Several Extensions Of Type-2 Fuzzy Theory And Their Applications

Fuzzy theory is an important part of the theory of uncertainty,which is used to solve many complex problems of objective reality.With the continuous improvement of people's cognitive level,the classical fuzzy theory has become increasingly mature,when people turn to study type-2 fuzzy theory and its application in order to cope with more complex problems.In this paper,the similarity measure,distance measure,soft set and interval type-2 fuzzy set are studied by using type-2 fuzzy context as principal line.This paper is divided into three main parts,these works in concrete are mainly as follows:In the first part,we introduce the concept,connotation and operation of type-2 fuzzy sets and define the distance measure under the type-2 fuzzy environment.According to the idea of maximizing deviation,we establish a nonlinear programming model to determine attribute weights based on the proposed type-2 fuzzy distance,this distance measure is used in multiple attributes decision making through TOPSIS method.This paper also defines similarity measure for type-2 fuzzy sets,then we compare with those results that are calculated by other several common similarity formulas to highlight its effectiveness and feasibility;finally,a net-making clustering algorithm is presented based on the type-2 fuzzy similarity degree,and the widespread data following Gauss distribution in daily life is successfully made reasonable clustering via a practical example.In the second part,we combine effectively the soft set theory with the type-2 fuzzy set.We first propose the concept of type-2 fuzzy soft set,and define its operations,then discuss its properties.At last,we make two aspects of applications about group decision making and pattern recognition by using the flexibility that soft set describes thing and the comprehensiveness that type-2 fuzzy set portrays matter.The third part first introduces the interval type-2 fuzzy set,then simplifies the set down to interval type-2 fuzzy number by its essence,and extends to the interval type-2 trapezoidal fuzzy number(IT2TrFN),on the basis of this concept,studies their operation rules;secondly,analytic hierarchy process(AHP)is applied to IT2TrFN and we get an interval type-2 fuzzy AHP to obtain weight vector;and then construct the likelihood for IT2TrFNs' binary size relationship in order to compare two IT2TrFNs and establish a preference relation under interval type-2 fuzzy information;finally,this article gives a decision method where the decision information is semantic form whose basic thinking is to transform linguistic variables into IT2TrFNs,and ultimately determines the overall ranking value for all alternatives.With that,we can rank those alternatives through a certain preference order and select the optimal one.