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1. Characterizations of sub-semihypergroups by various triangular norms

Creator:
Davvaz, B.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
semihypergroup, complete lattice, triangular norm, fundamental relation, and probability space
Language:
English
Description:
We investigate the structure and properties of $TL$-sub-semihypergroups, where $T$ is an arbitrary triangular norm on a given complete lattice $L$. We study its structure under the direct product and with respect to the fundamental relation. In particular, we consider $L=[0,1]$ and $T=\min $, and investigate the connection between $TL$-sub-semihypergroups and the probability space.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Convergence of sequences of sets with respect to lattice-valued possibilistic measures

Creator:
Kramosil , Ivan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Sequences of sets, convergence in measure, complete lattice, and lattice-valued possibilistic measure
Language:
English
Description:
Convergence in, or with respect to, s-additive measure, in particular, convergence in probability, can be taken as an important notion of the standard measure and probability theory, and as a powerful tool when analyzing and processing sequences of subsets of the universe of discourse and, more generally, sequences of real-valued measurable functions defined on this universe. Our aim is to propose an alternative of this notion of convergence supposing that the measure under consideration is a (complete) non-numerical and, in particular, lattice-valued possibilistic measure, i.e., a set function obeying the demand of (complete) maxitivity instead of that of s-additivity. Focusing our attention to sequences of sets converging in a lattice-valued possibilistic measure, some more or less elementary properties of such sequences are stated and proved.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Decision-making under uncertainty processed by lattice-valued possibilistic measures

Creator:
Kramosil, Ivan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
decision making under uncertainty, complete lattice, lattice-valued possibilistc measures, possibilistc decision function, and minimax and Bayesian optimization
Language:
English
Description:
The notion and theory of statistical decision functions are re-considered and modified to the case when the uncertainties in question are quantified and processed using lattice-valued possibilistic measures, so emphasizing rather the qualitative than the quantitative properties of the resulting possibilistic decision functions. Possibilistic variants of both the minimax (the worst-case) and the Bayesian optimization principles are introduced and analyzed.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. On a particular class of lattice-valued possibilistic distributions

Creator:
Kramosil, Ivan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Possibilistic distribution, possibilistic measure, lattice-valued uncertainty degrees, complete lattice, Boolean ordering, lexicographic ordering, and possibilistic entropy function
Language:
English
Description:
Investigated are possibilistic distributions taking as their values sequences from the infinite Cartesian product of identical copies of a fixed finite subset of the unit interval of real numbers. Uniform and lexicographic partial orderings on the space of these sequences are defined and the related complete lattices introduced. Lattice-valued entropy function is defined in the common pattern for both the orderings, naturally leading to different entropy values for the particular ordering applied in the case under consideration. The mappings on possibilistic distributions with uniform partial ordering under which the corresponding entropy values are conserved as well as approximations of possibilistic distributions with respect to this entropy function are also investigated.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. Possibilistic lattice-valued almost-measurability relation

Creator:
Kramosil, Ivan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
possibilistic measure, inner and outer measure, complete lattice, and almost measurable set
Language:
English
Description:
Possibilistic measures are usually defined as set functions ascribibg to each subset of the universe of cliscourse a real number from the unit interval and obeying sonie well-kiiown simple conditions. For the number of reasons, as a more realistic version of this model, let us consider partial possibilistic measures defined only for certain subsets and ascribing to them, instead of real numbers, elements from a more general structure. As a rule, a complete lattice will play this role, so let us pick up rather the qualitative and comparative than the quantitative features of particular degrees of possibility. Following the ideas of the standard measure theory, we define the inner and the outer measure induced by the partial latticevalued possibilistic measure in question. A subset of the basic universe is defined as ahnost measurable, if the difference (or rather distance) between the values of the inner and the outer measure ascribed to this set does not exceed, in the sense of the partial ordering relation defined in the used complete lattice, some given threshold value (a “small” fixed element from this lattice). Properties of systems of almost measurable sets are investigated in greater detail and some assertions related to them are introduced.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public