We first recall some basic concepts given in Zhou (1994). For a coalition S and a vector 
, we denote 
.
1.1. Definition 1.1
An n-person game V is with transferable utility (a TU game or cooperative game in coalition form) if there exists a function 
such that for every 
, 
.
Thus, every TU game V has an underlying function v.
Cooperative games have been studied extensively in the literature. A central question in cooperative games is to study solution concepts and their relationships, those well-known solution concepts include core, stable set, Shapley value, bargaining set, and so on. There are three major types of bargaining sets: the first one, called classical bargaining set and denoted by 
, is defined by R. J. Aumann and M. Maschler in 1964; the second one, denoted by MB, is given by Mas-Colell in 1989; and the third one is given by Zhou in 1994. The existence theorem for the Aumann-Maschler bargaining set has been established independently by Davis and Maschler (1963) and Peleg (1963), the existence for Mas-Colell bargaining set in a weakly superadditive TU game has been provided by Vohra (1991), and the existence of Zhou bargaining set for a TU game is given by Zhou (1994).
Our focus in this paper is on fuzzy Zhou bargaining sets. Let us first recall the concept of Zhou bargaining set. A payoff configuration of a TU game V is a pair 
, where x is a vector in 
, 
is a partition of N, and 
for each 
. Then the set of all payoff configurations is:
(1.1) where P is the set of all partitions of N.
Clearly, C is nonempty, closed, comprehensive, bounded from above, and contains the origin (i.e., zero vector) as an interior point.
We now define Zhou bargaining set which is based on C. Let V be a TU game and let 
be a payoff vector. An objection at x is a pair 
, where S is a non-empty coalition and y is a vector with indices in S satisfying 
and 
for each 
. A Z-counterobjection to this objection is a pair 
, where T is a coalition with 
satisfying that:
A payoff vector 
is said to belong to the Zhou bargaining set ZB(V) if for any objection at x, there exists a Z-counterobjection to it.
According to Zhou (1994), one good part by defining bargaining set on C is that it is free of any particular coalition structure. For the existence of Zhou bargaining sets, Zhou (1994) proved the following theorem.