FUZZY SUB-HOOPS BASED ON FUZZY POINTS

초록

Using the belongs to relation (subset of) and quasi-coincident with relation (q) between fuzzy points and fuzzy sets, the notions of an (is an element of, is an element of)-fuzzy sub-hoop, an (is an element of, is an element of Vq)-fuzzy sub-hoop and a (q, is an element of Vq)-fuzzy sub-hoop are introduced, and several properties are investigated. Characterizations of an (is an element of, is an element of)-fuzzy sub-hoop and an (is an element of, is an element of Vq)-fuzzy sub-hoop are displayed. Relations between an (is an element of, is an element of)-fuzzy sub-hoop, an (is an element of, is an element of Vq)-fuzzy sub-hoop and a (q, is an element of Vq)-fuzzy sub-hoop are discussed. Conditions for a fuzzy set to be a (q, is an element of Vq)-fuzzy sub-hoop are considered, and condition for an (is an element of, is an element of Vq)-fuzzy sub-hoop to be a (q, is an element of Vq)-fuzzy sub-hoop are provided.

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