Abstract
The purpose of this paper is to investigate a new connection between fuzzy sets and population genetics. More precisely, we consider the fuzzy set of alleles in a population, determine sequences of join spaces associated with each of its types, and investigate their fuzzy grades.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Al Tahan M, Davvaz B (2017) Algebraic hyperstructures associated to biological inheritance. Math Biosci 285:112–118
Angheluta C, Cristea I (2012) Fuzzy grade of the complete hypergroups. Iran J Fuzzy Syst 9(6):43–56
Corsini P (1993) Prolegomena of hypergroup theory (Aviani Editor)
Corsini P (1994) Join spaces, power sets, fuzzy sets. In: Proceedings of the Fifth Int. Congress of Algebraic Hyperstructures and Appl., 1993, Iasi, Romania, Hadronic Press
Corsini P (2003) A new connection between hypergroups and fuzzy sets. Southeast Asian Bull Math 27:221–229
Corsini P, Cristea I (2003) Fuzzy grade of i.p.s. hypergroups of order less than or equal to 6. Pure Math Appl 14(4):275–288
Corsini P, Cristea I (2004) Fuzzy grade of i.p.s. hypergroups of order 7. Iran J Fuzzy Syst 1(2):15–32
Corsini P, Leoreanu-Fotea V (2010) On the grade of a sequence of fuzzy sets and join spaces determined by a hypergraph. Southeast Asian Bull. Math. 34(2):231–242
Corsini P, Leoreanu V (2003) Applications of hyperstructures theory. Advanced in Mathematics. Kluwer Academic Publisher
Cristea I (2010) About the fuzzy grade of the direct product of two hypergroupoids. Iran J Fuzzy Syst 7(2):95–108
Darwin C (1868) The variation of animals and plants under domestication, vol 1. American Orange Judd and Co, New York
Davvaz B (2003) A brief survey of the theory of \(H_{v}\) structures. In: Algebraic Hyperstructures and Applications Spanidis, Xanthi, 39–70
Davvaz B (2013) Polygroup theory and related systems. World Scientic Publishing Co. Pte. Ltd., Hackensack, NJ, viii+200 pp
Davvaz B, Leoreanu-Fotea V (2007) Hyperring theory and applications. International Academic Press, Cambridge
Davvaz B, Dehghan Nezhad A, Heidari M (2013) Inheritance examples of algebraic hyperstructures. Inform Sci 224:180–187
Dehghan Nezhad A, Moosavi Nejad SM, Nadjakhah M, Davvaz B (2012) A physical example of algebraic hyperstructures: Leptons. Indian J Phys 86(11):1027–1032
Ghadiri M, Davvaz B, Nekouian R (2012) \(H_{v}\)-semigroup structure on \(F_{2}\)-ospring of a gene pool. Int J Biomathemat 5(4):1250011 (13 pages)
Griffiths AJF, Wessler SR, Carroll SB, Doebley J (2000) An introduction to genetic analysis, vol 7. WH Freeman, New York
Hardy GH (1908) Mendelian proportions in a mixed population. Science 28:49–50
Hartl DL, Clark AG (1997) Principles of population genetics, 3rd edn. Sinauer, Sunderland
Hartwell LH, Hood L, Goldberg ML, Reynolds AE, Silver LM, Veres RC (2008) Genetics: from genes to genomes, 3rd edn. Mc Graw Hill, New York
Jantosciak J (1991) Homomorphisms, equivalences and reductions in hypergroups. Riv Mat Pura Appl 9:23–47
Jantosciak J (1997) Transposition hypergroups: noncommutative join spaces. J. Algebra 187:97–119
Marty F (1934) Sur une generalization de la notion de group, In: 8th Congress Math. Scandenaves, pp. 45-49
Mendel G (1866) Versuche uber Panzen–Hybriden, Verh Naturforsheh. Ver. Brunn 4, 3-47 (in English in: J. R. Hortic. Soc. 26 (1901) 1-32)
Mittas J (1972) Hypergroups canoniques. Math Balkanica 2:165–179
Pierce BA (2022) Genetics, A conceptual approach, 4th edition, South Western University, New York
Prenowitz W (1950) Spherical geometries and multigroups. Can. J. Math. 2:100–119
Prenowitz W (1961) A contemporary approach to classical geometry. Am Math Mon 68:part II v+67
Prenowitz W, Jantosciak J (1979) Join geometries. Springer, UTM, Berlin
Spartalis S, Dramalides A, Vougiouklis T (1988) On \(H_v\)-group rings. Algebras Groups Geomet 15:47–54
Vougiouklis T (1990) The fundamental relation in hyperrings. The general hypereld, Algebraic hyperstructures and applications (Xanthi) 203–211. World Sci. Publ, Teaneck, NJ, p 1991
Vougiouklis T (1994) Hyperstructures and their representations, vol 115. Hadronic Press Inc, Palm Harber
Vougiouklis T (1997) Convolutions on WASS hyperstructures. Disc Math 174:347–355
Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353
Acknowledgements
The authors are highly grateful to referees, for their valuable comments and suggestions for improving the paper. Also, the authors would like to thank Iran National Science Foundation (INSF) and Yazd University for their support under Grant no. 96015489.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Declarations
The authors declare that they have no conflict of interest.
Additional information
Communicated by Leonardo Tomazeli Duarte.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sadrabadi, E.H., Davvaz, B. A new relationship between population genetics and fuzzy sets. Comp. Appl. Math. 41, 270 (2022). https://doi.org/10.1007/s40314-022-01979-z
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40314-022-01979-z