Three-way decision (T-WD) theory is about thinking, problem solving, and computing in threes. Behavioral decision making (BDM) focuses on effective, cognitive, and social processes employed by humans for choosing the optimal object, of which prospect theory and regret theory are two widely used tools. The hesitant fuzzy set (HFS) captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades. Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together, this paper reviews and examines advances in three-way behavioral decision making (TW-BDM) with hesitant fuzzy information systems (HFIS) from the perspective of the past, present, and future. First, we provide a brief historical account of the three topics and present basic formulations. Second, we summarize the latest development trends and examine a number of basic issues, such as one-sidedness of reference points and subjective randomness for result values, and then report the results of a comparative analysis of existing methods. Finally, we point out key challenges and future research directions. 

Three-Way Behavioral Decision Making With Hesitant Fuzzy Information Systems: Survey and Challenges

Three-way decision (T-WD) theory is about thinking, problem solving, and computing in threes. Behavioral decision making (BDM) focuses on effective, cognitive, and social processes employed by humans for choosing the optimal object, of which prospect theory and regret theory are two widely used tools. The hesitant fuzzy set (HFS) captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades. Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together, this paper reviews and examines advances in three-way behavioral decision making (TW-BDM) with hesitant fuzzy information systems (HFIS) from the perspective of the past, present, and future. First, we provide a brief historical account of the three topics and present basic formulations. Second, we summarize the latest development trends and examine a number of basic issues, such as one-sidedness of reference points and subjective randomness for result values, and then report the results of a comparative analysis of existing methods. Finally, we point out key challenges and future research directions.

A novel fuel supply system modelling approach for electric vehicles under Pythagorean probabilistic hesitant fuzzy sets

Multiple attribute group decision making based on quasirung orthopair fuzzy sets: Application to electric vehicle charging station site selection problem

In the field of decision making, three-way decision making has been proven more fruitful for providing scopes to make delayed decision along with acceptance and rejection simultaneously. As a result, the decision risk and loss, which could occur due to take rapid decisions in traditional two-way decision making, are effectively reduced. Accordingly, this paper offers a novel three-way multi-attribute decision making model by combining three-way decision making and multi-attribute decision making under an incomplete information system. The incertitude in the information system is illustrated by introducing interval-valued Fermatean connection number based on interval-valued Fermatean fuzzy number and set pair analysis theory. Thereafter, the achievement of this study is five-fold. First, a possibility dominance relation is developed under incomplete information system in the basis of possibility degree measure of interval-valued Fermatean connection number. Second, we put forward a novel procedure to set up the fuzzy state set. Third, the conditional probability is estimated in light of the fuzzy state set and probability dominance relation. Fourth, the relative utility functions are determined in the virtue of regret theory. Lastly, a three-way multi-attribute decision making model is implemented in incomplete information system and exploited to deal with incomplete multi-attribute decision making problems. Eventually, the propriety, stability and superiority of the proposed model is established via conducting the comparative and experimental analysis. • Introducing a novel uncertainty, namely, interval-valued Fermatean connection number. • Developing a new approach to derive fuzzy state set and conditional probability. • Calculating relative utility functions by using regret theory. • Proposing a novel three-way multi-attribute decision making model. 

Regret-based three-way decision making with possibility dominance and SPA theory in incomplete information system

In real world, a typical decision-making problem in the medical field can be seen as an uncertain hesitant fuzzy multiattribute decision-making problem when existing experiences of decision-makers are insufficient. A three-way decision model is an effective tool to deal with uncertain decision-making problems, which can realize the classification of objects. However, different psychological behaviors of decision-makers are likely to affect decision-making results in actual decision-making processes. In order to address this challenge, we first propose a regret-theory-based three-way decision model in hesitant fuzzy environments, which mainly combines regret theory with hesitant fuzzy sets to calculate the perceived utility value of objects. Second, since one of the core ingredients for regret theory is the regret–rejoice function, we put forward a new regret–rejoice function that preserves the original indecisive uncertainty in hesitant fuzzy environments. In addition, according to the inherent relationship of the used data, this article provides a three-way classification method based on the preference ranking organization method for enrichment evaluations I method. Finally, the practicability, rationality, and superiority of the proposed method are shown via the case analysis and comparative analysis in the medical field.

Regret Theory-Based Three-Way Decision Model in Hesitant Fuzzy Environments and Its Application to Medical Decision

As a cause of interfering with routine activities, freezing of gait (FOG) is a severe syndrome of Parkinson’s disease (PD) and usually performs as an abrupt and momentary inability to effective stepping forward. Advanced wearable acceleration sensors based on socially implemented Internet of medical things (IoMT) devices can remotely provide a platform for recognizing FOG. However, due to the diverse data acquisition modes that appear in classic IoMT devices, the obtained data may contain imprecise, hesitant, and incomplete ones. Meanwhile, the bounded rationality owned by neurologists usually has a big impact on using wearable acceleration sensors to predict illnesses. Therefore, the objective of this article lies in exploring a fuzzy intelligence learning approach based on bounded rationality in IoMT systems and providing a valid scheme for biomedical data analysis. Specifically, a brand-new three-way group decision-making approach by means of TODIM (an acronym in Portuguese for interactive multicriteria decision-making) with incomplete dual hesitant fuzzy (DHF) information and its applications in detecting FOG in PD using IoMT devices are systematically explored. First, taking advantage of DHF sets (DHFSs) when depicting realistic group decision information, the concept of multigranulation (MG) incomplete DHF information systems is built. Second, adjustable MG DHF probabilistic rough sets (PRSs) are further put forward via DHF similarity relations. Third, a three-way group decision-making approach is constructed by virtue of adjustable MG DHF PRSs and TODIM. Finally, the validity, effectiveness, and practicality of the constructed three-way group decision-making approach are investigated by a University of California, Irvine (UCI) dataset with several experimental analyses in the background of FOG detection in PD using IoMT devices. The experimental result indicates that the developed fuzzy intelligence learning approach achieves reasonable diagnostic conclusions for FOG detection in PD from the perspective of uncertain information processing abilities, decision risks, and bounded rationality. 

Jianming Zhan

Papers

Regret Theory-Based Three-Way Decision Model in Hesitant Fuzzy Environments and Its Application to Medical Decision

Fuzzy Intelligence Learning Based on Bounded Rationality in IoMT Systems: A Case Study in Parkinson’s Disease

Incomplete three-way multi-attribute group decision making based on adjustable multigranulation Pythagorean fuzzy probabilistic rough sets

Three-Way Behavioral Decision Making With Hesitant Fuzzy Information Systems: Survey and Challenges

A regret-theory-based three-way decision method with a priori probability tolerance dominance relation in fuzzy incomplete information systems