Term Functions and Fundamental Relation of Fuzzy Hyperalgebras

Authors

  • R. Ameri School of Mathematics, Statistics and Computer Science College of Sciences, University of Tehran. P.O. Box 14155-6455, Teheran, Iran
  • T. Nozari Department of Mathematics, Faculty of Basic Science, University of Mazandaran, Babolsar, Iran

Keywords:

Hyperalgebra, Fuzzy hyperalgebra, Equivalence relation, Term function, Fundamental relation, Quotient set.

Abstract

We introduce and study term functions over fuzzy hyperalgebras. We start from this idea that the set of nonzero fuzzy subsets of a fuzzy hyperalgebra can be organized naturally as a universal algebra, and constructing the term functions over this algebra. We present the form of generated subfuzzy hyperalgebra of a given fuzzy hyperalgebra as a generalization of universal algebras and multialgebras. Finally, we characterize the form of the fundamental relation of a fuzzy hyperalgebra.

References

R. Ameri, On categories of hypergroups and hypermodules , Italian journal of pure and applid mathematics, Vol. 6 (2003) 121-132.

R. Ameri and I. G. Rosenberg, Congruences of multialgebras, Multivalued Logic and Soft Computing (to appaear).

R. Ameri and M.M. Zahedi, Hyperalgebraic system, Italian journal of pure and applid mathematics, Vol. 6 (1999) 21-32.

R. Ameri and M.M. Zahedi, Fuzzy subhypermodules over fuzzy hyperrings, Sixth International on AHA, Democritus University, 1996, 1-14,(1997).

S. Burris, H. P. Sankappanavar, A course in universal algebra, Springer Verlage 1981.

P. Corsini, Prolegomena of hypergroup theory, Supplement to Riv. Mat.Pura Appl., Aviani Editor, 1993.

P. Corsini, V. Leoreanu, Applications of hyperstructure theory, Kluwer, Dordrecht 2003.

P. Corsini, I. Tofan, On fuzzy hypergroups, PU.M.A., 8 (1997) 29-37.

B. Davvaz, Fuzzy Hv-groups, Fuzzy sets and systems, 101 (1999) 191-195.

B. Davvaz, Fuzzy Hv-Submodules, Fuzzy sets and systems, 117 (2001) 477-484.

B. Davvaz, P. Corsini, Generalized fuzzy sub-hyperquasigroups of hyperquasigroups, Soft Computing, 10 (11) (2006), 1109-1114.

M. Mehdi Ebrahimi, A. Karimi and M. MahmoudiOn Quotient and Isomorphism Theorems of Universal Hyperalgebras, Italian Journal of Pure and Applied Mathe-matics, 18 (2005), 9-22.

G. Gratzer, Universal algebra, 2nd edition, Springer Verlage, 1970.

V. Leoreanu-Fotea, B. Davvaz, Fuzzy hyperrings, Fuzzy sets and systems, 2008, DOI 10.1016/j.fss.2008.11.007.

V. Leoreanu-Fotea, Fuzzy Hypermodules, Computes and Mathematics with Applica-tions, vol. 57 (2009) 466-475.

F. Marty, Sur une generalization de la nation de groupe, 8th congress des Mathe-maticiens Scandinaves, Stockholm (1934) 45-49.

J.N. Mordeson, M.S. Malik, Fuzzy commutative algebra, Word Publ., 1998.

C. Pelea, On the direct product of multialgebras, Studia uni. Babes-bolya, Mathemat-ica, vol. XLVIII (2003) 93-98.

C. Pelea, Multialgebras and termfunctions over the algebra of their nonvoid subsets, Mathematica (Cluj), vol. 43 (2001) 143-149.

C. Pelea, On the fundamental relation of a multialgebra, Italian Journal of Pure and Applid Mathematics, Vol. 10 (2001) 141-146.

H. E. Pickett, Homomorphism and subalgebras of multialgebras, Pacific J. Math, vol. 10 (2001) 141-146.

M.K. Sen, R. Ameri, G. Chowdhury, Fuzzy hypersemigroups, Soft Computing, 2007, DOI 10.1007/s00500-007-025709.

A. Rosenfeld , Fuzzy groups, J. Math. Anal. Appl. 35. (1971) 512-517.

D. Schweigert, Congruence Relations of Multialgebras , Discrete Mathematics 53 (1985) 249-253.

S. Spartalis, T. Vougiouklis, The Fundamental Relations on Hv−rings, Math. Pura Appl., 13 (1994) 7-20.

T. Vougiouklis, The fundamental Relations in Hyperrings, The general hyperfield Proc. 4th International Congress in Algebraic Hyperstructures and Its Applications (AHA 1990) World Scientific, (1990) 203-211.

T. Vougiouklis, Hyperstructures and their representations, Hardonic, press Inc., 1994.

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

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Published

2010-12-08

Issue

Vol. 20 (2010)

Section

Volume 20-2010

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