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The interval inclusion number of a partially ordered set

1991
*
Discrete Mathematics
*

West,

doi:10.1016/0012-365x(91)90014-s
fatcat:vfuqkcyw6vgy5dqczo653xye2u
*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. ...##
###
Page 232 of The American Mathematical Monthly Vol. 61, Issue 4
[page]

1954
*
The American Mathematical Monthly
*

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
*

An

doi:10.1109/coginf.2009.5250723
dblp:conf/IEEEicci/Yao09
fatcat:csvk2rqhgjf4tloj34soaenzf4
*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. ...##
###
Page 3180 of Mathematical Reviews Vol. , Issue 90F
[page]

1990
*
Mathematical Reviews
*

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
*

In view

doi:10.1016/j.camwa.2010.10.040
fatcat:vdls4cqsgfcwxmr4fjoikrvfiq
*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 ...##
###
Page 654 of Mathematical Reviews Vol. , Issue 94b
[page]

1994
*
Mathematical Reviews
*

*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
*

to

doi:10.1080/00029890.1954.11988449
fatcat:uniugjrelvdcfbxy5hktmpd5bi
*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. ...##
###
Page 724 of Mathematical Reviews Vol. 54, Issue 3
[page]

1977
*
Mathematical Reviews
*

*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
*

Sufficient conditions for

doi:10.1109/72.712161
pmid:18255773
fatcat:mgk2dmlrsnecjjg6qlhaqop6ri
*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. ...##
###
An upper bound on the "dimension of interval orders"

1978
*
Journal of combinatorial theory. Series A
*

*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*. ...

##
###
Inclusion within Continuous Belief Functions
[article]

2015
*
arXiv
*
pre-print

Within this paper we will propose and present two forms

arXiv:1501.06705v1
fatcat:54eqqzxyurh7ndwdwbflibxvma
*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*...##
###
An Introduction to Some Spaces of Interval Functions
[article]

2004
*
arXiv
*
pre-print

*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*. ...

##
###
Page 2417 of Mathematical Reviews Vol. , Issue 92e
[page]

1992
*
Mathematical Reviews
*

{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
*

In this way, we generalize

doi:10.9734/arjom/2020/v16i1030227
fatcat:vjtzjejfqbc5ravzurqfdl2ly4
*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*...##
###
Page 5126 of Mathematical Reviews Vol. , Issue 95i
[page]

1995
*
Mathematical Reviews
*

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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