Research On Fuzzy Linguistic Multiple Criteria Decision Making And Its Application

In the multi-attribute decision-making problem,because of the complexity of the environment and the fuzziness of people's cognition,it is very difficult for the decision makers to evaluate the problem with the exact value.At this time,people often use the linguistic value instead of the numerical value to evaluate the problem.Therefore,fuzzy linguistic multi-criteria decision making,that is,the evaluation value of alternatives is the linguistic value,has become the important research in multi-criteria decision making.In this paper,we consider the multi-criteria decision making based on the hesitant fuzzy linguistic set,the Fermatean fuzzy linguistic set and the linguistic q-rung orthopair fuzzy set,and apply the corresponding method to the practical decision problems in real life.The main contents are as follows:In Section 1,the current research situation of fuzzy linguistic set theory and TOPSIS method is briefly reviewed,and the main contents and structure of this paper are introduced.In Section 2,the relevant knowledge of decision making theory,the fuzzy linguistic set,the linguistic scale function and TOPSIS method is sorted out.In Section 3,we first define the cosine similarity measure and Euclidean distance measure between hesitant fuzzy linguistic sets(HFLTSs).Furthermore,a new similarity measure between HFLTSs is constructed based on the cosine similarity measure and Euclidean distance measure,and it is satisfied the axiom of similarity measure.Then according to the relationship between similarity measure and distance measure,the corresponding distance measure between HFLTSs is obtained.Furthermore,we generalize the TOPSIS method to the obtained distance measure of the HFLTSs.Finally,a case study is conducted to illustrate the feasibility and effectiveness of the proposed method,which is compared to the existing methods.In Section 4,the cosine similarity measure and Euclidean distance between Fermateam fuzzy linguistic set(FFLTSs)are defined based on the linguistic scale function.On this basis,we propose a new method to construct a similarity measure between FFLTSs based on the linguistic scale function,which not only combines the cosine function and Euclidean distance measure but also satisfies the axiom of the similarity measure.The corresponding distance measure is obtained according to the relationship between the distance measure and similarity measure,and it is applied to TOPSIS method.Furthermore,we develop the TOPSIS multicriteria decision making method under Fermatean fuzzy linguistic environment.Finally,in order to verify the effectiveness of the proposed method,the ranking results of the same numerical example are compared and analyzed with the existing methods.In Section 5,some new operations of linguistic q-rung orthopair fuzzy sets(Lq-ROFSs)are defned based on the semantics of linguistic term sets.Then we propose the linguistic q-rung orthopair fuzzy weighted average operator and linguistic q-rung orthopair fuzzy weighted geometric operator based on the new operational laws.Furthermore,the Minkovski distance measure based on the linguistic scale function and Lq-ROFS is proposed,which overcomes the shortcomings of the existing distance measure and satisfies the axiom of the distance measure.Then we develop the TOPSIS method based on the Lq-ROFS.Finally,the feasibility analysis of postgraduate entrance quality evaluation is carried out.The comparative analysis of the proposed method and existing methods are provided to show its validity.Some conclusions and future research are proposed in Section 6.