<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Due to some drawbacks of the cross entropy between Single Valued Neutrosophic Sets (SVNSs) in dealing with decision-making problems, the existing single valued neutrosophic cross entropy indicates an asymmetrical phenomenon or may produce an undefined (unmeaningful) phenomenon in some situations. In order to overcome these disadvantages, this paper proposes an improved cross entropy measure of SVNSs and investigates its properties, and then extends it to a cross entropy measure between interval neutrosophic sets (INSs). Furthermore, the cross entropy measures are applied to multicriteria decision making problems with single valued neutrosophic information and interval neutrosophic information. In decision making methods, through the weighted cross entropy measure between each alternative and the the ideal alternative, one can obtain the ranking order of all alternatives and the best one. The decision-making methods using the proposed cross entropy measures can efficiently deal with decision making problems with incomplete, indeterminate and inconsistent information which exist usually in real situations. Finally, two illustrative examples are provided to demonstrate the application and efficiency of the developed decision making approaches under single valued neutrosophic and interval neutrosophic environments.</p></abstract>

Due to some drawbacks of the cross entropy between Single Valued Neutrosophic Sets (SVNSs) in dealing with decision-making problems, the existing single valued neutrosophic cross entropy indicates an asymmetrical phenomenon or may produce an undefined (unmeaningful) phenomenon in some situations. In order to overcome these disadvantages, this paper proposes an improved cross entropy measure of SVNSs and investigates its properties, and then extends it to a cross entropy measure between interval neutrosophic sets (INSs). Furthermore, the cross entropy measures are applied to multicriteria decision making problems with single valued neutrosophic information and interval neutrosophic information. In decision making methods, through the weighted cross entropy measure between each alternative and the the ideal alternative, one can obtain the ranking order of all alternatives and the best one. The decision-making methods using the proposed cross entropy measures can efficiently deal with decision making problems with incomplete, indeterminate and inconsistent information which exist usually in real situations. Finally, two illustrative examples are provided to demonstrate the application and efficiency of the developed decision making approaches under single valued neutrosophic and interval neutrosophic environments.

Improved Cross Entropy Measures of Single Valued Neutrosophic Sets and Interval Neutrosophic Sets and Their Multicriteria Decision Making Methods

Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, Zhejiang Province 312000, China

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Due to some drawbacks of the cross entropy between Single Valued Neutrosophic Sets (SVNSs) in dealing with decision-making problems, the existing single valued...

Improved Cross Entropy Measures of Single Valued Neutrosophic Sets and Interval Neutrosophic Sets and Their Multicriteria Decision Making Methods

Published Online: Nov 26, 2015

Page range: 13 - 26

DOI: https://doi.org/10.1515/cait-2015-0051

Keywords
Neutrosophic set, single valued neutrosophic set, interval neutrosophic set, cross entropy, multicriteria decision making

© by Jun Ye

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Improved Cross Entropy Measures of Single Valued Neutrosophic Sets and Interval Neutrosophic Sets and Their Multicriteria Decision Making Methods

Published Online: Nov 26, 2015

Page range: 13 - 26

DOI: https://doi.org/10.1515/cait-2015-0051

KeywordsNeutrosophic set, single valued neutrosophic set, interval neutrosophic set, cross entropy, multicriteria decision making

© by Jun Ye

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Neutrosophic set, single valued neutrosophic set, interval neutrosophic set, cross entropy, multicriteria decision making