SIMPLIFIED NEUTROSOPHIC INDETERMINATE DECISION MAKING METHOD WITH DECISION MAKERS’ INDETERMINATE RANGES

Generalized ordered weighted harmonic averaging operator with trapezoidal neutrosophic numbers for solving MADM problems

Harmonic mean is suitable for algebraic calculation and other mathematical treatments and also suitable for directly aggregated negative indicators. In many different situations, harmonic mean improves the flexibility. In this paper, we develop some new aggregation operators under neutrosophic environment and apply with multi attribute decision making (MADM) problems. First, we provide a Single valued trapezoidal neutrosophic Generalized ordered weighted harmonic averaging(SVTNGOWHA) operator which is the extension of single valued trapezoidal neutrosophic ordered weighted harmonic averaging (SVTNOWHA) operator. To fix the operators on the mount, we have tested these methods in few illustrative examples, and the results have been presented.

Arccosine and arctangent similarity measures of refined simplified neutrosophic indeterminate sets and their multicriteria decision-making method

In indeterminate and inconsistent setting, existing simplified neutrosophic indeterminate set (SNIS) can be depicted by the neutrosophic number (NN) functions of the truth, falsity and indeterminacy. Then, the three NN functions in SNIS lack their refined expressions and then the simplified neutrosophic indeterminate decision making (DM) method cannot carry out the multicriteria DM problems with both criteria and sub-criteria in the setting of SNISs. To overcome the flaws, this study first proposes a new notion of a refined simplified neutrosophic indeterminate set (RSNIS), which is described by the refined truth, falsity and indeterminate NN information regarding both elements and sub-elements in a universe set, as the extension of SNIS. Next, we propose the arccosine and arctangent similarity measures of RSNISs and their multicriteria DM method with various indeterminate risk ranges so as to carry out multicriteria DM problems with weight values of both criteria and sub-criteria in RSNIS setting. Lastly, the proposed DM method is applied to a multicriteria DM example of slope design schemes for an open pit mine to illustrate its application in the indeterminate DM problem with RSNISs. The decision results and comparative analysis indicate the rationality and efficiency of the proposed DM method with different indeterminate risk ranges.

Some aggregation operators of neutrosophic Z-numbers and their multicriteria decision making method

As the generalization of the classical fuzzy number, the concept of Z-number introduced by Zadeh indicates more ability to depict the human knowledge and judgments of both restraint and reliability as an order pair of fuzzy numbers. In indeterminacy and inconsistent environment, a neutrosophic set is described by the truth, falsity, and indeterminacy degrees, but they lack measures related to reliability. To describe the hybrid information of combining the truth, falsity and indeterminacy degrees with their corresponding reliability degrees, this paper first proposes the concept of a neutrosophic Z-number (NZN) set, which is a new framework of neutrosophic values combined with the neutrosophic measures of reliability, as the generalization of the Z-number and the neutrosophic set. Then, we define the operations of neutrosophic Z-numbers (NZNs) and a score function for ranking NZNs. Next, we present NZN weighted arithmetic averaging (NZNWAA) and NZN weighted geometric averaging (NZNWGA) operators to aggregate NZN information and investigate their properties. Regarding the NZNWAA and NZNWGA operators and the score function, a multicriteria decision making (MDM) approach is developed in the NZN environment. Finally, an illustrative example about the selection problem of business partners is given to demonstrate the applicability and effectiveness of the developed MDM approach in NZN setting.