In complex systems, decision makers encounter uncertainty from various sources. In this paper, a new hybrid grey-based Multi-Criteria Decision Analysis (MCDA) approach is proposed to optimize the evaluation space in decision problems that are subject to subjective and objective uncertainty over different types of interrelated criteria. The four-phase methodology begins with the formulation of a decision problem through the analysis of the system of concern, its functionality, and substantial connections among evaluation criteria. The second phase involves the development of grey linguistic scales to handle the uncertainty of human judgements. The third phase integrates the grey linguistic scale, concepts of grey systems theory, and principles of Analytical Network Process to prioritize criteria. Finally, to evaluate and rank alternatives in such a complex setting, Preference Ranking Organization METHod for Enrichment Evaluation II is extended using a grey linguistic scale to articulate subjective uncertainty, grey numbers to account for objective uncertainty, grey operating rules to normalize evaluation measures, and the proposed approach of prioritizing evaluation criteria to establish relative preferences. To demonstrate the viability of the methodology, a case study is presented, in which a strategic decision is made within the context of innovation. To validate the methodology, a comparative analysis is provided.

Introduction

Decision makers usually encounter large amount of complex information. The complexity of decision problems increases when different evaluation criteria of different nature (e.g., qualitative and quantitative), different scales, and different values (e.g., continuous, discrete, and linguistic) are involved. Multi-Criteria Decision Analysis (MCDA) is therefore considered one of the most fruitful sub-disciplines of operations research. The main role of MCDA is to aid Decision Makers (DMs) in establishing a coherent picture about complex decision problems (Kurka and Blackwood, 2013). However, in many cases uncertainty-related aspects (i.e., uncertainty associated with limited objective information and uncertainty associated with subjective expert knowledge) are present. This adds to the complexity of analyzing the decision problems as the conventional MCDA approaches presume the availability of precise information (Kuang et al., 2015; Li et al., 2007). Various methods have been proposed to deal with different types of uncertainty-related aspects. Grey systems theory is recommended for decision problems with a relatively small amount of data (i.e., small samples) and poor information, which cannot be described by a probability distribution (Li et al., 2012; Li and Yuan, 2017; Liu and Lin, 2006). Accordingly, different researchers, which are presented in the next section, have considered the grey systems theory to address uncertainty in decision problems. The existing approaches assumed that DMs are able to assign the weights of the evaluation criteria precisely, did not consider the interrelationships among evaluation criteria, or did not consider the relations among evaluation criteria of different clusters, hence a better method is needed to address the existing research gaps.