Research And Application Of Multifactorial Decision-making On Type-2 Fuzzy Sets

With the development of society and the progress of science and technology,more and more decision-making problems occurred press for solution.Since most decision problems re-flect certain fuzziness and involve a variety of factors such as the inconsistency of decision expert knowledge,incomplete decision information,multiple decision objectives and uncertain decision environment etc,some fuzzy decision-making methods were put forward in the literature,such as fuzzy multi-attribute decision-making method,fuzzy multi-criteria decision-making method and fuzzy multiple objective programming method.With the increase of complexity of prob-lem,many difficulties encountered when the uncertainty in decision factors were represented by type-1 fuzzy sets,and thus type-2 fuzzy sets were used substituting for type-1 fuzzy sets in the representation of decision variables,and various decision making methods based on type-2 fuzzy sets were obtained.However,in various fuzzy decision-making methods,the specific role of factors in the decision-making process can not be reflected,which motives us to study the multifactorial decision-making method based on type-2 fuzzy sets in complex situation.The research is divided into the following contents:(1)Based on type-2 fuzzy sets and factor space theory,a multifactorial decision-making method based on type-2 fuzzy sets for known factor weights is proposed.In this method,type-2 fuzzy sets are used to represent the concept in factor space,and five kinds of multifactorial mappings are put forward.Then,a model of type-2 fuzzy sets based single-layer multifactorial decision-making(T2SLMDM)is formulated,and the theoretical foundation of T2SLMDM is analyzed.In the model,not only the fuzziness in decision phases can be reflected by tuning parameter,but also the specific role of factors can be reflected in the decision-making process.Finally,the proposed method is applied in scheme selection and cloth selection problems to verify the effectiveness and superiority.(2)To consider that factor weights in the complex problem are usually unknown or hard to estimate in advance,a new method of weight estimation based on the fuzzy analytic hierarchy process(AHP)is proposed.In the method,a fuzzy judgement matrix is established firstly,which is defuzzified by the incentre of triangular fuzzy number.And then,the extent analysis fuzzy incentre method is proposed,which calculates the relative important degree of factors by the incentre of the synthetic extent value,and avoids the case that the synthetic extent value in extent analysis fuzzy AHP method may be zero.The method is applied into a talent selection problem to verify the effectiveness.Finally,the algorithm complexity is compared with fuzzy least squares method and extent analysis fuzzy AHP method,and it is shown that the complexity of extent analysis fuzzy incentre method is lowest.(3)For a decision-making problem with various complicated factors,it is hard or impossible to complete all the decision making process once a time,and needs to be decomposed to some easy ones.To extend the generality of T2SLMDM and expand its application domain,a method of layered multifactorial decision making based on type-2 fuzzy sets(T2LMDM)is proposed,which can embody the specific role of factors in the decision-making process.In this method,a layered multifactorial structure model based on the factor space rattan theory is formulated firstly.Then,the T2LMDM method is proposed followed with theoretical foundation demonstration.Finally,the T2LMDM method is applied into the evaluation of teaching performance,and the decision result is explained intuitively by showing the specific role of factors.(4)To overcome the ranking failure existing in some common interval type-2 fuzzy sets ranking methods,the arithmetic operations of interval type-2 fuzzy sets is redefined,and two new interval type-2 fuzzy sets ranking methods are proposed.Firstly,the arithmetic operations of interval type-2 fuzzy sets is redefined by means of the definition of intuitionistic fuzzy sets,which can avoid the shortcomings in the existing arithmetic operations,and extend the applica-tion domain of interval type-2 fuzzy sets.Secondly,two ranking methods based on the incentre of fuzzy sets are proposed,which can overcome the ranking failure existing in other methods.Finally,a new method of multi-attribute group decision-making is proposed based on the tech-nique for order preference by similarity to ideal solution(TOPSIS),and the effectiveness of the proposed method is verified by an investment project evaluation.