Lattice of Interval-Valued $(\in, \in\vee\,q)$-Fuzzy $LI$-Ideals in Lattice Implication Algebras
Received:September 13, 2015  Revised:March 08, 2016
Key Word: lattice-valued logic   lattice implication algebra   interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideal   complete distributive lattice
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.60774073) and the Higher School Research Foundation of Inner Mongolia (Grant No.NJSY14283).
 Author Name Affiliation Chunhui LIU Department of Mathematics and Statistics, Chifeng University, Inner Mongolia 024001, P. R. China
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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.