Graphs Of lattice implication algebras based on fuzzy filter and fuzzy LI-ideal

In this paper, first the notions of fuzzy filter and fuzzy LI- ideal in a lattice implication algebra (??,˅,˄,´,→,0,??) are defined. Then by means of congruence classes ≡???? and ≡???? on a lattice implication algebra (??,˅,˄,´,→,0,??) which induced by fuzzy filter and fuzzy LI-ideal, respectively, four types of graphs of lattice implication algebra (??,˅,˄,´,→,0,??), denoted by ??????(??),??????(??),??????(??) and ??????(??), respectively, are defined, some their interesting properties such as connectivity, chordality, planarity are presented.

Keywords:

Lattice implication algebra , Chordal graph , Connected graph , Clique , Planar graph , Girth , Diameter , Fuzzy filter , Fuzzy LI- ideal.