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The recent boom of decision-making under uncertain information has attracted many researchers to the field of integrating various types of sets with decision-making methods. In this paper, a combined decision-making trial and evaluation laboratory (DEMATEL) with single-valued neutrosophic sets is proposed to solve the decision problem. This new model combines the advantages of multiplicative inverse of decision matrix in DEMATEL and neutrosophic numbers in linguistic variables, which can find the interrelationship among factors of decision problem. Differently from the typical multiplicative inverse of DEMATEL, which directly used inverse of matrix using real numbers, this method introduces the concept of inverse of matrix using the proposed left–right neutrosophic numbers. This step will enhance the validity of multiplicative inverse of decision matrix in the DEMATEL with neutrosophic numbers. The proposed neutrosophic DEMATEL is also be compared with the DEMATEL and fuzzy DEMATEL. This paper includes a case study that demonstrates the applicability of the neutrosophic DEMATEL in establishing the relationship among influential factors of coastal erosion. Extensive empirical studies using 12 factors of coastal erosion were presented to study the benefits of the proposed method. The result unveils the cause-and-effect relationships among the factors, where seven factors are identified as cause factors and five factors are grouped as effect factors. It is discovered that the factor 'imbalance sediment supply' gives a significant influence to coastal erosion. It is also shown that the degree of importance of the factors is almost consistent with the other two methods despite differences in type of numbers used in defining linguistic variables. [ABSTRACT FROM AUTHOR]

Previous theories have suggested that Bonferroni mean (BM) and its extensions can fulfil the desired properties to become a good aggregation operator in managing interrelationship between arguments under fuzzy decision-making environment. However, along with this growth, there are concerns regarding the limitation of the BM and its extensions where interrelationship between arguments is limited to a pair of input arguments. In contrast to previous works, a novel normalized weighted Bonferroni mean aggregation operator considering Shapley fuzzy measure has been introduced, where the overall interactions of input arguments are combined. Unlike other extensions of BM that are mostly considered under fuzzy environment, this aggregation operation introduces the Shapley fuzzy measure to deal with interactions of all arguments under the interval-valued neutrosophic environment. Specifically, the interval-valued neutrosophic Shapley normalized weighted Bonferroni mean (INSNWBM) is proposed in this paper. The properties of INSNWBM such as reducibility, idempotency, monotonicity, commutativity, and boundedness are also presented as to reflect the interrelationship among multiple input arguments. In addition, we have also proposed successive steps of a decision-making procedure in which the proposed INSNWBM is included. Together included is a numerical example as to illustrate the applicability of the INSNWBM in decision-making. The consistency of the ranking results is confirmed by variations of parameters of INSNWBM. It is shown that the ranking results are almost consistent despite the different usages of parameter values. Results obtained appear to support the idea that the proposed aggregation operator is able to address the interrelationship between arguments in decision-making. [ABSTRACT FROM AUTHOR]