Research On Several Interval Orthopair Fuzzy Multiple Attribute Decision Making Methods

With the continuous development of society and the increasing complexity of the decision-making environment,multi-attribute group decision-making has gradually become an important research domain of modern decision theory and decision science.Due to the uncertainty of decision-making,Zadeh not only proposed the concept of fuzzy set,which greatly improves the accuracy and completeness of information expression in the decision-making process,but also introduced the degree of membership and non-membership and extended the fuzzy set to the intuitionistic fuzzy set.On this basis,Yager proposed the Pythagorean fuzzy set,which combines the membership degree and non-membership and the degree is extended to the spatial range where the sum of squares does not exceed 1.Later,Yager established the Orthopair fuzzy set,and extended the membership and non-membership to the spatial range where the sum of q power does not exceed 1.The acceptable Orthopair space is also expanding as q increases,which greatly improves the ability of decision makers to judge the appropriate degree of membership in a given situation.In this paper,the multi-attribute decision making problem based on Orthopair fuzzy environment is deeply studied and explored.The main research work is as follows:The first chapter mainly introduces the research background and significance of the multi-attribute decision-making method based on Orthopair fuzzy numbers interval Orthopair fuzzy numbers,and analyzes the current research status and derives the main research content of this article.In chapter 2,the concepts of intuitionistic fuzzy set,Pythagorean fuzzy set,Orthopair fuzzy set and interval Orthopair fuzzy set are introduced,and then calculation formula and comparison of Orthopair fuzzy number and interval Orthopair fuzzy number are briefly investigated.Chapter 3 shows two multi-attribute group decision-making methods based on Orthopair fuzzy similarity measures.Firstly,the Orthopair fuzzy similarity measures based on gray correlation degree and Theil inequality coefficient are given respectively,and the comparison of the two fuzzy similarity measures is studied.Secondly,the attribute weights determination models based on the Orthopair fuzzy similarity measures of gray correlation degree and Theil inequality coefficient are constructed respectively.Finally,the multi-attribute decision making methods of Orthopair fuzzy similarity measures based on grey correlation degree and Theil inequality coefficient are proposed,and the proposed new methods are applied to the real estate investment decision making to illustrate the rationality and effectiveness of the method.Chapter 4 proposes a multi-attribute decision-making method based on the q-rung interval Orthopair fuzzy power average operator.First,the relevant definitions and properties of the power average(PA)operator and the definition of standardized Hamming distance are introduced.Then,a novel q-rung Orthopair fuzzy power average(q-RIVOFPA)operator is defined,and its expression is analyzed.At the same time,it is proved that the proposed operator has three properties: idempotency,boundness and commutativity.Subsequently,a multi-attribute decision-making method based on the q-RIVOFPA operator is established,and the feasibility and effectiveness of the method are proved by comparing the evaluation cases of automobile procurement with the existing methods.The influence of the parameter q on the decision results is also analyzed.In chapter 5,the TOPSIS method is extended to the q-rung interval Orthopair fuzzy environment,and a q-rung interval Orthopair fuzzy TOPSIS model is developed.Firstly,the q-rung interval Orthopair fuzzy distance measure is defined,and the q-rung interval Orthopair fuzzy standardized Hamming distance is proposed,and its properties are studied.And then,based on the q-rung interval Orthopair fuzzy distance measure,a q-rung interval Orthopair fuzzy multi-attribute group decision experts weights determination model is constructed.At the same time,a TOPSIS decision-making method based on the q-rung interval Orthopair fuzzy distance measure is proposed.Finally,this new method is applied to the selection of the optimal health industry investment project plan,and the sensitivity analysis of the parameters is investigated to highlight the feasibility and effectiveness of the new method.In chapter 6,a new VIKOR multi-attribute decision making method based on fuzzy distance measure is proposed for multi-attribute decision making with interval Orthopair fuzzy numbers.Firstly,a new interval orthopair fuzzy distance measure is put forward,and its properties,including non negativity,monotonicity,reflexivity and triangular inequality,are studied.At the same time,a VIKOR method based on interval Orthoair fuzzy distance measure is presented and applied to multi-attribute decision-making method.In the end,The feasibility and effectiveness of the developed method are verified by case analysis.Finally,the conclusions of this paper are summarized,and the future research direction is prospected.