Smart product-service systems (Smart PSS) are receiving increasing attention due to their potentials to satisfy customer needs and create sustainability to meet hybrid concerns. As a value co-creation business paradigm, various sustainable value propositions (SVPs) and their assessments come from stakeholders' subjective judgments, which values are imprecise, vague, and even inconsistent. The reliability of these values also varies with the confidence and cognitive bias of the respective stakeholder. How to evaluate these co-creative SVPs to ensure an objective and reliable result under such uncertain environments becomes a critical issue. To fill this gap, this paper proposes a rough-Z-number extended multi-criteria group decision-making framework integrating the rough-Z-number, DEMATEL (decision making trial and evaluation laboratory), and group decision-making strategy to evaluate the co-creative SVPs for Smart PSS. A novel rough-Z-number is presented to deal with the uncertainty and reliability representation of the stakeholder's individual assessment as well as the aggregation and subjectivity manipulation of these risk assessments from different stakeholders. A rough-Z-number extended DEMATEL is then proposed to determine the risk prioritization of the co-creative SVPs. Experimental results and comparative studies demonstrate the superiority of the proposed rough-Z-number-based DEMATEL in handling the uncertainty and reliability characterization as well as the subjectivity manipulation during the evaluation of the co-creative SVPs.

Biological inspiration evaluation has been widely acknowledged as one of the most important phases in biologically inspired design (BID) as it substantially determines the direction of the following-up design activities. However, it is inherently an interdisciplinary assessment, which includes both the engineering domain and the biological systems. Due to the lack of knowledge at the early stage of product design, the risk assessments mainly depend on experts' subjective judgments, which values are vague, imprecise, and even inconsistent. How to objectively evaluate the biological inspiration under such uncertain and interdisciplinary scenarios remains an open issue. To bridge such gaps, this study proposes a fuzzy rough number extended multi-criteria group decision-making (MCGDM) to evaluate the biological inspiration for BID. A fuzzy rough number is introduced to represent the individual decision maker's risk assessment and aggregate respective evaluation values within the decision-making group. A fuzzy rough number extended decision-making trial and evaluation laboratory is presented to determine the criteria weights and a fuzzy rough number extended multi-attribute ideal real comparative analysis is proposed to rank the candidate biological inspirations. Experimental results and comparative analysis validate the superiority of the proposed MCGDM in handling the subjectivity and uncertainty in biological inspiration evaluation.