Generalized fuzzy hyperideals of hyperrings

Authors:
Jianming Zhan;Bijan Davvaz;K. P. Shum
Affiliations:
Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province, 445000, PR China;Department of Mathematics, Yazd University, Yazd, Iran;Department of Mathematics, Hong Kong University, Pokulam Road, Hong Kong, China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalized concept of the quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued (@a,@b)-fuzzy hyperideals in a hyperring is introduced and consequently, a generalization of a fuzzy hyperideal is defined. In this paper, we study the related properties of the fuzzy hyperideals and in particular, the interval valued (@?,@?@?q)-fuzzy hyperideals in a hyperring will be investigated. Moreover, we also consider the concept of implication-based interval valued fuzzy hyperideals in a hyperring. Some recent results obtained by B. Davvaz and J.M. Zhan on hyperstructures are extended and consolidated.