Abstract
First of all, we discuss the generalization of quasi-concavity for membership functions defined on n-dimensional Euclidean space in this paper. Generally, quasi-concave functions are defined by using the minimum operation. Whereas we give the concept of the more generalized quasi-concave function by adopting some conjunctive aggregation function instead of by using the minimum operator. Then we derive some properties of the more generalized quasi-concave functions which we proposed.
Next, we focus the plural membership functions defined on n-dimensional Euclidean space. Besides, we define a fuzzy mathematical programming problem whose objective function is an aggregation function on the range space of the plural membership functions. An optimal solution of the fuzzy mathematical programming problem is called a compromise solution of the problem by Ramik and Vlach. Finally, we derive the properties of the compromise solutions by means of features of the more generalized quasi-concave functions.
