Managing temporal uncertainty in multi-mode Z-number fuzzy graph structures

Abstract

In this paper we introduce an NP-hard optimization problem and examine preferences of decision-maker towards imprecise alternatives (modes) in a fuzzy temporal graph structure model. Fuzzy Z-number preference matrix is introduced and types of generalized precedence relations in fuzzy multimode resource-constrained project scheduling problem (F-MRCPSP) based on expert estimation are discussed. Implementation of Z-numbers allows handling uncertain data and modelling preferences of expert towards uncertain variables. Multi-mode way for activity performance allows considering temporal uncertainty, expert estimations, flexibility in switching from mode to mode and resource levelling profile problem. Geometrical interpretation for fuzzy multi-mode problem (FMRCPSP) based on box packing is given.