A new view of fuzzy hypernear-rings

  • 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;Faculty of Science, The Chinese University of Hong Kong, Shatin, Hong Kong (SAR), PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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Abstract

In this survey article, we first introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. This concept is a generalized concept of quasi-coincidence of a fuzzy point within a fuzzy set. By using this new idea, we consider the interval valued (@?,@?@?q)-fuzzy sub-hypernear-rings (hyperideals) of a hypernear-ring, and hence, a generalization of a fuzzy sub-near-ring (ideal) is given. Some related properties of fuzzy hypernear-rings are described. Finally, we consider the concept of implication-based interval valued fuzzy sub-hypernear-rings (hyperideals) in a hypernear-ring, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.