Approximation Problem Of Intuitionistic Fuzzy Numbers

In recent years,fuzzy numbers and intuitionistic fuzzy numbers have been applied widely in various fields.It is easy to find that trapezoidal or triangular fuzzy numbers and trapezoidal or triangular intuitionistic fuzzy numbers are the most commonly used ones among these ap-plications.The issue about approximating general fuzzy numbers by trapezoidal or triangular fuzzy numbers have been elaborated on lots of literatures,but the research on approximation of intuitionistic fuzzy numbers is rare.Approximating general intuitionistic fuzzy numbers by real interval,trapezoidal or triangular fuzzy numbers can be found in existing papers,and ap-proximating general intuitionistic fuzzy numbers by trapezoidal or triangular intuitionistic fuzzy numbers remains a blank space.With the fast development of the high technology industry,en-gineering systems are growing in size and complexity.Reliability of systems has become one of the hot issues in engineering field.All failure rates of system components are presented by the same type of intuitionistic fuzzy numbers in many studies of reliability analysis of fuzzy systems.However,the situation rarely happens in reality.Few researches are found on system reliability about a system having components following different types of intuitionistic fuzzy failure rates.With respect to the above problems,the studies on the approximations of intu-itionistic fuzzy numbers and system reliability are presented in this thesis.The details are as follows:1.The methods of approximating general intuitionistic fuzzy numbers by trapezoidal and triangular intuitionistic fuzzy numbers are suggested respectively.Firstly,the existence and uniqueness of extended trapezoidal intuitionistic approximation are proved.The representation-s of approximating general intuitionistic fuzzy numbers by extended trapezoidal intuitionistic fuzzy numbers are discussed.Then the representations of trapezoidal or triangular intuitionistic approximation of intuitionistic fuzzy numbers are provided.The algorithms of trapezoidal or tri-angular intuitionistic approximation are given in order to apply conveniently the approximation methods.Finally,the problem of ranking general intuitionistic fuzzy numbers transforms into the problem of ranking trapezoidal intuitionistic fuzzy numbers by using the algorithms,which is simpler and more feasible compared with previous methods.2.The issue of approximation and aggregation of intuitionistic fuzzy numbers preserv-ing different parameters in different situations is investigated.The existence and uniqueness of weighted trapezoidal intuitionistic approximation are proved.The issue is addressed about ap-proximating the given intuitionistic fuzzy numbers or aggregating them and then approximating the output of aggregation preserving the expected interval by using weighted distance.A con-clusion is obtained that if we choose special aggregation operator.The issues of approximation and aggregation of intuitionistic fuzzy numbers preserving ambiguity,value and width by using Euclidean distance with similar method are investigated respectively.The conclusions can be used for aggregating intuitionistic fuzzy information and applied to multiple attribute decision making.3.The representations of approximating general intuitionistic fuzzy numbers by interval-value intuitionistic fuzzy numbers under some circumstances are found.The methods of interval-value intuitionistic approximation preserving expected interval,ambiguity and value,value and width are discussed for a type of intuitionistic fuzzy numbers,respectively.The repre-sentation provides an approach for transforming intuitionistic fuzzy numbers into interval-value intuitionistic fuzzy numbers in interval-value intuitionistic fuzzy environment when attribute vectors are composed of multiple information.And this representation proposes an convenient idea for solving the problem of heterogeneous multiple-attribute group decision making.This method is a better approach to heterogeneous multi-attribute group decision making which in-clude general intuitionistic fuzzy numbers.4.Reliability of fuzzy systems is studied with the application of trapezoidal intuitionistic approximating method proposed in this thesis.The representations of different type of intuition-istic fuzzy numbers approximating into trapezoidal intuitionistic fuzzy numbers and evaluation of the reliabil:ity of series and parallel fuzzy systems are done where failure probabilities of all components are represented by different types of intuitionistic fuzzy numbers based on arith-metic operations of trapezoidal intuitionistic fuzzy numbers.The approximation method ad-dresses the issue that failure probabilities of all components are represented by different types of intuitionistic fuzzy numbers.And arithmetic operations of trapezoidal intuitionistic fuzzy num-bers are adopted in the analysis of Reliability of fuzzy systems,which proves that it can save efforts of calculation compared with established methods mentioned above.At last the PCBA failure analysis proves that after the data are dealt with approximation,the fuzzy distribution is greatly reduced with higher confidence of the result compared with other calculations.