Version 1
: Received: 7 January 2018 / Approved: 8 January 2018 / Online: 8 January 2018 (11:04:02 CET)
How to cite:
Pramanik, S.; Dey, P.P.; Smarandache, F.; Ye, J. Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision Making. Preprints2018, 2018010065. https://doi.org/10.20944/preprints201801.0065.v1
Pramanik, S.; Dey, P.P.; Smarandache, F.; Ye, J. Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision Making. Preprints 2018, 2018010065. https://doi.org/10.20944/preprints201801.0065.v1
Pramanik, S.; Dey, P.P.; Smarandache, F.; Ye, J. Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision Making. Preprints2018, 2018010065. https://doi.org/10.20944/preprints201801.0065.v1
APA Style
Pramanik, S., Dey, P.P., Smarandache, F., & Ye, J. (2018). Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision Making. Preprints. https://doi.org/10.20944/preprints201801.0065.v1
Chicago/Turabian Style
Pramanik, S., Florentin Smarandache and Jun Ye. 2018 "Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision Making" Preprints. https://doi.org/10.20944/preprints201801.0065.v1
Abstract
Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of 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 its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods 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 methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
