequality related to Minkowski type for the Sugeno integral on abstract spaces is studied in a rather general form. Some previous results on Chebyshev type inequality obtained by the authors are generalized. Several examples are given to illustrate the validity of this inequality. The conditions such that this inequality becomes an equality are also discussed. Finally, conclusions and some problems for further investigations are included.

On the Chebyshev type inequality for seminormed fuzzy integral

The Chebyshev type inequality for seminormed fuzzy integral is discussed. The main results of this paper generalize some previous results obtained by the authors. We also investigate the properties of semiconormed fuzzy integral, and a related inequality for this type of integral is obtained.

New general extensions of Chebyshev type inequalities for Sugeno integrals

We provide new frameworks of Chebyshev type inequalities for Sugeno integrals on abstract spaces.

Berwald type inequality for Sugeno integral

Abstract Nonadditive measure is a generalization of additive probability measure. Sugeno integral is a useful tool in several theoretical and applied statistics which has been built on non-additive measure. Integral inequalities play important roles in classical probability and measure theory. The classical Berwald integral inequality is one of the famous inequalities. This inequality turns out to have interesting applications in information theory. In this paper, Berwald type inequality for the Sugeno integral based on a concave function is studied. Several examples are given to illustrate the validity of this inequality. Finally, a conclusion is drawn and a problem for further investigations is given.

General Chebyshev type inequalities for universal integral

A new inequality for the universal integral on abstract spaces is obtained in a rather general form. As two corollaries, Minkowskis and Chebyshevs type inequalities for the universal integral are obtained. The main results of this paper generalize some previous results obtained for special fuzzy integrals, e.g., Choquet and Sugeno integrals. Furthermore, related inequalities for seminormed integral are obtained.

SUGENO INTEGRAL AND THE COMONOTONE COMMUTING PROPERTY

Comonotone maxitivity and minitivity of Sugeno integral can be seen as commuting of the Sugeno integral and max, resp. min operator for comonotone functions. In the paper, we look for the other ope...

On some advanced type inequalities for Sugeno integral and T-(S-)evaluators

In this paper strengthened versions of the Minkowski, Chebyshev, Jensen and Holder inequalities for Sugeno integral and T-(S-)evaluators are given. As an application, some equivalent forms and some particular results have been established.

A conditionally cancellative left-continuous t-norm is not necessarily continuous

Abstract In this paper, we propose a new method for constructing non-continuous t-norms from a given t-norm. Using this method, we construct a family of conditionally cancellative left-continuous t-norms which are not continuous. Thus we answer an open question which is collected by Klement et al. [Problems on triangular norms and related operators, Fuzzy Sets and Systems 145 (2004) 471–479].