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The interval inclusion number of a partially ordered set
1991
Discrete Mathematics
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West, The interval inclusion number of a partially ordered set, Discrete Mathematics 88 (1991) 259-277. ...
We introduce the interval inclusion number (or interval number) i(P) as the smallest t such that P has a containment representation fin which each f(x) is the union of at most t intervals. ...
By a poset (partially ordered set) we mean a pair (P, CP), where P is a set of elements and cP is a partial order on P, i.e. an antisymmetric, irreflexive, transitive binary relation. ...
doi:10.1016/0012-365x(91)90014-s
fatcat:vfuqkcyw6vgy5dqczo653xye2u
Page 232 of The American Mathematical Monthly Vol. 61, Issue 4
[page]
1954
The American Mathematical Monthly
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If the partially ordered set is a chain, it has a “natural” topology defined by taking the open intervals, consisting of elements x such that a<x 3b), to be neighborhoods of each of their elements. ...
In a partially ordered set which is not a chain, this definition is not a useful one. ...
Interval sets and interval-set algebras
2009
2009 8th IEEE International Conference on Cognitive Informatics
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An interval set is an interval in the power set lattice based on a universal set and is a family of subsets of the universal set. ...
Two types of interval-set algebras are examined based on an inclusion ordering and a knowledge ordering, respectively. Related studies are summarized. ...
The relative sets consider both inclusion (truth) ordering and knowledge ordering of a bilattice. ...
doi:10.1109/coginf.2009.5250723
dblp:conf/IEEEicci/Yao09
fatcat:csvk2rqhgjf4tloj34soaenzf4
Page 3180 of Mathematical Reviews Vol. , Issue 90F
[page]
1990
Mathematical Reviews
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C. (1-BELL) Interval orders and circle orders. Order 5 (1988), no. 3, 225-234. There are two natural (partial) orderings on a set of intervals of real numbers. ...
As applications, the lattice of subsets of a finite set and the lattice of divisors of a natural number are considered.”
90f:06002 06A10 11A05 11D09 11F06 20HOS Beck, Istvan (N-OSLO-I) Partial orders and ...
FL-GrCCA: A granular computing classification algorithm based on fuzzy lattices
2011
Computers and Mathematics with Applications
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In view of this, this work proposes a partial order relation and lattice computing, respectively, for dealing with the aforementioned issues. ...
We compare the performance of FL-GrCCA with the performance of popular classification algorithms, including support vector machines (SVMs) and the fuzzy lattice reasoning (FLR) classifier, for a number ...
This work was supported in part by the National Natural Science Foundation of China (Grant No. 40701153, 40971233), Natural Science Foundation of Henan Province (102300410178, 2009B520025) and self-determined ...
doi:10.1016/j.camwa.2010.10.040
fatcat:vdls4cqsgfcwxmr4fjoikrvfiq
Page 654 of Mathematical Reviews Vol. , Issue 94b
[page]
1994
Mathematical Reviews
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A partially ordered set is called a k-sphere order if it is isomorphic to some set of balls in R‘, ordered by inclusion. ...
A partially ordered set is called a k-sphere order if it is isomorphic to some set of balls in R*, ordered by inclusion. ...
Ideals In Partially Ordered Sets
1954
The American mathematical monthly
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to the order relation of set inclusion. ...
This corresponds to the definition of order for the real numbers. This is a rela- tion of simple ordering, and determines a topology, using open intervals for neighborhoods. ...
doi:10.1080/00029890.1954.11988449
fatcat:uniugjrelvdcfbxy5hktmpd5bi
Page 724 of Mathematical Reviews Vol. 54, Issue 3
[page]
1977
Mathematical Reviews
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The authors study the partially ordered set (J(0, n), <) consisting
5059
06 ORDER, LATTICES, ORDERED ALGEBRAIC STRUCTURES
724
of all closed intervals of real numbers (including degenerate
intervals) with ...
