Redefined fuzzy implicative filters

Using the belongs to relation (c) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (theta, psi)-fuzzy implicative filters where theta, psi are any two of {is an element of, q is an element of V q, is an element of Lambda q} with theta not equal is an element of Lambda q is introduced, and related properties are discussed. Relations between (is an element of V q, is an element of V q)-fuzzy implicative filters and (is an element of, is an element of V q)-fuzzy implicative filters are investigated, and conditions for an (is an element of, is an element of V q)-fuzzy implicative filter to be an (is an element of, c)-fuzzy implicative filter are provided. Characterizations of (is an element of, is an element of V q)-fuzzy implicative filters are given, and conditions for a fuzzy set to be a (q, is an element of V q)-fuzzy implicative filter are provided. (c) 2006 Elsevier Inc. All rights reserved.