Abstract
The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced. By definition, we know that the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS) is a special case of the probabilistic interval neutrosophic hesitant fuzzy set (PINHFS). PSVNHFSs can satisfy all the properties of PINHFSs. An example is given to illustrate that PINHFS compared to PSVNHFS is more general. Then, PINHFS is the main research object. The basic operational relations of PINHFS are studied, and the comparison method of probabilistic interval neutrosophic hesitant fuzzy numbers (PINHFNs) is proposed. Then, the probabilistic interval neutrosophic hesitant fuzzy weighted averaging (PINHFWA) and the probability interval neutrosophic hesitant fuzzy weighted geometric (PINHFWG) operators are presented. Some basic properties are investigated. Next, based on the PINHFWA and PINHFWG operators, a decision-making method under a probabilistic interval neutrosophic hesitant fuzzy circumstance is established. Finally, we apply this method to the issue of investment options. The validity and application of the new approach is demonstrated.
Highlights
In real life, uncertainty widely exists, like an expert system, information fusion, intelligent computations and medical diagnoses
We find that the application of probabilistic interval neutrosophic hesitant fuzzy set (PINHFS) is wider than that of the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS), and it is closer to real life
Since PINHFS is more general than PSVNHFS, the situation of PINHFS is mainly discussed
Summary
Uncertainty widely exists, like an expert system, information fusion, intelligent computations and medical diagnoses. The probabilistic method is not always effective when we deal with epistemic uncertain problems [14] Those problems makes researchers attempt to combine fuzzy set theory with probability theory as a new fuzzy concept. If a neutrosophic multi-attribute decision making (MADM) problem under the probabilistic surroundings needs to be solved, the probabilities as a part of a fuzzy system will be lost. Until now, this problem has not given an effective solution. To solve the MADM problems under the probabilistic interval neutrosophic hesitant fuzzy circumstance, the concept of PINHFS is used.
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