Fixed Point Theorems for $L$-Fuzzy Monotone Multifunctions

Abstract

In this paper, we introduce three types of monotonicity of an $L$-fuzzy multifunction on a given $L$-fuzzy complete lattice and investigate their various properties. Furthermore, we show that any $L$-fuzzy multifunction with respect to these types of monotonicity has the fixed point property. Specific attention is paid to show for one type of these monotonicities that the set of fixed points of an $L$-fuzzy monotone multifunction is an $L$-fuzzy complete lattice.