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This paper summarises a mathematical theory of the measurement of both tangible and intangible factors, the Analytic Hierarchy Process (AHP) and its generalisation to dependence and feedback, the Analytic Network Process (ANP) and illustrates their application to making complex multicriteria decisions.

We develop a novel method that uses single-valued neutrosophic sets (NSs) to handle independent multisource uncertainty measures affecting the reliability of experts' assessments in group multi-criteria decision-making (GMCDM) problems. NSs are characterized by three independent membership magnitudes (falsity, truth and indeterminacy) and can be employed to model situations characterized by complex uncertainty. In the proposed approach, the neutrosophic indicators are defined to explicitly reflect DMs' credibility (voting power), inconsistencies/errors inherent to the assessing process, and DMs' confidence in their own evaluation abilities. In contrast with most of the existing studies, single-valued NSs are used not only to formalize the uncertainty affecting DMs' priorities, but also to aggregate them into group estimates without the need to define neutrosophic decision matrices or aggregation operators. Group estimates are synthesized into crisp evaluations through a two-step deneutrosophication process that converts (1) single-valued NSs in fuzzy sets (FSs) using the standard Euclidean metric and (2) FSs in representative crisp values using defuzzification. Theoretical and practical implications are discussed to highlight the flexibility of the proposed approach. An illustrative example shows how taking into account the uncertainty inherent to the experts' evaluations may deeply affect the results obtained in a standard fuzzy environment even when dealing with very simple ranking problems.

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