| Lattice of Interval-Valued $(\in, \in\vee\,q)$-Fuzzy $LI$-Ideals in Lattice Implication Algebras |
| Received:September 13, 2015 Revised:March 08, 2016 |
| Key Words:
lattice-valued logic lattice implication algebra interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideal complete distributive lattice
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.60774073) and the Higher School Research Foundation of Inner Mongolia (Grant No.NJSY14283). |
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| Abstract: |
| In the present paper, the interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideal theory in lattice implication algebras is further studied. Some new properties of interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideals are given. Representation theorem of interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideal which is generated by an interval-valued fuzzy set is established. It is proved that the set consisting of all interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideals in a lattice implication algebra, under the partial order $\sqsubseteq$, forms a complete distributive lattice. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2016.04.002 |
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