Abstract
The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar neutrosophic set is a hybridization of the bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove their basic properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove their basic properties. Thereafter, we develop two novel multi-attribute decision-making strategies based on the proposed cross entropy measures. In the decision-making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision-making problems and compare the obtained result with the results of other existing strategies to show the applicability and effectiveness of the developed strategies. At the end, the main conclusion and future scope of research are summarized.
Highlights
Shannon and Weaver [1] and Shannon [2] proposed the entropy measure which dealt formally with communication systems at its inception
We develop a new multi-attribute decision-making (MADM) strategy based on weighted cross entropy to solve MADM problems in an interval bipolar neutrosophic sets (IBNSs) environment
Consider an interval bipolar neutrosophic MADM problem studied in [91] with four possible alternatives with the aim to invest a sum of money in the best choice
Summary
Shannon and Weaver [1] and Shannon [2] proposed the entropy measure which dealt formally with communication systems at its inception. According to Shannon and Weaver [1] and Shannon [2], the entropy measure is an important decision-making apparatus for computing uncertain information. Shannon [2] introduced the concept of the cross entropy strategy in information theory. The meaning of fuzzy entropy is quite different from the classical. Shannon entropy because it is defined based on a nonprobabilistic concept [3,4,5], while Shannon entropy is defined based on a randomness (probabilistic) concept. Sander [8] presented Shannon fuzzy entropy and proved that the properties sharpness, valuation, and general additivity have to Axioms 2018, 7, 21; doi:10.3390/axioms7020021 www.mdpi.com/journal/axioms
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