Abstract
In order to quantify the fuzziness in the simplified neutrosophic setting, this paper proposes a generalized distance-based entropy measure and a dimension root entropy measure of simplified neutrosophic sets (NSs) (containing interval-valued and single-valued NSs) and verifies their properties. Then, comparison with the existing relative interval-valued NS entropy measures through a numerical example is carried out to demonstrate the feasibility and rationality of the presented generalized distance-based entropy and dimension root entropy measures of simplified NSs. Lastly, a decision-making example is presented to illustrate their applicability, and then the decision results indicate that the presented entropy measures are effective and reasonable. Hence, this study enriches the simplified neutrosophic entropy theory and measure approaches.
Highlights
Since entropy is an effective measure approach in quantifying the uncertainty degree of the objects, with the development of fuzzy theory, a lot of research on fuzzy entropy has been done so far
Thereafter, the generalized parametric exponential fuzzy entropy of order-α was introduced by Verma and Sharma [6], which reduces to the Pal and Pal exponential entropy [3] when α = 1, and becomes the De-Luca and Termini logarithmic entropy [2]
This study originally presented the generalized distance-based entropy measure and the dimension root entropy measure of simplified neutrosophic sets (NSs), containing both the SvSN and IvSN generalized distance-based entropy measures and the SvSN and IvSN neutrosophic dimension root entropy measures
Summary
Since entropy is an effective measure approach in quantifying the uncertainty degree of the objects, with the development of fuzzy theory, a lot of research on fuzzy entropy has been done so far. For an intuitionistic fuzzy set (IFS) extended by adding a non-membership degree to a fuzzy set (FS), Burillo and Bustince [7] first proposed IFS and interval-valued IFS entropy measures and their axiom requirements. Szmidt and Kacprzyk [8] redefined De-Luca and Termini’s axioms [2] in IFS setting and presented an intuitionistic non-probabilistic fuzzy entropy measure by a geometric interpretation and a ratio of distance of IFSs. Valchos and Sergiadis [9]. Tian et al [18] proposed a pair of generalized entropy measure on IFSs and IvIFSs. Recently, the neutrosophic set (NS) was introduced to describe the uncertainty and inconsistency information by an indeterminacy degree added to the IFS.
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