Bipolar Fuzzy Entropy and Correlation Co-efficient with Application to Vaccine Selection
Keywords:
Fuzzy entropy; bipolar fuzzy set; bipolar fuzzy entropy; bipolar correlation; MCDM.Abstract
The fuzzy set theory is very popular and viable approach to model the uncertainty. The uncertainty in the real cases is due to different factors like the lack of expertise, erroneous data, hesitancy, indeterminacy, existence of the counter-presence of a property. Various fuzzy set extensions offer different approaches for better modelling of the real systems in view of the underlying structural uncertainty of the real system. Bipolar fuzzy theory is also an extension of fuzzy theory that has not been investigated in much detail. In bipolar fuzzy theory, we deal with those real systems where a linguistic variable needs to be investigated for the level of satisfaction as well as counter-satisfaction. In this paper, we define certain operations on a bipolar fuzzy set and examine some of their properties. We also introduce an axiomatic framework for defining bipolar fuzzy entropy and establish a characterization theorem. We introduce three bipolar fuzzy entropy measures and a bipolar fuzzy correlation coefficient with application to a problem of multiple criteria decision-making (MCDM) that needs to be modelled with bipolar fuzzy logic.
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