Probabilistic Hesitant Fuzzy Elements Research Articles

Fuzzy Techniques for Decision Making

This book contains the successful invited submissions [1–21] to a Special Issue of Symmetry on the subject area of “Fuzzy Techniques for Decision Making”.[...]

Correlation Coefficients of Probabilistic Hesitant Fuzzy Elements and Their Applications to Evaluation of the Alternatives

Correlation coefficient is one of the broadly use indexes in multi-criteria decision-making (MCDM) processes. However, some important issues related to correlation coefficient utilization within probabilistic hesitant fuzzy environments remain to be addressed. The purpose of this study is introduced a MCDM method based on correlation coefficients utilize probabilistic hesitant fuzzy information. First, the covariance and correlation coefficient between two PHFEs is introduced, the properties of the proposed covariance and correlation coefficient are discussed. In addition, the northwest corner rule to obtain the expected mean related to the multiply of two PHFEs is introduced. Second, the weighted correlation coefficient is proposed to make the proposed MCDM method more applicable. And the properties of the proposed weighted correlation coefficient are also discussed. Finally, an illustrative example is demonstrated the practicality and effectiveness of the proposed method. An illustrative example is presented to demonstrate the correlation coefficient propose in this paper lies in the interval [−1, 1], which not only consider the strength of relationship between the PHFEs but also whether the PHFEs are positively or negatively related. The advantage of this method is it can avoid the inconsistency of the decision-making result due to the loss of information.

Multi-attribute group decision making under probabilistic hesitant fuzzy environment with application to evaluate the transformation efficiency

Hesitant fuzzy sets were introduced by Torra to efficiently address situations in which the membership degree of an element in a set is expressed by several different values. However, there is a large shortcoming in hesitant fuzzy sets—the serious loss of information. Therefore, in this paper, we improve upon hesitant fuzzy sets by implementing a probabilistic hesitant fuzzy set (PHFS). Then, we introduce some new basic operations on the probabilistic hesitant fuzzy elements (PHFEs) using the Frank t-conorm and t-norm. Based on these proposed operations, we further develop probabilistic hesitant fuzzy weighted arithmetic and geometric aggregation operators. The desired properties and the relationships among them are investigated in detail. In addition, an approach to multi-attribute group decision making (MAGDM) is investigated on the basis of the new operators. Finally, a numerical example of public company efficiency evaluation is provided to illustrate the application and validity of the proposed approach.