Linguistic Q-Rung Orthopair Fuzzy Sets And Its Aggregation Operators

With the development of modern science,decision analysis theory has penetrated into all fields of society.While the decision theory is developing towards application,related quantitative models and methods are increasingly standardized.Considering the complexity and multi-faceted natures of the objects that will be evaluated,and psychological preference of decision makers,the linguistic intuitionistic fuzzy sets and linguistic Pythagorean fuzzy sets are undoubtedly effective description tools,which can solve the incomplete description problem of single data and facilitate decision makers to express information.In recent years,research on linguistic intuitionistic fuzzy sets and linguistic Pythagorean fuzzy sets has become an important topic.However,there still exist some shortcomings in the multi-attribute decision-making methods based on the linguistic intuitionistic fuzzy sets and linguistic Pythagorean fuzzy sets:(1)The description ranges of the linguistic intuitionistic fuzzy sets and linguistic Pythagorean fuzzy sets are limited and cannot fully express the information required for decision makers;(2)The operational laws of the linguistic intuitionistic fuzzy sets and linguistic Pythagorean fuzzy sets can lead to the lack of flexibility and invalid information of the results;(3)The related aggregation operators and multi-attribute decision making methods still need to be improved,and the robustness and effectiveness need to be further improved.In order to solve the above problems,the following research contents are carried out:(1)This paper proposes the concept of linguistic q-rung orthopair fuzzy sets,as well as a novel multi-attribute group decision-making method to solve the selection problem of nursing institutions.Firstly,in order to solve the problem that the description ranges of linguistic intuitionistic fuzzy sets and linguistic Pythagorean fuzzy sets are limited,the concept of linguistic q-rung orthopair fuzzy sets is proposed and the hesitation degree is defined.According to the score value and accuracy value,a comparison method for linguistic q-rung orthopair fuzzy numbers is proposed.Secondly,non-interactional operational laws and interactional operational laws are proposed for linguistic q-rung orthopair fuzzy numbers.Then,combing with the linguistic q-rung orthopair fuzzy set,interactional operational laws and partitioned geometric Heronian mean operator,the linguistic q-rung orthopair fuzzy interactional partitioned geometric Heronian mean(Lq ROFIPGHM)operator is proposed and applied to the multi-attribute group decision making.A novel multi-attribute group decision-making method is proposed.Finally,the novel multi-attribute group decision-making method is applied to the selection of nursing institutions to prove its effectiveness and superiority.(2)To reduce the influence of extreme values on the result of Heronian mean operator,this paper proposes the linguistic q-rung orthopair fuzzy Dombi power Heronian mean(Lq-ROFDPHM)operator and its multi-attribute decision making model based on this novel aggregation operator.Firstly,the operational laws based on Dombi T-norm and T-conorm under linguistic q-rung orthopair fuzzy environment information is proposed.Secondly,the power mean operator is combined with the Heronian mean operator,the Lq-ROFDPHM operator is proposed and its related properties are studied.Then,the novel aggregation operator is combined with the MULTIMOORA method,and a novel multi-attribute decision making method is proposed.Finally,the novel decision-making method will be applied to the VR head show evaluation case.(3)To further show the influence of the correlation between the attributes on the aggregation results,this paper proposes the linguistic q-rung orthopair fuzzy partitioned Maclaurin symmetric mean(Lq-ROFPMSM)operator.Firstly,the Lq-ROFPMSM operator is proposed,and its Idempotency,Boundedness and Monotonicity are studied.Secondly,a linguistic q-rung orthopair fuzzy partitioned dual Maclaurin symmetric mean(Lq-ROFPDMSM)operator is proposed.Finally,a multi-attribute decision-making model is constructed based on this novel aggregation operator and its effectiveness is validated by examples.