Uncertain probabilistic linguistic multi-criteria decision-making models: Applications in evaluation systems

Resumen

Generally, multi-criteria [HXD10] evaluation means that the decision makers (DMs) do evaluations based on the multiple criteria which cannot be substituted for each other. In the current complex and changeable decision-making environment, the DMs are often hard to quantify the criterion accurately. Therefore, it is necessary to invite the relevant experts to qualitatively analyze and hierarchically semi-quantitative describe those criteria that are di¿cult to be quanti¿ed or can¿t be quanti¿ed in the process of evaluating alternatives. Meanwhile, there are usually multiple evaluators involved in the evaluation process. The combination of the uncertainty of objective things, the limitation of human cognitive level and the ambiguity of thinking mode has caused a situation that the experts cannot always provide the well-measured evaluation information. Hence, how to realize the inter-conversion between qualitative and quantitative and re¿ect the ability of soft reasoning in language expression always has been a hot topic in the evaluation of uncertain systems and decision-making areas. Probabilistic linguistic term sets (PLTSs) [PWX16], which can adopt the qualitative and quantitative form to show the decision-making information, are suitable for dealing with the evaluation problems of uncertain system in the decision-making process. Moreover, considering the advantages of the PLTSs, Lin et al. [LXZY17] proposed the probabilistic uncertain linguistic term sets (PULTSs) constructed by the PLTSs and the uncertain linguistic variables [Xu06b]. PULTSs inherit the good properties of both. From the angle of the composition of the elements, it keeps the non-determinacy of the uncertain linguistic variables. Combined with the homologous proportions of the given uncertain linguistic variables, it fully demonstrates the intricacy of the decision-making environment and the uncertainty of the DMs. Since its inception, its research mainly focuses on the basic measure [LXZY17] and the consensus [XRXW18], the other research is very few, such as the research for the consistency for the probabilistic uncertain linguistic preference relations (PULPRs), the research for incomplete probabilistic uncertain linguistic preference relations (IPULPRs) and so on. Choosing the applicable linguistic evaluation scale is the foundation of making fuzzy linguistic decision-making. The two most commonly used linguistic evaluation scale are additive linguistic evaluation scale [BFP97, Xu04b, Xu06b, Xu05, Xu15] and the multiplicative linguistic evaluation scale [Xu04a, Xu06a]. In general, the most commonly used additive linguistic evaluation scale is a zero-centered symmetric linguistic evaluation scale [Xu05] and its subscript is almost uniformly distributed. The multiplicative linguistic evaluation scale is a locally heterogeneous linguistic evaluation scale. This thesis based on the multiplicative linguistic evaluation scale [Xu06a] de¿nes the probabilistic uncertain multiplicative linguistic term sets (PUMLTSs) and the corresponding probabilistic uncertain multiplicative linguistic preference relations (PUMLPRs). As we all know, for a variety of reasons, DMs are impossible to grasp all the involved knowledge of the decision-making problem. Therefore, the incomplete decision-making phenomenon is common. This thesis studies the management of incomplete probabilistic uncertain multiplicative linguistic preferences in decision-making. Moreover, based on the idea of dual hesitant fuzzy sets [ZXX12], the PLTSs is extended to the dual probabilistic linguistic term sets (DPLTSs) [XXR17]. The DPLTSs that can contain both the membership degree and non-membership degree. While the membership degree represents the epistemic certainty, and the non-membership degree represents the epistemic uncertainty. It can make the DMs ¿exibly give their suggestions and reduce the irresolution of the DMs for one thing or another when it is hard for them to reach a ¿nal agreement to some extent. For now, the research of DPLTSs is still in the new stage. Whether the basic concepts or the decision-making methods has a large research space. Therefore, it is necessary to improve existing uncertain probabilistic linguistic multi-criteria methods or develop new methods on the application of uncertain evaluation system. In terms of measures, the superiority of correlation coe¿cient is to demonstrate the inter-relationship of the variables. This thesis studies the correlation coe¿cient between the DPLTSs, the weighted correlation coe¿cient, the entropy, comparable degree and distance measure. Moreover, as for decision-making methods, based on the de¿ned weighted correlation coe¿cient, the thesis provides the multi-attribute decision-making method. As for the comparable degree, it is essentially similar to the distance measure. On the foundation of comparable degree, the thesis constructs the dual probabilistic linguistic grey relational analysis multi-criteria decision-making method. After that, with regard to preference relations, this thesis de¿nes the dual probabilistic linguistic preference relations (DPLPRs), then based on the de¿ned distance measure studies the consistency of the DPLPRs. Furthermore, this thesis based on the comparable degree studies the consensus of DPLPRs. Furthermore, in order to demonstrate the validity of proposed theories and methods, this thesis extracts decision problems from recent high-pro¿le events, such as 5G, arti¿cial intelligence, cloud computing and so on. Then this thesis applies the proposed theories and methods to those decision-making problems and veri¿es the e¿ectiveness and feasibility. Overall, for the research of probabilistic uncertain linguistic decision-making, the innovation points of the thesis can be summarized as follows: (1) Rede¿ne the possibility degree between the PULTSs for acquiring the priority; (2) De¿ne the PUMLTSs on the multiplicative linguistic label and the PUMLPRs; (3) Consider the incomplete PUMLPRs; (4) Put forward pertinently the corresponding repairing method to obtain complete PUMLPRs; (5) Probe the consistency of the PUMLPRs. For the research of dual probabilistic linguistic decision-making, the innovation points of the thesis can be divided as follows: 1) It de¿nes the dual probabilistic linguistic correlation coe¿cient and the weight dual probabilistic linguistic correlation coe¿cient. Then describes the multi-attribute group decision-making problem under the dual probabilistic linguistic context, divides the weight vector into the subjective and objective forms, de¿nes the entropy measure for the DPLTSs for the sake of obtaining the ¿nal comprehensive weight vector, and introduces the complete dual probabilistic linguistic multi-attribute group decision-making process. Moreover, it uses a simulation experiment related to the in¿uence evaluations for AI to clarify the feasibility and practicality of the dual probabilistic linguistic multi-attribute group decision-making process. 2) It de¿nes the dual probabilistic multiplicative linguistic term sets (DPMLTSs), the basic operations among the DPMLTSs, the comparable degree between the individual dual probabilistic multiplicative linguistic preference relations (DPMLPRs), and study the consistency, consensus of the DPMLPRs. Then it computes the weights of criteria, introduces the expanding grey relational analysis (EGRA) method, and the integrated multi-criteria decision-making procedure. Moreover, it utilizes a simulation case relevant to the cloud computing industry to clarify the potential and reality of the dual probabilistic multiplicative linguistic multi-criteria group decision-making procedure. 3) It constructs a new multi-criteria decision model based on the incomplete dual probabilistic linguistic preference relations (IDPLPRs). It ¿rst proposes a step-by-step repairing method to repair the linguistic section and probabilistic section of IDPLPRs separately. The superiority is that this step-by-step method conforms to the principle of element generation. After that, the consistency index based on the distance measure between the DPLPRs is de¿ned to check and improve the consistency of DPLPRs. Then the weights of criteria can be obtained by information fusion. Moreover, it constructs optimistic and pessimistic data envelopment analysis models under the dual probabilistic linguistic environment to do the sorting process. Optimistic and pessimistic data envelopment analysis models can demonstrate the e¿ciency of each decision-making unit (DMU) from the perspective of the most and least favorable. Finally, it simulates a cased of 5G industry market to help enterprises choose appropriate 5G partners by using proposed methods.