A Binary Logarithm Similarity Measure with Roughness Approximation

Abstract

Roughness measures for uncertainty data occur with less consideration since the data involve indeterminacy and inconsistency. The indeterminacy plus inconsistency can be solved by a rough neutrosophic set with roughness approximation. Therefore, a binary logarithm similarity measure for a rough neutrosophic set with roughness approximation was proposed in this research. A rough neutrosophic set was chosen as the uncertainty set theory information, which includes the upper and lower approximation with a boundary set approximation. The objectives of this research are to define a binary logarithm similarity measure for a rough neutrosophic set, to formulate the properties satisfied by the proposed similarity measure, and to develop a decision-making model by using a binary logarithm similarity measure for a case study (COVID-19). The roughness approximation was used in the derivation of the binary logarithm similarity measure. The proving result was finalized. Then, the derivation of binary logarithm similarity measures of a rough neutrosophic set was well defined. As a validation process, the similarity properties for identifying the most important priority group for COVID-19 vaccines were used such as age, health state, women, and job types. Following that, the decision-making for identifying the most important priority group for COVID-19 vaccines is presented.