A New Approach Towards Intuitionistic Fuzzy Multisets

2. Preliminaries

In this section some preliminary definitions and results regarding multisets and its generalizations are given.

• Definition 2.1 (Multisets) (Miyamoto, 2001) A multiset M of the universe X is characterized by the count function C_M: X→N, where N= {0, 1, 2, .....}. Thus, C_M(x) is the number of occurrences of the element x of the universe X.

• Definition 2.2 (Fuzzy Multisets) (Yagar, 1986) A fuzzy multiset (FMS) A drawn from the universe X is characterized by a function ‘count membership’ of A denoted by CM_A such that CM_A:X→P([0,1]). Thus for each element x of the universe X, we get a membership sequence which is defined as a decreasingly ordered sequence of elements from [0, 1]. Thus

• Definition 2.3 (Intuitionistic fuzzy sets) (Atanassov, 1986) An intuitionistic fuzzy set (IFS) A in X is an object having the form where the functions define the degree of membership and degree of non-membership of the element

• Definition 2.4 (Intuitionistic fuzzy multisets) (Shinoj & John, 2013) An IFMS A over X is characterized by two functions: ‘count membership’ of A (denoted by CM_A) and ‘count non-membership’ of A (denoted by CN_A) given respectively as: CM_A, CN_A: X→P([0,1]). Now for each