Soft Comput (2007) 11:1053–1057 DOI 10.1007/s00500-007-0152-4 ORIGINAL PAPER On fuzzy isomorphism theorems of hypermodules Jianming Zhan · Bijan Davvaz · K. P. Shum Published online: 9 March 2007 © Springer-Verlag 2007 Abstract We introduce the concept of normal fuzzy subhypermodules of hypermodules and establish three isomorphism theorems of hypermodules by using nor- mal fuzzy subhypermodules. Keywords Hypermodule · Normal fuzzy subhypermodule · Isomorphism theorems Mathematics Subject Classification (2000) 16Y99 · 20N20 · 16A78 1 Introduction The concept of hyperstructure was first introduced by Marty (1934) at the eighth Congress of Scandinavian Mathematicians in 1934. Later on, people have observed that hyperstructures have many applications in both pure and applied sciences. A comprehensive review of the theory of hyperstructures can be found in (Corsini 1993; Corsini and Leoreanu 2003; Davvaz 2003; Vougiouklis 1994). In the literature, the simplest algebric J. Zhan (B ) Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province, 445000, People’s Republic of China e-mail: zhanjianming@hotmail.com B. Davvaz Department of Mathematics, Yazd University, Yazd, Iran e-mail: davvaz@yazduni.ac.ir K. P. Shum Faculty of Science, The Chinese University of Hong Kong Shatin, Hong Kong (SAR), People’s Republic of China e-mail: kpshum@math.cuhk.edu.hk hyperstructure is the semihypergroup which possess the closure and associativity properties. However, the con- cept of “hyperring” was initiated by Krasner (1983) till 1983, in fact, a hyperring is essentially a ring with appro- priate modified axioms in which the “addition opera- tion” is a “hyper-operation”, that is, “a + b” is a set, but not an element. The hyperrings have been studied by many authors, the reader is referred to (Ameri 2003; Davvaz 1999, 2003, 2005; Davvaz and Poursalavati 1999; Davvaz and Koushky 2004; Neggers et al. 1999; Olson and Ward 1997; Rosenfeld 1971; Rota 1996; Vougiouklis 1991). As an extension of the theory of hyperrings, the theory of hypermodules has been recently developed by Massouros (1998), Vougiouklis (1994), Davvaz (2003, 2002, 1999), Ameri (2003), Zhan and Dudek (2006), Zhan (2006), Zhan et al. (2007a,b). After introducing the concept of fuzzy sets by Zadeh (1965), the theory of fuzzy sets has been developed fast and has many applications in many branches of sci- ences. In mathematics, the study of fuzzy algebraic struc- tures was first initiated by a pioneer paper of Rosenfeld (1971). He first studied the fuzzy subgroupoid (the sub- group) of a groupoid (a group) and since then, many researchers have been engaged in extending the con- cepts and results of abstract algebra based on a broaden framework of fuzzy settings. Recently, the authors Zhan et al. (2007a) have con- sidered three isomorphism theorems and the Jordan– Holder theorem for hypermodules. In addition, the fundamental relation “ǫ ∗ ” was defined on a hyper- module and consequently, a fundamental theorem of hypermodules was established in Zhan et al. (2007a). In this paper, we consider the normal fuzzy subhyper- module of a hypermodule and investigate the fuzzy iso- morphism of hypermodules by using the normal fuzzy