Three-way Multi-attribute Decision Making Methods And Applications Under Q-Rung Orthopair Fuzzy Linguistic Environment

In the multi-attribute decision-making(MADM)problem,the traditional twoway decisions theory not only has high requirements on the integrity of the information,but also can only give two results of accepting or rejecting.Based on two-way decisions,three-way decisions(3WD)allow decision makers(DMs)to make a third decision,that is,no-commitment decision-making,which can effectively reduce the risk or loss in the situation with incomplete information.With the increasing complexity of the multiattribute decision-making environment,it is often difficult to obtain accurate attribute evaluation values,and ambiguity has become a common phenomenon in decisionmaking problems.As the combination of linguistic terms sets and q-rung orthopair fuzzy sets in describing fuzzy information,q-rung orthopair fuzzy linguistic sets(qROFLSs)can provide DMs with more freedom in terms of information representation.This paper studies the three-way multi-attribute decision-making(3WMADM)problems under the q-rung orthopair fuzzy linguistic environment,the main work includes the following three parts:(1)Under the condition with known conditional probability,for the problem with association relationships between attributes,a 3WMADM method based on the q-rung orthopair fuzzy linguistic geometric Heronian mean operator(q-ROLGHM)is proposed.Firstly,a three-way multi-attribute decision-making model is established in q-rung orthopair fuzzy linguistic environment,and a set of decision-making rules based on the score function is given subsequently.Secondly,considering the advantages of integrating the relationship between attributes,this paper develops a group of Heronian mean operators of q-rung orthopair fuzzy linguistic number.The formulation and properties(idempotency,monotonicity,boundedness)are deduced further.Finally,the specific steps of our method based on q-ROLGHM operator are given,and the effectiveness is verified by an example.(2)Aiming at the 3WMADM problem with unknown conditional probability,a conditional probability estimation method is proposed based on VIKOR.Since the qrung orthopair fuzzy linguistic numbers(q-ROFLNs)cannot be directly processed in the calculation procedure of decision parameters,this paper utilized the shadow set to model the linguistic terms.The Euclidean distance between q-ROFLNs is derived further.Then,the distance measure information is integrated into the VIKOR method,and the conditional probability of the alternatives is estimated by calculating the tradeoff value.Finally,the method is applied to an enterprise venture capital problem,sensitivity analysis and comparative analysis are carried out subsequently.Considering the psychological behavior of decision makers in the face of gains and losses,a 3WMADM method based on prospect theory is constructed to solve problems in which the decision information is represented by q-ROFLSs.According to the attribute evaluation information,by establishing relative loss function and relative benefit function,the relative value function of alternatives is obtained firstly.Then,the conditional probability information is nonlinearly transformed to obtain the weight function.The comprehensive prospect value of the alternatives is used to establish3 WMADM rules based on the prospect score value.Finally,the method is explained using the enterprise venture capital problem.Under q-rung orthopair fuzzy linguistic environment,the 3WMADM methods studied in this paper can not only provide more free expression space in information representation,but also is able to obtain more scientific decision-making results,helping to reduce decision risk.The research not only enrich the relevant theories of the3 WMADM,but also provide methods and tools for practical problems such as investment decision-making.