scholarly journals Aggregation of L-Probabilistic Quasi-Uniformities

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1980
Author(s):  
Tatiana Pedraza ◽  
Jesús Rodríguez-López
Keyword(s):  
Partially Ordered Sets ◽  
Complete Characterization ◽  
Binary Relations ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Aggregation Procedure ◽  
Complete Study

The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of attention in the last years due to its application in several fields. Here, we face the problem of studying which properties must satisfy a function in order to merge an arbitrary family of (bases of) L-probabilistic quasi-uniformities into a single one. These fuzzy structures are special filters of fuzzy binary relations. Hence we first make a complete study of functions between partially-ordered sets that preserve some special sets, such as filters. Afterwards, a complete characterization of those functions aggregating bases of L-probabilistic quasi-uniformities is obtained. In particular, attention is paid to the case L={0,1}, which allows one to obtain results for functions which aggregate crisp quasi-uniformities. Moreover, we provide some examples of our results including one showing that Lowen’s functor ι which transforms a probabilistic quasi-uniformity into a crisp quasi-uniformity can be constructed using this aggregation procedure.

A Characterization of Partially Ordered Sets with Linear Discrepancy Equal to 2

Order ◽  
2007 ◽  
Vol 24 (3) ◽  
pp. 139-153 ◽  
Author(s):  
David M. Howard ◽  
Mitchel T. Keller ◽  
Stephen J. Young
Keyword(s):  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Linear Discrepancy ◽  
Partially Ordered

Properties of m-ideals in partially ordered sets

2020 ◽  
pp. 601-606
Author(s):  
J. Catherine ◽  
B. Elavarasan
Keyword(s):  
Partially Ordered Sets ◽  
Prime Ideals ◽  
Ordered Sets ◽  
Partially Ordered

In this paper, we study the notion of $M$-ideals in partially ordered sets and examine the various properties of $M$-ideals. Further, the relations between $M$-ideals and $\alpha$-ideals in partially ordered sets are discussed. Moreover, a characterization of prime ideals to be $M$-ideals is obtained.

scholarly journals On the Möbius function of a non-singular binary relation

1970 ◽  
Vol 3 (2) ◽  
pp. 155-162 ◽  
Author(s):  
P. D. Finch
Keyword(s):  
Binary Relation ◽  
Partially Ordered Sets ◽  
Möbius Function ◽  
Binary Relations ◽  
Ordered Sets ◽  
Finite Sets ◽  
Partially Ordered ◽  
Mobius Function

Some of the results in the theory of Möbius functions of finite partially ordered sets are extended to arbitrary non-singular binary relations on finite sets.

Decidability and finite axiomatizability of theories of ℵ0-categorical partially ordered sets

1981 ◽  
Vol 46 (1) ◽  
pp. 101-120 ◽  
Author(s):  
James H. Schmerl
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Finite Width ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Decidable Theory ◽  
Axiomatizable Theory ◽  
Finitely Axiomatizable Theory

AbstractEvery ℵ0-categorical partially ordered set of finite width has a finitely axiomatizable theory. Every ℵ0-categorical partially ordered set of finite weak width has a decidable theory. This last statement constitutes a major portion of the complete (with three exceptions) characterization of those finite partially ordered sets for which any ℵ0-categorical partially ordered set not embedding one of them has a decidable theory.

scholarly journals Maximal dimensional partially ordered sets II. characterization of 2n-element posets with dimension n

1973 ◽  
Vol 5 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Kenneth P. Bogart ◽  
William T. Trotter
Keyword(s):  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

scholarly journals Maximal dimensional partially ordered sets III: a characterization of Hiraguchi's inequality for interval dimension

1976 ◽  
Vol 15 (4) ◽  
pp. 389-400 ◽  
Author(s):  
William T. Trotter ◽  
Kenneth P. Bogart
Keyword(s):  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

Relational Sets and Categorical Equivalence of Algebras

1997 ◽  
Vol 07 (05) ◽  
pp. 561-576 ◽  
Author(s):  
László Zádori
Keyword(s):  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Categorical Equivalence ◽  
Partially Ordered ◽  
Finite Case

We study relation varieties, i.e. classes of relational sets (resets) of the same type that are closed under the formation of products and retracts. The notions of an irreducible reset and a representation of a reset are defined similarly to the ones for partially ordered sets. We give a characterization of finite irreducible resets. We show that every finite reset has a representation by minimal resets which are certain distinguished irreducible retracts. It turns out that a representation by minimal resets is a smallest one in some sense among all representations of a reset. We prove that non-isomorphic finite irreducible resets generate different relation varieties. We characterize categorical equivalence of algebras via product and retract of certain resets associated with the algebras. In the finite case the characterization involves minimal resets. Examples are given to demonstrate how the general theorems work for particular algebras and resets.

On the Characterization of Foam Decay with Diagram Lattices and Majorization

2006 ◽  
Vol 61 (3-4) ◽  
pp. 153-165 ◽  
Author(s):  
Sonja Sauerbrei ◽  
Uwe Sydow ◽  
Peter J. Plath
Keyword(s):  
Diffusion Process ◽  
Bubble Size ◽  
Partially Ordered Sets ◽  
Bubble Size Distribution ◽  
Size Distributions ◽  
Temporal Development ◽  
Ordered Sets ◽  
Equal Distribution ◽  
Partially Ordered

We present possibilities of comparing and characterizing bubble size distributions during foam decay. We know that the temporal development of bubble size distributions does not follow an ordinary diffusion process. Instead of an equal distribution, we obtain a multi-modal distribution at the end of the rearrangement phase. It turns out that bubble size distributions are comparable to partition diagrams generating Ruch lattices which are expandable by permutations leading to partially ordered sets. If we map the partition diagrams and the bubble size distributions on the Shannon entropy, we obtain similar functions. Furthermore, the set of partition diagrams of a Ruch lattice and the set of the bubble size distributions of foam decay are both partially ordered. Via the theorems of Muirhead and of Hardy, Littlewood and Pólya (classical majorization) we construct transitions between every partition diagram of a Ruch lattice and between every bubble size distribution. These transitions can be reversible or irreversible

To the spectral theory of partially ordered sets

2018 ◽  
Vol 60 (3) ◽  
pp. 578-598
Author(s):  
Yu. L. Ershov ◽  
M. V. Schwidefsky
Keyword(s):  
Spectral Theory ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered
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