This paper presents characterizations of M-fuzzifying matroids bymeans of two kinds of fuzzy operators, called M-fuzzifying derived operatorsand M-fuzzifying difference derived operators.

an l-fuzzifying matroid is a pair (e, i), where i is a map from2e to l satisfying three axioms. in this paper, the notion of closure operatorsin matroid theory is generalized to an l-fuzzy setting and called l-fuzzifyingclosure operators. it is proved that there exists a one-to-one correspondencebetween l-fuzzifying matroids and their l-fuzzifying closure operators.

In this article, we develop the basic theory of digital topological groups. The definitions directly lead to two separate types, based on details continuity required group multiplication. We define NP1- and NP2-digital groups, investigate their properties algebraic structure. NP2-type is very restrictive, give a complete classification also many examples NP1-digital homomorphisms, describe coun...