Afr. Mat. DOI 10.1007/s13370-017-0511-y A note on the lattice of fuzzy hyperideals of a hyperring D. Bayrak 1 · S. Yamak 2 Received: 26 July 2016 / Accepted: 7 June 2017 © African Mathematical Union and Springer-Verlag GmbH Deutschland 2017 Abstract Many studies have investigated lattices of fuzzy algebraic systems. One of them belongs to Borzooei et al. (Soft Comput 12:739–749, 2008) who found some properties of lattices of fuzzy algebraic structures. In this study, we solve the problem of finding necessary and sufficient conditions for distributivity and modularity of lattice of fuzzy hyperideals of a hyperring which was one of the open problems in Borzooei’s paper. Keywords Distributive lattice · Modular lattice · Fuzzy hyperideal Mathematics Subject Classification 20N20 · 03E72 · 08A72 1 Introduction Hyperstructure theory was introduced by Marty [12] in 1934. Since then many researchers have studied the theory of hyperstructures and developed it [4, 5]. Hyperring theory is an important branch of hyperstructure and has studied by a variety of authors. Some review of hyperring theory can be found in [6]. A special case of the hyperring is introduced by Krasner [11]. The concept of fuzzy sets was introduced by Zadeh [15] in 1965 and after that Rosenfeld developed the theory of fuzzy subgroups. To the present day, similarly, fuzzy subalgebraic structures were developed and many significant results were obtained. Fuzzy algebraic hyper- structures are a generalization of classical algebraic structures [7]. B D. Bayrak dbayrak@nku.edu.tr S. Yamak syamak@ktu.edu.tr 1 Department of Mathematics, Namik Kemal University, 59000 Tekirdag, Turkey 2 Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turkey 123