Totally optimal decision rules

Handle URI:
http://hdl.handle.net/10754/626257
Title:
Totally optimal decision rules
Authors:
Amin, Talha ( 0000-0003-3035-8612 ) ; Moshkov, Mikhail ( 0000-0003-0085-9483 )
Abstract:
Optimality of decision rules (patterns) can be measured in many ways. One of these is referred to as length. Length signifies the number of terms in a decision rule and is optimally minimized. Another, coverage represents the width of a rule’s applicability and generality. As such, it is desirable to maximize coverage. A totally optimal decision rule is a decision rule that has the minimum possible length and the maximum possible coverage. This paper presents a method for determining the presence of totally optimal decision rules for “complete” decision tables (representations of total functions in which different variables can have domains of differing values). Depending on the cardinalities of the domains, we can either guarantee for each tuple of values of the function that totally optimal rules exist for each row of the table (as in the case of total Boolean functions where the cardinalities are equal to 2) or, for each row, we can find a tuple of values of the function for which totally optimal rules do not exist for this row.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Amin T, Moshkov M (2017) Totally optimal decision rules. Discrete Applied Mathematics. Available: http://dx.doi.org/10.1016/j.dam.2017.10.024.
Publisher:
Elsevier BV
Journal:
Discrete Applied Mathematics
Issue Date:
22-Nov-2017
DOI:
10.1016/j.dam.2017.10.024
Type:
Article
ISSN:
0166-218X
Sponsors:
Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST) . The authors are grateful to the anonymous reviewer for useful comments and suggestions.
Additional Links:
http://www.sciencedirect.com/science/article/pii/S0166218X17304791
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAmin, Talhaen
dc.contributor.authorMoshkov, Mikhailen
dc.date.accessioned2017-11-30T07:06:49Z-
dc.date.available2017-11-30T07:06:49Z-
dc.date.issued2017-11-22en
dc.identifier.citationAmin T, Moshkov M (2017) Totally optimal decision rules. Discrete Applied Mathematics. Available: http://dx.doi.org/10.1016/j.dam.2017.10.024.en
dc.identifier.issn0166-218Xen
dc.identifier.doi10.1016/j.dam.2017.10.024en
dc.identifier.urihttp://hdl.handle.net/10754/626257-
dc.description.abstractOptimality of decision rules (patterns) can be measured in many ways. One of these is referred to as length. Length signifies the number of terms in a decision rule and is optimally minimized. Another, coverage represents the width of a rule’s applicability and generality. As such, it is desirable to maximize coverage. A totally optimal decision rule is a decision rule that has the minimum possible length and the maximum possible coverage. This paper presents a method for determining the presence of totally optimal decision rules for “complete” decision tables (representations of total functions in which different variables can have domains of differing values). Depending on the cardinalities of the domains, we can either guarantee for each tuple of values of the function that totally optimal rules exist for each row of the table (as in the case of total Boolean functions where the cardinalities are equal to 2) or, for each row, we can find a tuple of values of the function for which totally optimal rules do not exist for this row.en
dc.description.sponsorshipResearch reported in this publication was supported by King Abdullah University of Science and Technology (KAUST) . The authors are grateful to the anonymous reviewer for useful comments and suggestions.en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0166218X17304791en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Discrete Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Applied Mathematics, [, , (2017-11-22)] DOI: 10.1016/j.dam.2017.10.024 . © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectDecision rulesen
dc.subjectPatternsen
dc.subjectLengthen
dc.subjectCoverageen
dc.titleTotally optimal decision rulesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalDiscrete Applied Mathematicsen
dc.eprint.versionPost-printen
kaust.authorAmin, Talhaen
kaust.authorMoshkov, Mikhailen
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