Abstract
Owing to the indeterminacy, incompleteness, and inconsistency of decision makers’ arguments/cognitions regarding complicated decision-making problems, the truth, falsity, and indeterminacy degrees given by decision makers may imply the partial certainty and partial uncertainty information. In this case, a simplified neutrosophic set (SNS) cannot express the uncertainty degrees of the truth, falsity, indeterminacy arguments. To depict the hybrid information of SNS and neutrosophic (indeterminate) numbers (NNs) together, this study presents a simplified neutrosophic indeterminate set (SNIS) to describe the uncertainty degrees of the truth, falsity, indeterminacy, and then based on the de-neutrosophication technology using the parameterized SNSs of SNISs we introduce the q-indeterminate correlation coefficients of SNISs with a parameter q ∈ [0, 1]. Next, a simplified neutrosophic indeterminate multicriteria decision-making method using the qindeterminate correlation coefficients of SNISs is established along with decision makers’ risk attitudes, such as the small risk for q = 0, the moderate risk for q = 0.5, and the large risk for q = 1, to carry out multicriteria decision-making problems in SNIS setting. Eventually, the proposed decision-making approach is applied in an example of selecting a satisfactory slope design scheme for an open pit mine to indicate the practicality and flexibility in SNIS setting.
Highlights
Smarandache (1998) firstly presented a neutrosophic set from philosophical viewpoint as a powerful general formal framework to depict the inconsistent and indeterminate information in the real life
Existing neutrosophic correlation coefficients cannot deal with such a multicriteria decision-making (MDM) problem with the uncertainty degrees of the truth, falsity, indeterminacy arguments and lack decision makers’ risk attitudes in indeterminate decision-making applications. Motivated by both the hybrid information of simplified neutrosophic set (SNS) and neutrosophic (indeterminate) numbers (NNs) and the decision makers’ risk attitudes in indeterminate decision-making problems, this study proposes a simplified neutrosophic indeterminate set (SNIS) for the first time to describe the uncertainty degrees of the truth, indeterminacy, falsity, and based on the de-neutrosophication technology using the parameterized single-valued neutrosophic sets (SvNSs) of SNISs we introduce two q-indeterminate correlation coefficients of SNISs with a parameter q ∈ [0, 1] and their MDM approach with decision makers’ risk attitudes in SNIS setting to solve MDM problems with SNIS information under inconsistent and indeterminate environment
Regarding the indeterminacy of simplified neutrosophic information in indeterminate decision-making setting, this study presented SNIS to express the hybrid information of both SNS and NN, which is depicted by the truth, falsity and indeterminacy NNs in indeterminate and inconsistent situations
Summary
Smarandache (1998) firstly presented a neutrosophic set from philosophical viewpoint as a powerful general formal framework to depict the inconsistent and indeterminate information in the real life. Existing neutrosophic correlation coefficients cannot deal with such a MDM problem with the uncertainty degrees of the truth, falsity, indeterminacy arguments and lack decision makers’ risk attitudes in indeterminate decision-making applications.
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