Fuzzy nn-ary polygroups related to fuzzy points

Recently, fuzzy nn-ary sub-polygroups were introduced and studied by Davvaz, Corsini and Leoreanu-Fotea [B. Davvaz, P. Corsini, V. Leoreanu-Fotea, Fuzzy nn-ary sub-polygroups, Comput. Math. Appl. 57 (2008) 141–152]. Now, in this paper, the concept of (∈,∈∨q)(∈,∈∨q)-fuzzy nn-ary sub-polygroups, (∈¯,∈¯∨q¯)-fuzzy nn-ary sub-polygroups and fuzzy nn-ary sub-polygroup with thresholds of an nn-ary polygroup are introduced and some characterizations are described. Also, we give the definition of implication-based fuzzy nn-ary sub-polygroups in an nn-ary polygroup, in particular, the implication operators in Łukasiewicz system of continuous-valued logic are discussed.