Abstract
In this article we introduce the notion of \(n\)-dimensional fuzzy sets, fuzzy hyperideals and fuzzy prime hyperideals in semihyperrings with identity. We also discuss some basic properties of \(n\)-dimensional fuzzy prime hyperideals and characterize the \(n\)-dimensional fuzzy prime hyperideals. We also investigate the topology on \(n\)-dimensional fuzzy hyperideals and fuzzy prime hyperideals.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Abdullah S, Aslam M, Anwar T (2011) A note on M-hypersystems and N-hypersystems in \(\Gamma\)-semihypergroups. Quasigroups Relat Syst 19:169–172
Abdullah S, Hila K, Aslam M (2012) On bi-\(\Gamma\)-hyperideals in \(\Gamma\)-semihypergroups. U P B Sci Bull Ser A 74(4):79–90
Abdullah S (2014) N-dimensional \((\alpha,\beta )\)-fuzzy H-ideals in hemirings. Int J Mach Learn Cybern 5(4):635–645
Ahsan J, Saifullah K (1993) Fuzzy semiring. Fuzzy sets Syst 60:309–320
Ameri R, Nozari T (2011) Fuzzy hyperalgebras. Comput Math Appl 61:149–154
Ameri R, Hedayati H (2010) Homomorphism and quotient of fuzzy \(k\)-hyperideals. Ratio Math 20
Ameri R, Hedayati H (2007) On \(k\)-hyperideals of semihyperrings. J Discr Math Sci Cryptogr 10(1):41–54
Aslam M, Abdullah S, Davvaz B, Yaqoob N (2012) Raugh M-hypersystems and fuzzy M-hypersystems in \(\Gamma\)-semihypergroups. Neural Comput Appl 21:281–287
Khan A, Muhammad N (2014) On \((\in ,\in vq)\)-intuitionistic fuzzy ideals of soft semigroups. Int J Mach Learn Cybern doi:10.1007/s13042-014-0263-z
Chaopraknoi S, Hobuntund S, Pianskool S (2008) Admitting a semihyperring with zero of certain linear transformation subsemigroups of \(L_{R}(V, W)\) part (ii). J Math 45–58
Corsini P, Leoreanu V (2003) Applications of hyperstructure theory, advances in mathematics (Dordrecht). Kluwer, Dordrecht
Corsini P (1993) Prolegomena of hypergroup theory, Aviani editor, Italy
Cristea I (2009) On the fuzzy subhypergroups of some particular complete hypergroups. World Appl Sci J 7:57–63
Davvaz B (2002) Approximations in Hv-modules. Taiwan J Math 6(4):499–505
Davvaz B (2001) Fuzzy Hv-groups. Fuzzy Set Syst 117:477–484
Davvaz B (2009) Fuzzy hyperideal in ternary semihyperrings. Iran J Fuzzy Syst 6(4):21–36
Davvaz B, Dudek WA (2009) Fuzzy n-ary groups as a generalization of Rosenfield’s fuzzy groups. J Multiple Valued Logic Soft Comput 15(5–6):471–488
Davvaz B, Leoreanu-Fotea V (2010) Structures of fuzzy1 \(\Gamma\)-hyperideals of a \(\Gamma\)-semihypergroups. Accepted by Journal of Multiple Valued Logic Soft Computing
Davvaz B, Poursalavati NS (1999) On polygroup hyperrings and representations of polygroups. J Korean Math Soc 36(6):1021–1031
Yousafzai F, Yaqoob N, Zeb A (2014) On generalized fuzzy ideals of ordered AG-groupoids. Int J Mach Learn Cybern doi:10.1007/s13042-014-0305-6
Golan JS (1992) The theory of semirings with applications in mathematics and theoretical computer science. Pitman monographs and surveys in pure and applied mathemaatics, no 54. Longman, New York
Klir GY, Yuan B (1995) Fuzzy sets fuzzy logic. Theory and applications. Prentice-Hall, New Jersey
Li XS, Yuan XH, Lee ES (2009) The three-dimensional fuzzy sets and their cut sets. Comput Math Appl 58:1349–1359
Marty F (1934) On a generalization of the notion of group. In: 8th congress Mathematics, Scandinaves, Stockholm, pp 45–49
Mittas CG (1979) Hypergroups canoniques. Mathematica Balkanica 2:165–179
Negoita CV, Ralescu DA (1975) Applications of fuzzy sets to system analysis. Birkhauser, Basel
Sen MK, Ameri R, Chowdhury G Fuzzy hypersemigroups. Soft Comput 12:891–900
Shang Y, Yuan X, Lee ES (2010) The \(n\)-dimensional fuzzy sets and Zadeh fuzzy sets based on the finite valued fuzzy sets. Comput Math Appl 60(3):442–463
Vougiouklis T (1994) Hyperstructures and their representations. Hadronic Press Inc., Palm Harbor
Vougiouklis T (1990) On some representation of hypergroups. Annales Scientifiques de l’Universite de Clermont Serie Mathematique 26:21–29
Wee WG, Fu KS (1969) A formulation of fuzzy automata and its application as a model of learning systems. IEEE Trans Syst Sci Cybern SSC-5 215–223
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–358
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-1. Inf Control 18:199–249
Zhan J, Davvaz B, Shum KP (2008) A new view of fuzzy hypernear-rings. Inf Sci 178(2):425–438
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ahmed, A., Aslam, M. & Abdullah, S. n-Dimensional fuzzy hyperideals in semihyperrings. Int. J. Mach. Learn. & Cyber. 8, 255–262 (2017). https://doi.org/10.1007/s13042-014-0319-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-014-0319-0