Marek Kaluszka

On Chebyshev type inequalities for generalized Sugeno integrals

Abstract We give the necessary and sufficient conditions guaranteeing the validity of Chebyshev type inequalities for generalized Sugeno integrals in the case of functions belonging to a much wider class than the comonotone functions. For several choices of operators, we characterize the classes of functions for which the Chebyshev type inequality for the classical Sugeno integral is satisfied.

On the Jensen type inequality for generalized Sugeno integral

We prove necessary and sufficient conditions for the validity of Jensen type inequalities for generalized Sugeno integral. Our proofs make no appeal to the continuity of neither the fuzzy measure nor the operators. For several choices of operators, we characterize the classes of functions for which the corresponding inequalities are satisfied.

On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application

In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-H{o}lder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi in General Minkowski type and related inequalities for seminormed fuzzy integrals, Sahand Communications in Mathematical Analysis 1 (2014) 9--20 is not true. Next, we study the Minkowski-H{o}lder inequality for the lower Sugeno integral and the class of

On risk aversion under fuzzy random data

mu

On S-homogeneity property of seminormed fuzzy integral

-subadditive functions introduced in On Chebyshev type inequalities for generalized Sugeno integrals, Fuzzy Sets and Systems 244 (2014) 51--62. The results are applied to derive new metrics on the space of measurable functions in the setting of nonadditive measure theory. We also give a partial answer to the open problem 2.22 posed by Borzova-Molnarova and et al in The smallest semicopula-based universal integrals I: Properties and characterizations, Fuzzy Sets and Systems 271 (2015) 1--17.

On conditions under which some generalized Sugeno integrals coincide: A solution to Dubois' problem

In this paper, we generalize classical results on risk aversion by analyzing the case, when the available data about cash flows are fuzzy numbers, random fuzzy numbers, type-2 fuzzy sets, random type-2 fuzzy sets, etc. We prove that the ArrowPratt measures are also risk aversion measures when an agent measures her risk using the Jensen-type operators. We also provide numerous examples of the Jensen-type operators.

On Carlson's inequality for Sugeno and Choquet integrals

We give an?answer to Problem 9.3 stated by Mesiar and Stupňanova 8. We show that the class of semicopulas solving this problem contains any associative semicopula S such that for each a ? 0, 1 the function x ? S(a, x) is continuous and increasing on a countable number of intervals.

On comonotone commuting and weak subadditivity properties of seminormed fuzzy integrals

Abstract In the paper, we characterize the class of all pairs of fuzzy implications and dual fuzzy implications such that the q-integral and q-cointegral coincide. This gives a solution to the problem posed by Didier Dubois during the conference FSTA 2016, the 13th International Conference on Fuzzy Set Theory and Applications. As a corollary, we obtain the necessary and sufficient conditions under which the seminormed fuzzy integral and the semiconormed fuzzy integral are equal for all measurable functions.

Translation-invariant semicopula-based integrals

We present axa0Carlson type inequality for the Sugeno integral and axa0much wider class of functions than the comonotone functions. We also provide three Carlson type inequalities for the Choquet integral. Our inequalities generalize many known results.

Steffensen type inequalities for fuzzy integrals

Abstract In the paper, we characterize the class of all the binary operators ∘-commuting with the generalized Sugeno integral generated by a strict t -norm. For the Sugeno integral, this problem was solved by Ouyang and Mesiar. We also present the necessary and sufficient conditions for the weak subadditivity of the generalized Sugeno integral.