Novel Decision Making Methodology under Pythagorean Probabilistic Hesitant Fuzzy Einstein Aggregation Information

This research proposes multicriteria decision-making(MCDM)-based real-time Mesenchymal stem cells(MSC)transfusion framework.The testing phase of the methodology denotes the ability to stick to plastic surfaces,the upregulation and downregulation of certain surface protein markers,and lastly,the ability to differentiate into various cell types.First,two scenarios of an enhanced dataset based on a medical perspective were created in the development phase to produce varying levels of emergency.Second,for real-timemonitoring ofCOVID-19 patients with different emergency levels(i.e.,mild,moderate,severe,and critical),an automated triage algorithmbased on a formal medical guideline is proposed,taking into account the improvement and deterioration procedures fromone level to the next.For this strategy,Einstein aggregation information under the Pythagorean probabilistic hesitant fuzzy environment(PyPHFE)is developed.Einstein operations on PyPHFE such as Einstein sum,product,scalar multiplication,and their properties are investigated.Then,several Pythagorean probabilistic hesitant fuzzy Einstein aggregation operators,namely the Pythagorean probabilistic hesitant fuzzy weighted average(PyPHFWA)operator,Pythagorean probabilistic hesitant fuzzy Einstein weighted geometric(PyPHFEWG)operator,Pythagorean probabilistic hesitant fuzzy Einstein ordered weighted average(PyPHFEOWA)operator,Pythagorean probabilistic hesitant fuzzy Einstein ordered weighted geometric(PyPHFEOWG)operator,Pythagorean probabilistic hesitant fuzzy Einstein hybrid average(PyPHFEHA)operator and Pythagorean probabilistic hesitant fuzzy Einstein hybrid geometric(PyPHFEHG)operator are investigated.All the above-mentioned operators are helpful in design the algorithm to tackle uncertainty in decision making problems.In last,a numerical case study of decision making is presented to demonstrate the applicability and validity of the proposed technique.Besides,the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.

Two-Sided Matching Decision Making with Multi-Attribute Probabilistic Hesitant Fuzzy Sets

In previous research on two-sided matching(TSM)decision,agents’preferences were often given in the form of exact values of ordinal numbers and linguistic phrase term sets.Nowdays,the matching agent cannot perform the exact evaluation in the TSM situations due to the great fuzziness of human thought and the complexity of reality.Probability hesitant fuzzy sets,however,have grown in popularity due to their advantages in communicating complex information.Therefore,this paper develops a TSM decision-making approach with multi-attribute probability hesitant fuzzy sets and unknown attribute weight information.The agent attribute weight vector should be obtained by using the maximum deviation method and Hamming distance.The probabilistic hesitancy fuzzy information matrix of each agent is then arranged to determine the comprehensive evaluation of two matching agent sets.The agent satisfaction degree is calculated using the technique for order preference by similarity to ideal solution(TOPSIS).Additionally,the multi-object programming technique is used to establish a TSM method with the objective of maximizing the agent satisfaction of two-sided agents,and the matching schemes are then established by solving the built model.The study concludes by providing a real-world supply-demand scenario to illustrate the effectiveness of the proposed method.The proposed method is more flexible than prior research since it expresses evaluation information using probability hesitating fuzzy sets and can be used in scenarios when attribute weight information is unclear.

A Novel Multi-Attribute Decision-Making Method Based on Probabilistic Hesitant Fuzzy Soft Set and Its Application

The probabilistic hesitant fuzzy multi-attribute group decision-making method introduces probability and hesitation into decision-making problems at the same time,which can improve the reliability and accuracy of decision-making results,and has become a research hotspots in recent years.However,there are still many problems,such as overly complex calculations and difficulty in obtaining probability data.Based on these,the paper proposes a multi-attribute group decision-making model based on probability hesitant fuzzy soft sets.Firstly,the definition of probabilistic hesitant fuzzy soft set is given.Then,based on soft set theory and probabilistic hesitant fuzzy set,the similarity measure of probabilistic hesitant fuzzy soft set is proposed,and the two measures are further combined.Finally,it is applied to the construction of multi-attribute group decision-making model,and the effectiveness and rationality of the model are verified by an example.The example shows that the new similarity calculation formula and algorithm model in this paper have higher accuracy,and the calculation process is more simple,it provides a feasible method for multi-attribute group decision making problems.

Pythagorean probabilistic hesitant triangular fuzzy aggregation operators with applications in multiple attribute decision making

As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.