The set of all subgraphs of a graph ordered by inclusion forms a distributive lattice L(G) so that a result of R. P. ...
Fuzzy lattice neural network (FLNN): a hybrid model for learning
1998
IEEE Transactions on Neural Networks
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Sufficient conditions for the existence of an inclusion measure in a mathematical lattice are shown. ...
Hence a novel theoretical foundation is introduced in this paper, that is the framework of fuzzy lattices or FL-framework, based on the concepts fuzzy lattice and inclusion measure. ...
In conclusion is a partially ordered set. Consider the following lemma. ...
doi:10.1109/72.712161
pmid:18255773
fatcat:mgk2dmlrsnecjjg6qlhaqop6ri
An upper bound on the "dimension of interval orders"
1978
Journal of combinatorial theory. Series A
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The main results of this paper are two distinct characterizations of interval orders and an upper bound on the dimension of an interval order as a function of its height. ...
In particular, interval orders of height 1 have dimension of at most 2. ...
(X, P) is an interval order if and only if H,(X) is linearly ordered by set inclusion. ...
doi:10.1016/0097-3165(78)90032-8
fatcat:fj45ipjndrajhpt3d5i3htpada
Inclusion within Continuous Belief Functions
[article]
2015
arXiv
pre-print
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Within this paper we will propose and present two forms of inclusion: The strict and the partial one. In order to develop this relation, we will study the case of consonant belief function. ...
Defining and modeling the relation of inclusion between continuous belief function may be considered as an important operation in order to study their behaviors. ...
Partial inclusion between belief densities induced by normal distributions The partial inclusion is defined in order to give us the proportion of the intersection between two pdf s. 1) Partial inclusion ...
arXiv:1501.06705v1
fatcat:54eqqzxyurh7ndwdwbflibxvma
An Introduction to Some Spaces of Interval Functions
[article]
2004
arXiv
pre-print
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The paper gives a brief account of the spaces of interval functions defined through the concepts of H-continuity, D-continuity and S-continuity. ...
Various ways in which the spaces of H-continuous, D-continuous and S-continuous interval functions complement the spaces of continuous real functions are discussed. ...
A partial order naturally related to interval spaces is the relation inclusion. ...
arXiv:math/0408013v1
fatcat:ofgev3jygzbhdmn5fozvgznqya
Page 2417 of Mathematical Reviews Vol. , Issue 92e
[page]
1992
Mathematical Reviews
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{For the entire collection see MR 92b:05001.}
92e:06012 06A07 Madej, Tom (1-IL-C); West, Douglas B. (1-IL) The interval inclusion number of a partially ordered set. ...
We introduce the interval inclusion number (or interval number) i(P) as the smallest ¢ such that P has a containment representation f in which each f(x) is the union of at most ¢ intervals. ...
Fuzzy Alexandrov Topologies Associated to Fuzzy Interval Orders
2020
Asian Research Journal of Mathematics
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In this way, we generalize a well known result by Rabinovitch (1978), according to which a crisp partial order is a crisp interval order if and only if the family of all the strict upper sections of the ...
We characterize the fuzzy T0 - Alexandrov topologies on a crisp set X, which are associated to fuzzy interval orders R on X. ...
In this way, we generalize a well known result by [4] , according to which a crisp partial order is a crisp interval order if and only if the family of all the strict upper sections of the partial order ...
doi:10.9734/arjom/2020/v16i1030227
fatcat:vjtzjejfqbc5ravzurqfdl2ly4
Page 5126 of Mathematical Reviews Vol. , Issue 95i
[page]
1995
Mathematical Reviews
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An ordered set P is called a bounded bitolerance order if for each x € P there exist a closed interval J, = [a(x),d(x)] (probably of the set of all real numbers, although this is not explicitly stated) ...
(English
summary )
Order 11 (1994), no.2, 127-134.
Let &,(s,t) be the partially ordered set consisting of all subsets
with size s or ¢ of an n-element set, ordered by inclusion. ...
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