| With the rapid development of intelligent technology,especially in artificial intelligence technology,it is more and more urgent and important to improve the efficiency and satisfaction of the system task execution via the efficient human-machine collaboration.Moreover,it has already appeared in various fields,such as intelligent manufacturing,military,aeronautics and astronautics,etc.The human-machine task allocation,as a core problem of human-machine cooperation,has issues on how to scientifically and reasonably determine the task domain or the work domain between human and machine.Thus,it is helpful that human and machine can establish a more reasonable division of labor and a more mutual trust mechanism with cooperation.However,the research on this aspect is still in the exploratory stage.Therefore,this paper combines the complementary advantages of both the subjective evaluation of intuitionistic fuzzy sets and the objective knowledge acquisition of decision-theoretic rough sets(DTRSs)together.Then,we study three-way intuitionistic fuzzy decision(3WIFD)methods based on DTRSs from both sides of the acquisition of their condition probability and the determination of their probability thresholds.Thus,these methods can obtain the results of three-way classification,which provide a novel solution to soft solving strategies for the human-machine task allocation.Specific research contents and innovations of this paper mainly include the following four aspects:(1)A 3WIFD method is proposed based on intuitionistic fuzzy information systems.For some issues on existing intuitionistic fuzzy similarity degrees(IFSDs)without considering practical semantics of membership and non-membership degrees,and some IFSDs exist counterintuitive results in some cases,we develop a novel intuitionistic fuzzy similarity degree.Then,the proposed measure is introduced into the intuitionistic fuzzy information system,and the concept of(α,β)-level cut set is defined under this measure.Meanwhile,the(α,β)-lower and upper approximation of the objective set and its three regions of positive,negative and boundary regions are induced by using the rough membership function served as the evaluation function.Furthermore,an intuitionistic fuzzy three-way decision model with multiple risk preferences is con-structed using the Bayesian decision theory and then the corresponding thresholds are induced.Based on which we propose a 3WIFD method on the basis of intuitionistic fuzzy information systems,and apply it to the task assignment of aircraft expected operations.(2)An approach to 3WIFD is proposed based on the rankings of intuitionistic fuzzy numbers.With respect to the problem where the developed 3WIFD method above leads to information loss in the conversion of an intuitionistic fuzzy loss function matrix,we analyze the advantages and disadvantages of six types of intuitionistic fuzzy ranking methods with the aid of existing intuitionistic fuzzy achievements and opertions.Based on that,two classes of 3WIFD mechanisms are respectively designed by considering the intuitionistic fuzzy single ranking function and the intuitionistic fuzzy double ranking function.Finally,these two mechanisms are unified into the framework of three-way decisions,and we then propose a novel 3WIFD approach based on these two ranking functions.(3)A 3WIFD method is developed based on an equivalent model of DTRSs.Considering,in some cases,the existing methods have difficulty in the determina-tion of probability thresholds of DTRSs under the intuitionistic fuzzy environment,we study an equivalent model for classical DTRSs from optimization views.After that,this model is respectively extended to the determination of interval linear and nonlinear rankings-based interval DTRSs,linear and nonlinear rankings of triangular fuzzy numbers-based triangular fuzzy DTRSs and linguistic DTRSs,and thus the corresponding optimization models are constructed to determine the pair of thresholds.The theoretical analysis and experimental results show that,the proposed models not only obtain the same numerical solution to the thresholds as existing methods under these linear ranking methods of fuzzy numbers,but also derive their numerical solution under the nonlinear ranking methods.This illustrates the feasibility and validity of the proposed equivalent models.Inspired by these ideas,we extend these models to the determination of probability thresholds of DTRSs with intuitionistic fuzzy semantics,and thus establish similar nonlinear optimization models.Meanwhile,the existence and uniqueness of their optimal solutions are theoretically proven.With the help of optimization technology,we search for optimal solutions to these models and then determine the threshold pair.Therefore,our method can overcome the shortcomings of existing approaches having difficulty in determining the thresholds under nonlinear ranking approaches to these fuzzy numbers.At last,the proposed models and methods are applied to the operation task allocation on manned spaceflights.(4)An approach to three-way intuitionistic fuzzy group decisions(3WIFGD)is proposed based on intuitionistic fuzzy aggregating operators.Most of the traditional 3WIFD models are based on an intuitionistic fuzzy loss function matrix given by the single decision maker,but there are few researches on the evaluations of intuitionistic fuzzy loss function matrix given by multiple decision makers.In fact,only one decision maker usually exists one-sidedness and singularity of evaluation behaviors.For this type of problem,we utilize the intuitionistic fuzzy weighted average operator and the intuitionistic fuzzy weighted geometric operator to aggregate different intuitionistic fuzzy preference losses given by decision makers,and obtain the collective intuitionistic fuzzy group preference loss.Thus,the models for determining the thresholds of IFDTRSs are proposed under the group decision environment.Moreover,the 3WIFGD mechanism and algorithm are respectively designed based on intuitionistic fuzzy aggregating operators.Finally,we take a mission assignment of aircraft expected operations as examples to discuss the applications of proposed method in Human-machine task allocation.In a word,this paper systemically investigates 3WIFD methods by combining intuitionistic fuzzy sets and DTRSs together,and we further apply these methods to the Human-machine task allocations with different scenarios.The study not only enriches the theories of intuitionistic fuzzy sets,decision-theoretic rough sets and three-way decisions,but also broaden the application scope of these theories. |
