arXiv subjects

Michał Boczek

Publications and source records attributed to Michał Boczek.

9 recordsLinked to original sources

arXiv2026

On admissible pairs of aggregation functions based on quasi-linear means and related families

Admissible orders play a key role in ranking subintervals of the unit interval. In 2013, Bustince et al. proposed constructing such relations by means of admissible pairs of aggregation functions. The only significant example in the literature is a pair of weighted arithmetic means with different weights. In this paper, we present a method for constructing admissible pairs of aggregation functions, which allows us to verify the admissibility of various function classes, including quasi-linear means, Archimedean t-norms (and t-conorms), and certain strictly Schur-convex (or Schur-concave) functions. Furthermore, we examine the relationship between admissible orders generated by admissible pairs of aggregation functions and the (α, \b{eta})-order, identifying cases where these two notions do not coincide.

math.GM↗

arXiv2024

The Choquet-like operator with respect to an admissible order as a tool for aggregating multivalued data

In this paper, we propose a new generalization of the classical discrete Choquet integral to the multivalued framework in terms of an admissible order that refines the natural partial order on the considered value set. The new Choquet-like operator takes as input a finite number of values of a given type, in particular real numbers, intervals, and vectors, and returns a~single output value of the same type as the input values. We give necessary and sufficient conditions for the operator to be monotone with respect to the admissible order. We then provide a complete characterization of the Choquet-like operator as an aggregation function with respect to the admissible order and study its selected special cases.

math.GM↗

arXiv2020

New monotone measure-based integrals inspired by scientific impact problem

In this paper, we define new functionals generalizing scientometric indices proposed by Mesiar and Gągolewski in 2016 to overcome some limitations of h-index. These functionals are integrals with respect to a monotone measure as well as aggregation functions under some mild conditions. We derive numerous properties of the new integrals and analyze subadditivity property in detail. We also give a partial solution to the problem posed by Mesiar and Stupňanová to find an algorithm for computing the pseudo-decomposition integral of n-th order based on operations $\oplus=+$ and $\odot=\wedge,$ which will be useful in multi-criteria decision problems.

math.FA↗

arXiv2018

Sharp bounds of Jensen type for the generalized Sugeno integral

In this paper we provide two-sided attainable bounds of Jensen type for the generalized Sugeno integral of {\it any} measurable function. The results extend the previous results of Román-Flores et al. for increasing functions and Abbaszadeh et al. for convex and concave functions. We also give corrections of some results of Abbaszadeh et al. As a by-product, we obtain sharp inequalities for symmetric integral of Grabisch. To the best of our knowledge, the results in the real-valued functions context are presented for the first time here.

math.FA↗

arXiv2015

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-Hölder 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-Hölder inequality for the lower Sugeno integral and the class of $μ$-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 Borzová-Molnárová and et al in The smallest semicopula-based universal integrals I: Properties and characterizations, Fuzzy Sets and Systems 271 (2015) 1--17.

math.FA↗

arXiv2015

On Carlson's inequality for Sugeno and Choquet integrals

We present a Carlson type inequality for the generalized Sugeno integral and a much 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.

math.FA↗

arXiv2015

Convergence theorems for seminormed fuzzy integrals: Solutions to Hutnìk's open problems

In this note, we give solutions to Problems $9.4$ and $9.5,$ which were presented by Mesiar and Stupňanová [{\it Open problems from the 12th International Conference on Fuzzy Set Theory and Its Applications}, Fuzzy Sets and Systems 261 (2015)] and by Borzová-Molnárová, Halucinová and Hutník, in [{\it The smallest semicopula-based universal integrals I: properties and characterizations,} Fuzzy Sets and Systems (2014), http://dx.doi.org/ 10.1016/j.fss.2014.09.024].

math.ST↗

arXiv2014

On some properties of seminormed fuzzy integrals

We give solutions to Problems 2.21, 2.31 and 2.32, which were posed Borzowá-Molnárová, Halčinová and Hutník in [{\it The smallest semicopula-based universal integrals I: properties and characterizations,} Fuzzy Sets and Systems (2014), http://dx.doi.org/ 10.1016/j.fss. 2014.09.0232014].

math.GM↗

arXiv2014

The solution of Hutník's open problem

In this note, we give a solution to Problem $9.2$, which was presented by Mesiar and Stupňanová [{\it Open problems from the 12th International Conference on Fuzzy Set Theory and Its Applications}, Fuzzy Sets and Systems (2014), http://dx.doi.org/10.1016/ j.fss.2014.07.012]. We show that the class of semicopulas solving Problem $9.2$ contains only the Łukasiewicz t-norm.

math.ST↗