Abstract
Entropy is one of many important mathematical tools for measuring uncertain/fuzzy information. As a subclass of neutrosophic sets (NSs), simplified NSs (including single-valued and interval-valued NSs) can describe incomplete, indeterminate, and inconsistent information. Based on the concept of fuzzy exponential entropy for fuzzy sets, this work proposes exponential entropy measures of simplified NSs (named simplified neutrosophic exponential entropy (SNEE) measures), including single-valued and interval-valued neutrosophic exponential entropy measures, and investigates their properties. Then, the proposed exponential entropy measures of simplified NSs are compared with existing related entropy measures of interval-valued NSs to illustrate the rationality and effectiveness of the proposed SNEE measures through a numerical example. Finally, the developed exponential entropy measures for simplified NSs are applied to a multi-attribute decision-making example in an interval-valued NS setting to demonstrate the application of the proposed SNEE measures. However, the SNEE measures not only enrich the theory of simplified neutrosophic entropy, but also provide a novel way of measuring uncertain information in a simplified NS setting.
Highlights
Entropy is an important mathematical tool for measuring the fuzziness of a fuzzy event
Indeterminate, and inconsistent information in the real world, Smaradache [18] presented the concept of the neutrosophic set (NS), which is described independently by truth, falsity, and indeterminacy membership functions defined in real standard [0, 1] or non-standard ]− 0, 1+ [ intervals
Since a single-valued NS is a special case of an interval-valued NS corresponding to the equality of the two endpoints of the truth, indeterminacy, and falsity intervals in an interval-valued NS, this section only adopts an example from the literature [24] in order to compare our proposed exponential entropy measures of simplified NSs with the entropy measures of interval-valued NSs introduced by Ye and
Summary
Entropy is an important mathematical tool for measuring the fuzziness of a fuzzy event. Ye [11] proposed cosine and sine entropy measures of intuitionistic FSs. As a generalization of fuzzy exponential entropy in Reference [3], Verma and Sharma [12] introduced an intuitionistic fuzzy exponential entropy measure based on the concept of fuzzy entropy. Zhang et al [17] defined an axiom of interval-valued intuitionistic fuzzy distance-based entropy and some entropy measures for interval-valued intuitionistic FSs, along with their relationship, based on inclusion measures, and similarity measures of interval-valued intuitionistic FSs. Since there is incomplete, indeterminate, and inconsistent information in the real world, Smaradache [18] presented the concept of the neutrosophic set (NS), which is described independently by truth, falsity, and indeterminacy membership functions defined in real standard [0, 1] or non-standard ]− 0, 1+ [ intervals.
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