On the category of hyper MV‐algebras

Abstract

In this paper we study the category of hyper MV-algebras and we prove that it has a terminal object and a coequalizer. We show that Jia's construction can be modified to provide a free hyper MV-algebra by a set. We use this to show that in the category of hyper MV-algebras the monomorphisms are exactly the one-to-one homomorphisms.

Fuzzy $$\mathsf{H}_v\mathsf{MV}$$ H v MV -algebras

“…In [4] a wealth of applications can be found, too. There are applications to the following subjects: geometry, hypergraphs, binary relations, lattices, fuzzy set and rough sets, automata, cryptography, combinatorics, codes, artificial intelligence and probabilities.Recently, Ghorbani et al [5] applied the hyperstructures to MV-algebras and introduced the concept of hyper MV-algebra and investigated some related results. The ideal theory of hyper MV-algebras were studied by Torkzadeh and Ahadpanah [10] and Jun et al [6][7][8].…”

“…Recently, Ghorbani et al [5] applied the hyperstructures to MV-algebras and introduced the concept of hyper MV-algebra and investigated some related results. The ideal theory of hyper MV-algebras were studied by Torkzadeh and Ahadpanah [10] and Jun et al [6][7][8].…”