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Start Over Creator Kalina, Martin

1. Conditional states and joint distributions on MV-algebras

Creator:
Kalina, Martin and Nánásiová, Oľga
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
semi-simple MV-algebra, conditional distribution, and joint distribution
Language:
English
Description:
In this paper we construct conditional states on semi-simple MV-algebras. We show that these conditional states are not given uniquely. By using them we construct the joint probability distributions and discuss the properties of these distributions. We show that the independence is not symmetric.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Fuzzy orness measure and new orness axioms

Creator:
Jin, LeSheng, Kalina, Martin, and Qian, Gang
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
aggregation function, OWA operator, and orness measure
Language:
English
Description:
We have modified the axiomatic system of orness measures, originally introduced by Kishor in 2014, keeping altogether four axioms. By proposing a fuzzy orness measure based on the inner product of lattice operations, we compare our orness measure with Yager's one which is based on the inner product of arithmetic operations. We prove that fuzzy orness measure satisfies the newly proposed four axioms and propose a method to determine OWA operator with given fuzzy orness degree.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras

Creator:
Kalina, Martin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
lattice effect algebra, center, atom, and Mac Neille completion
Language:
English
Description:
If element z of a lattice effect algebra (E,⊕,0,1) is central, then the interval [0,z] is a lattice effect algebra with the new top element z and with inherited partial binary operation ⊕. It is a known fact that if the set C(E) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C(E) in E equals to the top element of E, then E is isomorphic to a subdirect product of irreducible effect algebras (\cite{R2}). This means that if there exists a MacNeille completion E^ of E which is its extension (i.e. E is densely embeddable into E^) then it is possible to embed E into a direct product of irreducible effect algebras. Thus E inherits some of the properties of E^. For example, the existence of a state in E^ implies the existence of a state in E. In this context, a natural question arises if the MacNeille completion of the center of E (denoted as MC(C(E))) is necessarily the same as the center of E^, i.e., if MC(C(E))=C(E^) is necessarily true. We show that the equality is not necessarily fulfilled. We find a necessary condition under which the equality may hold. Moreover, we show also that even the completeness of C(E) and its bifullness in E is not sufficient to guarantee the mentioned equality.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. On central atoms of Archimedean atomic lattice effec algebras

Creator:
Kalina, Martin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
lattice effect algebra, center, atom, and bitfullness
Language:
English
Description:
If element z of a lattice effect algebra (E,⊕,0,1) is central, then the interval [0,z] is a lattice effect algebra with the new top element z and with inherited partial binary operation ⊕. It is a known fact that if the set C(E) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C(E) in E equals to the top element of E, then E is isomorphic to a direct product of irreducible effect algebras (\cite{R2}). In \cite{PR} Paseka and Riečanová published as open problem whether C(E) is a bifull sublattice of an Archimedean atomic lattice effect algebra E. We show that there exists a lattice effect algebra (E,⊕,0,1) with atomic C(E) which is not a bifull sublattice of E. Moreover, we show that also B(E), the center of compatibility, may not be a bifull sublattice of E.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public