Structures of compactly generated lattices described by cut sets of L-valued sets

Structures of compactly generated lattices described by cut sets of L-valued sets This paper describes the distributivity, the modularity, the semimodularity and the lower semimodularity of compactly gener- ated lattices from a view of cut sets of L-valued sets, respectively. Applying terms of cut sets of L-valued sets, it gives some sufficient and necessary conditions which can be used to determine whether a compactly generated lattice is distributive, modular, semimodular and lower semimodular, respectively. Keywords L-valued set · Cut set · Compactly generated lattice · Distributive lattice · Modular lattice · Semimodular lattice · Lower semimodular lattice 1 Introduction possible to present an ordered structure by cut sets of a suit- able fuzzy set μ and consequently by the mapping μ itself Lattice-valued mathematics had undergone a significant as pointed out by Šešelja and Tepavce ˇ vic( ´ 2003a, b). This development from Goguen’s (1967) first paper. In this way, topic has been discussed by many scholars (see, e.g., Jiménez bridges had been created between fuzzy mathematics and et al. 2010, 2011a, b; Gorjanac-Ranitovic´ and Petojevic´ other branches like automata and tree series (Borchardt 2014; Gorjanac-Ranitovic´ and Tepavce ˇ vic´ 2018; Šešelja et al. et al. 2006), theoretical computer science (Chechik et al. 2008). On the other hand, the distributivity, the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Soft Computing Springer Journals

Structures of compactly generated lattices described by cut sets of L-valued sets

Loading next page...
 
/lp/springer_journal/structures-of-compactly-generated-lattices-described-by-cut-sets-of-l-tFwjiS96vu
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Engineering; Computational Intelligence; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Control, Robotics, Mechatronics
ISSN
1432-7643
eISSN
1433-7479
D.O.I.
10.1007/s00500-018-3275-x
Publisher site
See Article on Publisher Site

Abstract

This paper describes the distributivity, the modularity, the semimodularity and the lower semimodularity of compactly gener- ated lattices from a view of cut sets of L-valued sets, respectively. Applying terms of cut sets of L-valued sets, it gives some sufficient and necessary conditions which can be used to determine whether a compactly generated lattice is distributive, modular, semimodular and lower semimodular, respectively. Keywords L-valued set · Cut set · Compactly generated lattice · Distributive lattice · Modular lattice · Semimodular lattice · Lower semimodular lattice 1 Introduction possible to present an ordered structure by cut sets of a suit- able fuzzy set μ and consequently by the mapping μ itself Lattice-valued mathematics had undergone a significant as pointed out by Šešelja and Tepavce ˇ vic( ´ 2003a, b). This development from Goguen’s (1967) first paper. In this way, topic has been discussed by many scholars (see, e.g., Jiménez bridges had been created between fuzzy mathematics and et al. 2010, 2011a, b; Gorjanac-Ranitovic´ and Petojevic´ other branches like automata and tree series (Borchardt 2014; Gorjanac-Ranitovic´ and Tepavce ˇ vic´ 2018; Šešelja et al. et al. 2006), theoretical computer science (Chechik et al. 2008). On the other hand, the distributivity, the

Journal

Soft ComputingSpringer Journals

Published: Jun 2, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off