A New Approach to Concavity Fuzzification

Abstract

In this paper, we introduce a more general approach to the fuzzification of fuzzy concavity. More specifically, the degree of $\left(L,M\right)$ -fuzzy concavity is introduced and characterized as a generalization of $L$ -concave structure and $\left(L,M\right)$ -fuzzy concave structure. Based on that, the degree of $\left(L,M\right)$ -fuzzy concavity preserving and $\left(L,M\right)$ -fuzzy concave-to-concave of a function are defined. Some properties and relationships between the degree of $\left(L,M\right)$ -fuzzy concavity preserving and $\left(L,M\right)$ -fuzzy concave-to-concave functions are discussed.