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A new view of fuzzy hypernear-rings |
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| Authors: | Jianming Zhan Bijan Davvaz |
| Affiliation: | a Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, PR China b Department of Mathematics, Yazd University, Yazd, Iran c Faculty of Science, The Chinese University of Hong Kong, Shatin, Hong Kong (SAR), PR China |
| 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. |
| Keywords: | Hypernear-ring Interval valued _method=retrieve& _eid=1-s2 0-S0020025507003696& _mathId=si2 gif& _pii=S0020025507003696& _issn=00200255& _acct=C000069490& _version=1& _userid=6211566& md5=0a61f1aec4c5e4191bfc4cd5ae218bff')" style="cursor:pointer (&isin" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">(&isin &isin &or q)-fuzzy sub-hypernear-rings (hyperideal) Fuzzy logic Implication operator |
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