[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7468/jksmeb.2018.25.4.253

FIBONACCI SEQUENCES ON MV-ALGEBRAS

Jahanshahi, Morteza Afshar (Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman)
Saeid, Arsham Borumand (Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman)

Publication Information

The Pure and Applied Mathematics / v.25, no.4, 2018 , pp. 253-265 More about this Journal

Abstract

In this paper, we introduce the concept of Fibonacci sequences on MV-algebras and study them accurately. Also, by introducing the concepts of periodic sequences and power-associative MV-algebras, other properties are also obtained. The relation between MV-algebras and Fibonacci sequences is investigated.

Keywords

Fibonacci sequences; Boolean algebras; MV-algebras;

Citations & Related Records

Reference

1	K.T. Atanassov, V. Atanassova, A.G. Shannon & J.C. Turner: New Visual Perspectives On Fibonacci Numbers. World Scientific, Singapore, 2002.
2	R.L.O. Cignoli, I.M.L.D. Ottaviano & D. Mundici: Algebraic foundations of many-valued reasoning ser. Trends in Logic-Studia Logica Library. Dordrecht: Kluwer Academic Publishers, Vol 7, 2000.
3	C.C. Chang: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467-490. DOI
4	E.J. Dubuc & J.C. Zilber: Some remarks on infinitesimals in MV -algebras. Multiple-Valued Logic and Soft Computing 29 (2017), 647-656.
5	R.A. Dunlap: The Golden Ratio and Fibonacci Numbers. World Scientific, Singapore, 1997.
6	J.S. Han, H.S. Kim & J. Neggers: Fibonacci sequences in groupoids. Adv. Differ. Eq. 19 (2012).
7	Y. Imai & K. Iseki: On axiom systems of propositional calculi. Proc. Japan Academic bf 42 (1966), 19-22. DOI
8	H.S. Kim, J. Neggers & K.S. So: Generalized Fibonacci sequences in groupoids. Adv. Differ. Eq. 26 (2013).
9	J. Meng & Y.B. Jun: BCK-algebras. Kyung Moon Sa Co. Seoul, Korea, 1994.
10	D. Mundici: MV -algebras are categorically equivalent to bounded commutative BCK-algebras. Math. J. 31 (1986), 889-894.
11	D. Piciu: Algebras of fuzzy logic. Ed. Universitaria Craiova, 2007.
12	S. Tanaka: On ${\wedge}$ -commutative algebras. Math. Sem. Notes Kobe 3, 59-64, 1975.