New types of hyper MV‐deductive systems in hyper MV‐algebras

Jun, Young Bae; Kang, Min Su; Kim, Hee Sik

doi:10.1002/malq.200910011

Cited by 6 publications

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“…The ideal theory of hyper MV-algebras were studied by Torkzadeh and Ahadpanah [10] and Jun et al [6][7][8].…”

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confidence: 99%

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

Bakhshi

2015

Afr. Mat.

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The aim of this paper is to study H v MV-algebras from fuzzy set theory point of view. Some types of fuzzy ideals are introduced and many properties, characterizations and related results are given. Particularly, the fuzzy weak H v MV-ideal generated by a fuzzy subset is characterized. In the sequel, some kinds of fuzzy congruences are introduced and characterizations of them are obtained. Finally, some homomorphism theorems are stated and proved.Keywords Algebras of many-valued logics · MV-algebra · H v MV-algebra · H v MV-ideal · Fuzzy algebraic structure 1 Introduction In 1958, Chang [3], introduced the concept of an MV-algebra as an algebraic proof of completeness theorem for ℵ 0 -valued Łukasiewicz propositional calculus. After that many mathematicians have worked on MV-algebras and obtained significant results.The hyperstructure theory (called also multialgebras) was introduced in 1934 by Marty [9]. Around the 40's, several authors worked on hypergroups, especially in France and in the United States, but also in Italy, Russia and Japan. Hyperstructures have many applications to several sectors of both pure and applied sciences. 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].

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“…The ideal theory of hyper MV-algebras were studied by Torkzadeh and Ahadpanah [10] and Jun et al [6][7][8].…”

mentioning

confidence: 99%