On Ω-Subgroup

Authors

  • Elijah Eghosa Edeghagba Department of Mathematical Sciences, Bauchi State University, Gadau, Nigeria

DOI:

https://doi.org/10.54117/gjpas.v1i1.7

Keywords:

Ω-set, Ω-groupoid, Ω-group, Ω-subgroup, Ω-Equality, Complete lattice

Abstract

In the framework of Ω-sets, where Ω is a complete lattice, we present particular kinds of Ω-subgroups: ...based on Ω-group in the language of one binary operation.

References

Bělohlávek, R. (2002). Fuzzy Relational Systems: Foundations and Principles, Kluwer Academic/Plenum Publishers, New York.

Bělohlávek, R. and Vychodil, V. (2006). Algebras with fuzzy equalities, Fuzzy Sets and Systems 157: 161—201.

Bleblou, O.S.A., Šešelja, B. and Tepavčević, A. (2018). Normal Ω-subgroup , Faculty of Sciences and Mathematics, University of Nis, Serbia, 32 , (19):6699-6711.

Brown, J. G. (1971). A Note on Fuzzy Sets, Information and Control, 18: 32-39.

Budimirović, B., Budimirović, V., Šešelja, B. and Tepavčević, A. (2012). Fuzzy equational classes, Fuzzy Systems (FUZZ-IEEE), IEEE International Conference, 1-6.

Budimirović, B., Budimirović, V., Šešelja, B. and Tepavčević, A. (2013). Fuzzy Equational Classes are Fuzzy Varieties, Iranian Journal of Fuzzy Systems 10: 1-18.

Budimirović, B., Budimirović, V., Šešelja, B. and Tepavčević, A. (2014). Fuzzy Identities with Application to Fuzzy Semigroups, Information Sciences, 266: 148-159.

Budimirović, B., Budimirović, V., Šešelja, B. and Tepavčević, A. (2016). E-Fuzzy Groups, Fuzzy Sets and Systems 289: 94-112.

Demirci, M. (2003). Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations part I: fuzzy functions and their applications, part II: vague algebraic notions, part III: constructions of vague algebraic notions and vague arithmetic operations, Int. J. General Systems 32 (3): 123-155, 157-175, 177-201.

Di Nola, A and Gerla, G. (1987). Lattice Valued Algebras, Stochastica 11: 137—150.

Edeghagba, E. E. and Muhammad, F. U. (2022). An Introduction to Ω-Subgroup, Journal of Mathematical Sciences and Optimization: Theory and Applications, In print.

Edeghagba, E.E., Šešelja, B. and Tepavčević, A. (2017). Congruences and Homomorphisms on Ω- Algebras , Kybernetika, 53,( 5): 892-910.

Edeghagba, E.E., Šešelja, B. and Tepavčević, A. (2019). Representation Theory for Complete L-Lattices , J. of Mult.-Valued Logic and Soft Computing, 33 , (6):593-617. 25p.

Filep, L. (1992). Structure and Constructing of Fuzzy Subgroups of a Group, Fuzzy Sets Syst. 51: 105-109.

Fourman, M.P and Scott, D.S. (1979). Sheaves and Logic, in: M.P. Fourman, C.J. Mulvey D.S. Scott (Eds.), Applications of Sheaves, Lecture Notes in Mathematics, vol. 753, Springer, Berlin, Heidelberg, New York, 302—401.

Goguen, J.A.(1967). L-fuzzy Sets, J. Math. Anal. Appl. (18): 145-174.

Gottwald, S. (2006). Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory, Part II: Category theoretic approaches, Studia Logica, 84(1): 23-50. 1143-1174.

Höhle, U. (1988). Quotients with respect to Similarity Relations, Fuzzy Sets and Systems 27: 31-44.

Höhle, U. (2007). Fuzzy Sets and Sheaves. Part I: Basic Concepts, Fuzzy Sets and Systems, (11): 1-58. Klir, G. and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic, Prentice Hall P T R, New Jersey.

Höhle, U. and Šostak, A.P. (1999). Axiomatic Foundations of Fixed-basis Fuzzy Topology, Springer US, 123-272.

Krapeža, A., Šešelja, B. and Tepavčević, A. (2019). Solving Linear Equations in Fuzzy Quasigroups , Information Sciences, 491: 179-189.

Malik, D.S., Mordeson , J.N. and Kuroki, N. (2003). Fuzzy Semigroups Studies in Fuzziness and Soft Computing, vol. 131, Springer-Verlag, Berlin, Heidelberg.

Mordeson, J.N., Bhutani, K.R. and Rosenfeld, A. (2005). Fuzzy Group Theory Studies in Fuzziness and Soft Computing, vol. 182, Springer-Verlag, Berlin, Heidelberg.

Rosenfeld, A. (1971). Fuzzy groups, J. Math. Anal, 35: 512–517.

Sanchez, E. (1976). Resolution of Composite Fuzzy Relation Equations, Information and Control, 30: 38-48.

Šešelja, B and Tepavčević, A. ( 2009). Fuzzy Identities, Proc. of the IEEE International Conference on Fuzzy Systems, 1660—1664.

Šešelja, B. and Tepavčević, A. (1993). Partially Ordered and Relational Valued Algebras and Congruences, Review of Research, Faculty of Science, Mathematical Series 23: 273—287.

Šešelja, B. and Tepavčević, A. (1994). On Generalizations of Fuzzy Algebras and Congruences, Fuzzy Sets and Systems 65: 85—94.

Šešelja, B. and Tepavčević, A. (2019). Ω-group in the Language of Ω-groupiod, Fuzzy Sets and Systems, 397: 152-167.

Wen-Xiang, G and De-Gang, C. (1994). A Fuzzy Subgroupoid which is not a Fuzzy Group, Fuzzy Sets Syst. 62: 115–116.

Zadeh, L.A. (1965). Fuzzy Sets, Information and Control, 8, 338-353.

 On Ω-Subgroup

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Published

2022-07-09

How to Cite

Edeghagba, E. E. (2022). On Ω-Subgroup . Gadau Journal of Pure and Allied Sciences, 1(1), 55–67. https://doi.org/10.54117/gjpas.v1i1.7