The Improvement Of Interval Decision Making Method Based On KPCA And OWA Operator And Its Application Research

When human beings survive in an increasingly complex social environment,they often face many complicated decision-making(DM)problems.With the development of economies and societies changing,the decision-making environment has become more diverse and uncertain.In an uncertain environment,decision makers(DMs)prefer to give evaluation information with interval nature and uncertainty.Therefore,it has become a hot topic for scholars to choose which description method to describe decision information.This paper mainly focuses on the interval DM problem in three different environments:interval number,interval-valued q-rung orthopair fuzzy number(IVq-ROFN)and interval-valued Pythagorean fuzzy linguistic number(IVPFLN).(1)Under the environment of interval numbers,we propose a multi-attribute decision-making(MADM)method based on IB^r,q-OWA operator.The BON^r,q-OWA operator cannot aggregate attribute information in the form of interval numbers.Therefore,the BON^r,q-OWA operator is extended to the interval numbers,and the IB^r,q-OWA operator is defined.In addition,some properties of these operators,such as commutativity,monotonicity,and boundedness of the operator are studied.When the parameters change,it will further degenerate into mean,geometric aggregation operator,etc.We combine the IB^r,q-OWA operator with interval numbers ranking method based on Boolean matrix,and a DM model is established to make the decision results more reasonable.Finally,we give an example of investment enterprise evaluation and make a comparative analysis.(2)Under the environment of interval-valued q-rung orthopair fuzzy,we propose a MADM method based on interval-valued q-rung orthopair fuzzy IOWA operator.The IOWA operator has the characteristic of reordering parameters through induced variables,and the q-ROFIOWA operator can only make decisions in a deterministic environment.Therefore,the q-ROFIOWA operator is extended to IVq-ROFSs,and an interval-valued generalized orthogonal fuzzy IOWA operator is defined,namely the IVq-ROFIOWA operator.In addition,some properties of these operators,such as commutativity,monotonicity,and boundedness of the operator are studied.Finally,we give an energy plant evaluation example and make a comparative analysis.(3)Under the interval-valued q-rung orthopair fuzzy environment,from the perspective of distance measure,we propose a TODIM decision-making method based on interval-valued q-rung orthopair fuzzy distance measure.Considering the limitations of the existing interval-valued generalized orthogonal fuzzy distance measures,a new distance measure between IVq-ROFSs is proposed based on the constraints and hesitation of IVq-ROFS.Considering the psy-chological behavior of DMs and the limitations of traditional TODIM theory,a TODIM DM method based on IVq-ROFSs is proposed.Finally,a medical provider evaluation example is given and a comparative analysis is carried out.(4)Under the context of interval-valued Pythagorean fuzzy language environment,we propose an emergency group decision-making method based on the interval-valued Pythagore-an fuzzy language KPCA model based on TOPSIS.Most DMS prefer a combination of qualitative and quantitative in particular decisions.When the decision data has problems such as high dimension and data nonlinearity,the KPCA theory is used to reduce the dimension of decision information.First,we define the distance measure between interval value Pythagorean fuzzy language sets,and obtain a reasonable attribute weight and DMs weight through the cumulative contribution rate(CCR).The TOPSIS method is applied to the decision-making model.Finally,an example of emergency earthquake assessment is given and a comparative analysis is made.