Averaging fuzzy biopolymers
Let d be a metric on the set FP ( X ) of fuzzy subsets of a finite set X. A midpoint of two fuzzy subsets μ , ν ∈ FP ( X ) is any fuzzy subset ξ ∈ FP ( X ) such that d ( ξ , μ ) = d ( ξ , ν ) = 1 2 d ( μ , ν ) . These midpoints can be used to represent “middle ways” or “compromises” between two situ...
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| Published in | Fuzzy sets and systems Vol. 152; no. 1; pp. 139 - 158 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
16.05.2005
|
| Subjects | |
| Online Access | Get full text |
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| Abstract | Let
d be a metric on the set
FP
(
X
)
of fuzzy subsets of a finite set
X. A midpoint of two fuzzy subsets
μ
,
ν
∈
FP
(
X
)
is any fuzzy subset
ξ
∈
FP
(
X
)
such that
d
(
ξ
,
μ
)
=
d
(
ξ
,
ν
)
=
1
2
d
(
μ
,
ν
)
. These midpoints can be used to represent “middle ways” or “compromises” between two situations described by the fuzzy subsets
μ
and
ν
. Now, the imprecise knowledge of a nucleic acid or protein sequence of length
N can be modeled by means of a
fuzzy biopolymer, a fuzzy subset of a
kN-element set with
k the number of bases, 4, in the case of nucleic acids, and of amino acids, 20, in the case of proteins. Thus, a midpoint of two fuzzy biopolymers of the same length can be understood as an average of the knowledge of the sequences represented by them. In this paper we explicitly describe the midpoints of two fuzzy biopolymers with respect to distances obtained by aggregating, through several suitable mappings, metrics on each position of the sequences represented by the fuzzy biopolymers. |
|---|---|
| AbstractList | Let
d be a metric on the set
FP
(
X
)
of fuzzy subsets of a finite set
X. A midpoint of two fuzzy subsets
μ
,
ν
∈
FP
(
X
)
is any fuzzy subset
ξ
∈
FP
(
X
)
such that
d
(
ξ
,
μ
)
=
d
(
ξ
,
ν
)
=
1
2
d
(
μ
,
ν
)
. These midpoints can be used to represent “middle ways” or “compromises” between two situations described by the fuzzy subsets
μ
and
ν
. Now, the imprecise knowledge of a nucleic acid or protein sequence of length
N can be modeled by means of a
fuzzy biopolymer, a fuzzy subset of a
kN-element set with
k the number of bases, 4, in the case of nucleic acids, and of amino acids, 20, in the case of proteins. Thus, a midpoint of two fuzzy biopolymers of the same length can be understood as an average of the knowledge of the sequences represented by them. In this paper we explicitly describe the midpoints of two fuzzy biopolymers with respect to distances obtained by aggregating, through several suitable mappings, metrics on each position of the sequences represented by the fuzzy biopolymers. |
| Author | Casasnovas, J. Rosselló, F. |
| Author_xml | – sequence: 1 givenname: J. surname: Casasnovas fullname: Casasnovas, J. email: jaume.casasnovas@uib.es – sequence: 2 givenname: F. surname: Rosselló fullname: Rosselló, F. email: cesc.rossello@uib.es |
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| Cites_doi | 10.1007/BFb0030790 10.1093/nar/24.19.3836 10.1093/comjnl/9.4.373 10.1007/978-1-4612-0901-0 10.1016/S0893-9659(03)90131-5 10.1016/0076-6879(90)83011-W 10.1006/jmbi.2001.5293 10.1073/pnas.84.13.4355 10.1016/S0933-3657(02)00080-5 10.1016/S0888-613X(02)00063-4 10.1016/0165-0114(93)90141-4 10.1016/S1076-5670(03)80063-0 10.1093/bioinformatics/btg032 10.1016/S0933-3657(99)00032-9 |
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| References_xml | – year: 1992 ident: bib11 article-title: Neural Networks and Fuzzy Systems contributor: fullname: Kosko – volume: 30 start-page: 91 year: 2002 end-page: 105 ident: bib15 article-title: Divergence measure between fuzzy sets publication-title: Internat. J. Approx. Reason. contributor: fullname: Bertolouzza – volume: 56 start-page: 171 year: 1993 end-page: 174 ident: bib18 article-title: A comparative assessment of measures of similarity of fuzzy values publication-title: Fuzzy Sets and Systems contributor: fullname: Karacapilidis – year: 1986 ident: bib13 article-title: Introduction to Linear Algebra, Undergraduate Texts in Mathematics contributor: fullname: Lang – volume: 9 start-page: 373 year: 1967 end-page: 380 ident: bib12 article-title: A general theory of classificatory sorting strategies I publication-title: Comput. 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Appl. Biosci. contributor: fullname: Gotoh – year: 1986 ident: 10.1016/j.fss.2004.10.019_bib13 contributor: fullname: Lang – volume: 315 start-page: 1257 year: 2002 ident: 10.1016/j.fss.2004.10.019_bib24 article-title: Within the twilight zone publication-title: J. Mol. Biol. doi: 10.1006/jmbi.2001.5293 contributor: fullname: Yona – volume: 84 start-page: 4355 year: 1987 ident: 10.1016/j.fss.2004.10.019_bib8 article-title: Profile analysis publication-title: Proc. Natl. Acad. Sci. USA doi: 10.1073/pnas.84.13.4355 contributor: fullname: Gribskov – volume: 9 start-page: 201 year: 1998 ident: 10.1016/j.fss.2004.10.019_bib5 article-title: Predicting disordered regions from amino acid sequence publication-title: Genome Inf. contributor: fullname: Garner – volume: 27 start-page: 81 year: 2003 ident: 10.1016/j.fss.2004.10.019_bib16 article-title: Midpoints for fuzzy sets and their application in medicine publication-title: Artificial Intelligence Med. doi: 10.1016/S0933-3657(02)00080-5 contributor: fullname: Nieto – volume: 30 start-page: 91 year: 2002 ident: 10.1016/j.fss.2004.10.019_bib15 article-title: Divergence measure between fuzzy sets publication-title: Internat. J. Approx. Reason. doi: 10.1016/S0888-613X(02)00063-4 contributor: fullname: Montes – volume: 56 start-page: 171 year: 1993 ident: 10.1016/j.fss.2004.10.019_bib18 article-title: A comparative assessment of measures of similarity of fuzzy values publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(93)90141-4 contributor: fullname: Pappis – ident: 10.1016/j.fss.2004.10.019_bib1 doi: 10.1016/S1076-5670(03)80063-0 – ident: 10.1016/j.fss.2004.10.019_bib2 – volume: 19 start-page: 587 year: 2003 ident: 10.1016/j.fss.2004.10.019_bib22 article-title: The fuzzy polynucleotide space publication-title: Bioinformatics doi: 10.1093/bioinformatics/btg032 contributor: fullname: Torres – volume: 18 start-page: 1 year: 2000 ident: 10.1016/j.fss.2004.10.019_bib21 article-title: Fuzzy genomes publication-title: Artificial Intelligence Med. doi: 10.1016/S0933-3657(99)00032-9 contributor: fullname: Sadegh-Zadeh |
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| Snippet | Let
d be a metric on the set
FP
(
X
)
of fuzzy subsets of a finite set
X. A midpoint of two fuzzy subsets
μ
,
ν
∈
FP
(
X
)
is any fuzzy subset
ξ
∈
FP
(
X
)... |
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| SubjectTerms | Distance Fuzzy polynucleotide Fuzzy polypeptide Metric Midpoint Profile |
| Title | Averaging fuzzy biopolymers |
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