In this paper, a new multi-criteria problem solving method—the Full Consistency Method (FUCOM)—is proposed. The model implies the definition of two groups of constraints that need to satisfy the optimal values of weight coefficients. The first group of constraints is the condition that the relations of the weight coefficients of criteria should be equal to the comparative priorities of the criteria. The second group of constraints is defined on the basis of the conditions of mathematical transitivity. After defining the constraints and solving the model, in addition to optimal weight values, a deviation from full consistency (DFC) is obtained. The degree of DFC is the deviation value of the obtained weight coefficients from the estimated comparative priorities of the criteria. In addition, DFC is also the reliability confirmation of the obtained weights of criteria. In order to illustrate the proposed model and evaluate its performance, FUCOM was tested on several numerical examples from the literature. The model validation was performed by comparing it with the other subjective models (the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP)), based on the pairwise comparisons of the criteria and the validation of the results by using DFC. The results show that FUCOM provides better results than the BWM and AHP methods, when the relation between consistency and the required number of the comparisons of the criteria are taken into consideration. The main advantages of FUCOM in relation to the existing multi-criteria decision-making (MCDM) methods are as follows: (1) a significantly smaller number of pairwise comparisons (only n − 1), (2) a consistent pairwise comparison of criteria, and (3) the calculation of the reliable values of criteria weight coefficients, which contribute to rational judgment.

Sustainability is one of the main challenges of the recent decades. In this regard, several prior studies have used different techniques and approaches for solving this problem in the field of sustainability engineering. Multiple criteria decision making (MCDM) is an important technique that presents a systematic approach for helping decisionmakers in this field. The main goal of this paper is to review the literature concerning the application of MCDM methods in the field of sustainable engineering. The Web of Science (WoS) Core Collection Database was chosen to identify 108 papers in the period of 2008–2018. The selected papers were classified into five categories, including construction and infrastructure, supply chains, transport and logistics, energy, and other. In addition, the articles were classified based on author, year, application area, study objective and problem, applied methods, number of published papers, and name of the journal. The results of this paper show that sustainable engineering is an area that is quite suitable for the use of MCDM. It can be concluded that most of the methods used in sustainable engineering are based on traditional approaches with a noticeable trend towards applying the theory of uncertainty, such as fuzzy, grey, rough, and neutrosophic theory.