Cross-Entropy of Dual Hesitant Fuzzy Sets for Multiple Attribute Decision-Making

2016 ◽  
Vol 8 (3) ◽  
pp. 20-30 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multiple Attribute Decision Making ◽  
Cross Entropy ◽  
Entropy Measure ◽  
Fuzzy Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
The Cross

This paper proposes a cross-entropy measure between dual hesitant fuzzy sets (DHFSs) as an extension of the cross-entropy measures of intuitionistic fuzzy sets. Then the cross-entropy measure between DHFSs is applied to multiple attribute decision making under dual hesitant fuzzy environments. Through the weighted cross-entropy measure between each alternative and the ideal alternative, we can obtain the ranking order of all alternatives and the best one. The decision-making method based on the cross-entropy measure of DHFSs can deal with dual hesitant fuzzy multiple attribute decision making problems and can automatically take into account much more information than existing hesitant (or intuitionistic) fuzzy decision-making methods and the differences of the evaluation data given by different experts or decision makers. Finally, a practical example about investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

Entropy Analysis on Intuitionistic Fuzzy Sets and Interval-Valued Intuitionistic Fuzzy Sets and its Applications in Mode Assessment on Open Communities

2018 ◽  
Vol 22 (1) ◽  
pp. 147-155 ◽  
Author(s):  
Hang Tian ◽  
Jiaru Li ◽  
Fangwei Zhang ◽  
Yujuan Xu ◽  
Caihong Cui ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Entropy Measures ◽  
Interval Valued

This paper identifies four variables to reveal the internal mechanisms of the entropy measures on intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs). First, four variables are used to propose a pair of generalized entropy measures on IFSs and IVIFSs. Second, three specific entropy measures are put forward to illustrate the effectiveness of the generalized entropy measure functions. Third, a novel multiple attribute decision-making approach under an intuitionistic fuzzy environment is proposed. The superiority of the decision-making approach is that the weight values of the attributes are obtained by their related entropy measures. Finally, the performance of the proposed entropy regulations on IFSs and IVIFSs is illustrated through a mode assessment example on open communities.

scholarly journals PICTURE FUZZY CROSS-ENTROPY FOR MULTIPLE ATTRIBUTE DECISION MAKING PROBLEMS

2016 ◽  
Vol 17 (4) ◽  
pp. 491-502 ◽  
Author(s):  
Guiwu WEI
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Resource Planning ◽  
Multiple Attribute Decision Making ◽  
Cross Entropy ◽  
Planning System ◽  
Multiple Attribute ◽  
Picture Fuzzy Set ◽  
The Cross ◽  
Picture Fuzzy Sets

In this paper, we investigate the multiple attribute decision making problems with picture fuzzy information. The advantage of picture fuzzy set is easily reflecting the ambiguous nature of subjective judgments because the picture fuzzy sets are suitable for capturing imprecise, uncertain, and inconsistent information in the multiple attribute decision making analysis. Thus, the cross entropy of picture fuzzy sets, called picture fuzzy cross entropy, is proposed as an extension of the cross entropy of fuzzy sets. Then, a multiple attribute decision making method based on the proposed picture fuzzy cross entropy is established in which attribute values for alternatives are picture fuzzy numbers. In decision making process, we utilize the picture fuzzy weighted cross entropy between the ideal alternative and an alternative to rank the alternatives corresponding to the cross entropy values and to select the most desirable one(s). Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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