Radko Mesiar
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View article: Element-Oriented Construction Methods for Nullnorms on Bounded Lattices
Element-Oriented Construction Methods for Nullnorms on Bounded Lattices Open
Nullnorms are aggregation functions with an annihilator and are generalizations of t-norms and t-conorms. After the introduction of the concept of nullnorms on bounded lattices by Karaçal et al., the studies on their construction methods i…
View article: Element-Based Construction Methods for Uninorms on Bounded Lattices
Element-Based Construction Methods for Uninorms on Bounded Lattices Open
Uninorms are aggregation operators that generalize the t-norms (t-conorms), which are extensions of the logical connectives ∧(∨) to the fuzzy set theory. The methods of constructing uninorms on more general algebraic structures (such as bo…
View article: On comprehensive families of copulas involving the three basic copulas and transformations thereof
On comprehensive families of copulas involving the three basic copulas and transformations thereof Open
Comprehensive families of copulas including the three basic copulas (at least as limit cases) are useful tools to model countermonotonicity, independence, and comonotonicity of pairs of random variables on the same probability space. In th…
View article: A new family of aggregation functions for intervals
A new family of aggregation functions for intervals Open
Aggregation operators are unvaluable tools when different pieces of information have to be taken into account with respect to the same object. They allow to obtain a unique outcome when different evaluations are available for the same elem…
View article: n-K-Increasing Aggregation Functions
n-K-Increasing Aggregation Functions Open
We introduce and discuss the concept of n-ary K-increasing fusion functions and n-ary K-increasing aggregation functions, K being a subset of the index set {1,…,n} indicating in which variables a considered function is increasing. It is al…
View article: Multivariate Asymmetric Distributions of Copula Related Random Variables
Multivariate Asymmetric Distributions of Copula Related Random Variables Open
It is known that normal distribution plays an important role in analysing symmetric data. However, this symmetric assumption may not hold in many real word and in such cases, asymmetric distribution, including skew normal distribution, are…
View article: A framework for generalized monotonicity of fusion functions
A framework for generalized monotonicity of fusion functions Open
The relaxation of the property of monotonicity is a trend in the theory of aggregation and fusion functions and several generalized forms of monotonicity have been introduced, most of which are based on the notion of directional monotonici…
View article: Applications of Special Functions to Approximate Stochastic Bi-Homomorphisms and Stochastic Bi-Derivations in FB-Algebras and FC-⋄-Algebras of the Matrix Type
Applications of Special Functions to Approximate Stochastic Bi-Homomorphisms and Stochastic Bi-Derivations in FB-Algebras and FC-⋄-Algebras of the Matrix Type Open
We apply special functions and use the concept of the aggregation function to introduce a new class of fuzzy control functions, and based on this, we obtain the best approximation for the stochastic bi-homomorphisms and stochastic bi-deriv…
View article: Choquet type integrals for single-valued functions with respect to set-functions and set-multifunctions
Choquet type integrals for single-valued functions with respect to set-functions and set-multifunctions Open
Due to their numerous applications such as in decision making, information fusion, game theory, and data mining, Choquet integrals have recently attracted much attention. In this study, two generalization types of Choquet integrals are pre…
View article: On asymmetric distributions of copula related random variables which includes the skew-normal ones
On asymmetric distributions of copula related random variables which includes the skew-normal ones Open
Assuming that CX,Y is the copula function of X and Y with marginal distribution functions FX (x) and FY (y), in this work we study the selection distribution Z d = (X|Y ∈ T ).We present some special cases of our proposed distribution, amon…
View article: New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS
New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS Open
By using a class of aggregation control functions, we introduce the concept of multiple-HU-OS1-stability and get an optimum approximation for a nonlinear single fractional differential equation (NS-ABC-FDE) with a Mittag–Leffler kernel. We…
View article: Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM
Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM Open
In this article, we propose the generalized version of the extended, partitioned Bonferroni mean (EPBM) operator with a systematic investigation of its behavior and properties. It can aggregate data of various dimensions in one formulation…
View article: Abstract homogeneity of interval-valued functions
Abstract homogeneity of interval-valued functions Open
In this paper we develop the idea of abstract homogeneity in the context of interval-valued (IV) functions endowed with admissible orders and investigate some of its properties.
View article: On Monotonicities of Interval Valued Functions
On Monotonicities of Interval Valued Functions Open
In this paper, we develop the notions of weak/directional monotonicity (developed by Sesma-Sara et al. in terms of the \emph{Kulisch-Miranker order}) and the notion of $ G $-monotonicity (introduced by Santiago et al. for $ [0,\!1]$) for i…
View article: Comprehensive Rules-Based and Preferences Induced Weights Allocation in Group Decision-Making with BUI
Comprehensive Rules-Based and Preferences Induced Weights Allocation in Group Decision-Making with BUI Open
Decision-makers’ subjective preferences can be well modeled using preference aggregation operators and related induced weights allocation mechanisms. However, when several different types of preferences occur in some decision environment w…
View article: Special Issue on Set Valued Analysis 2021
Special Issue on Set Valued Analysis 2021 Open
Set Valued Analysis plays an important role in the study of statistics, biology, economics, social sciences, optimal control, differential inclusions, image reconstruction and fixed point theory [...]
View article: Analysis of Interval-Valued Intuitionistic Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making
Analysis of Interval-Valued Intuitionistic Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making Open
When dealing with the haziness that is intrinsic in decision analysis-driven decision making procedures, interval-valued intuitionistic fuzzy sets (IVIFSs) can be quite effective. Our approach to solving the multiple attribute decision mak…
View article: Fuzzy Caratheodory’s Theorem and Outer ∗-Fuzzy Measure
Fuzzy Caratheodory’s Theorem and Outer ∗-Fuzzy Measure Open
The goal of this paper is to introduce two new concepts ∗-fuzzy premeasure and outer ∗-fuzzy measure, and to further prove some properties, such as Caratheodory’s Theorem, as well as the unique extension of ∗-fuzzy premeasure. This theorem…
View article: Optimum Approximation for ς–Lie Homomorphisms and Jordan ς–Lie Homomorphisms in ς–Lie Algebras by Aggregation Control Functions
Optimum Approximation for ς–Lie Homomorphisms and Jordan ς–Lie Homomorphisms in ς–Lie Algebras by Aggregation Control Functions Open
In this work, by considering a class of matrix valued fuzzy controllers and using a (κ,ς)-Cauchy–Jensen additive functional equation ((κ,ς)-CJAFE), we apply the Radu–Mihet method (RMM), which is derived from an alternative fixed point theo…