| Because decision making is closely related to human thinking and cognition,decision science is a very complicated system science.In many real decision making processes,due to the complexity and uncertainty of the decision making problem,the fuzziness of human thinking and cognition and personal preferences of evaluation experts,a kind of uncertain decision making problems which include linguistic value data is formed.This kind of decision making problem containing linguistic information is always a difficult point in decision science research.Professor Zadeh set up fuzzy set theory in the 60s of last century,which provided a powerful tool for people to deal with vague linguistic information.But in practical applications,words can mean different things to different people,so everyone uses fuzzy sets to express words and uses different degrees of membership.In order to overcome the limitation of fuzzy sets in representing linguistic uncertainties by crisp membership degree,Zadeh introduced Type-2 fuzzy sets(T2FSs)and previous fuzzy sets are called Type-1 fuzzy sets(T1FSs).The membership function of the Type-2 fuzzy set is three dimensional,which provides more freedom and can directly control multiple fuzzy uncertain information.However,the three-dimensional membership function also brings high complexity to its understanding and operations,which makes it difficult to be used in the engineering and management environment that needs real-time operation.This greatly hinders development of theory and application of Type-2 fuzzy sets.In order to simplify the computation of Type-2 fuzzy sets,Mendel put forward the concept of interval Type-2 fuzzy sets(IT2FSs).Since then,many scholars have established interval Type-2 fuzzy multiple attribute decision making models from different aspects.However,theory and application about representation and computation of non-interval(general)Type-2 fuzzy set are stopped.In fact,it is of great theoretical and practical significance to extend interval Type-2 fuzzy decision models to(general)Type-2 fuzzy decision models.So,aiming at multiple attribute decision making problems with linguistic data,in this paper,the method of simulating linguistic value by using Type-2 fuzzy numbers is proposed,the analytic representation and computation of Type-2 fuzzy numbers are deeply studied,Type-2 fuzzy multiple attribute decision making models are established which provides a new idea for solving fuzzy multiple attribute decision making problems with linguistic data and mixed data.The main work of this paper is focused on the following aspects:(1)Research on mathematical foundation of type-2 fuzzy multi attribute decision making.The complexity of computation of Type-2 fuzzy sets comes from the complexity of its own representation.Type-2 fuzzy numbers are studied from a new perspective,which are regarded as the result of fuzzification of one or more parameters of Type-1 fuzzy numbers.Based on structured element,analytic representations of Type-2 fuzzy numbers are introduced,its arithmetic operations are simplified and the accurate calculation method and an approximation calculation method are provided for the centroid of the norm Type-2 fuzzy set.The theoretical preparation is made for the application of non interval Type-2 fuzzy numbers.The representations of real numbers,interval numbers,Type-1 fuzzy numbers and Type-2 fuzzy numbers are unified,which lays a foundation for solving hybrid fuzzy multi-attribute decision making problem.(2)Construction of three kinds of Type-2 fuzzy multiple attribute decision making models.In order to extend the interval Type-2 fuzzy decision making models to(general)Type-2 fuzzy decision making models,by defining three kinds of uncertainty measures of Type-2 fuzzy numbers,that is,ranking index,possibility degree and distances.Three kinds of Type-2 fuzzy multi-attribute decision making models are constructed which are Type-2 ranking value model,Type-2 possibility degree model and Type-2 fuzzy TOPSIS model.The proposed models can deal with hybrid fuzzy multi-attribute decision making which contain real numbers,interval numbers,Type-1 fuzzy numbers and Type-2 fuzzy numbers.Examples of linguistic value and hybrid data instances show that the proposed models are small in calculation,reasonable in decision-making process and reliable in results.The paper consists of 45drawings,21 tables and 120 references. |
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