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Incompatibility of Metric Structure in Recombination Space

by Tazid Ali, Chandra Kanta Phukan
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 43 - Number 14
Year of Publication: 2012
Authors: Tazid Ali, Chandra Kanta Phukan
10.5120/6168-8581

Tazid Ali, Chandra Kanta Phukan . Incompatibility of Metric Structure in Recombination Space. International Journal of Computer Applications. 43, 14 ( April 2012), 1-6. DOI=10.5120/6168-8581

@article{ 10.5120/6168-8581,
author = { Tazid Ali, Chandra Kanta Phukan },
title = { Incompatibility of Metric Structure in Recombination Space },
journal = { International Journal of Computer Applications },
issue_date = { April 2012 },
volume = { 43 },
number = { 14 },
month = { April },
year = { 2012 },
issn = { 0975-8887 },
pages = { 1-6 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume43/number14/6168-8581/ },
doi = { 10.5120/6168-8581 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:33:22.273505+05:30
%A Tazid Ali
%A Chandra Kanta Phukan
%T Incompatibility of Metric Structure in Recombination Space
%J International Journal of Computer Applications
%@ 0975-8887
%V 43
%N 14
%P 1-6
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Recombination is a binary operator in the set X of all chromosomes, i.e., it is a function R : X × X  P ( X ) , the power set of X. This notion of recombination induces a closure operator given by Cl ( A ) = { R ( x , y ) : ( x , y )  A × A }. However the neighbourhood structure so induced is not in general a topological space. In this paper we have attempted to study the recombination space in fuzzy setting by assigning possibilities to each offspring under the recombination operator. We have shown that a fuzzy pretopology is naturally generated in the recombination set. We have studied two unequal crossover models viz. unrestricted and restricted in this setting. We have further observed that both the models are incompatible with metric measures.

References
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  6. Stadler, B.M.R., Stadler, P. F., Shapk, M., Wanger, G. P. 2002: Recombination spaces, metrics, and pretopologies, Z. Phys. Chem., 216: 217-234.
  7. Stadler, B.M.R., Stadler, P.F. 2004: The Topology of Evolutionary Biology, I G. Ciobanu and G. Rozenerg, editors, Modelling in Molecular Biology, pages 267-286, Springer Verlag.
  8. Stadler, P. F., Wagner, G. P. 1996: Recombination induced hypergraphs: A new approach to mutation-recombination isomorphism, Complexity, 2: 37-43.
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy Recombination Set Fuzzy Metric Fuzzy Closure Fuzzy Metrizable Unequal Crossover

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