Research On Multi-attribute Decision Making Problem In Management And Fractional Operator Method

Multi-attribute decision making is an important research direction ofmanagement science and engineering, as well as an important branch of modernscientific decision making. Its theories and methods, no matter in theory or in practice,have been widely used in engineering design, economic management, military affairsand other fields. The environments of the decision problems become indeterminableand the issues involved are more complex as the rapid changes of society. Hence, theresearch about the new methods of multi-attribute decision making becomes the focusof attention for many researchers, while the theories and methods of operator havebeen occupied an important position in the study of multi-attribute decision making.In this dissertation, the methods and applications of multi-attribute decision makingare studied with the help of the idea of fractional differential operators, and some newresults are obtained, mainly include as follow:In chapter one, the research background, purpose and significance areexpounded. The research status of the method of fractional differential operators andthe theory of multi-attribute decision making are described for a comprehensiveoverview, and the main contents and approaches of this dissertation are summarized.In chapter two, the Cauchy problem of fractional differential equations involvedtime delay and impulse is studied. The criteria of the solvability and uniqueness of theCauchy problem are proposed by declaring the existence of the fixed points of thecorresponding fractional differential operators. These results generalize theconclusions in relevant references and provide new theoretical basis to solve theequilibrium problems of economic and management.In chapter three, some boundary value problems for coupled systems offractional differential equations are discussed. At first, a kind of multi-pointsboundary value problems for a coupled system of sequence fractional differentialequations is discussed, and then another kind with impulse interference is alsoconsidered. The equations discussed are transformed into the operator equation L (u, v) N (u, v)by establishing the proper Banach spaces. Moreover, the sufficientconditions and criteria about the solvability of the coupled systems are obtained byusing the coincidence degree theory as the main tool. These results generalize themain conclusions in relevant references in many aspects.In chapter four, fractional differential operator in the case of time scale isresearched. The obtained results greatly broaden the scope of its applications.Meanwhile, these results provide the theoretical support for some practical problem ineconomic and management.According the multi-attribute decision making problems with the type of realnumbers for attribute values, in chapter five, the new concept of generalizedprecedence ordering number is provided by constructing the fractional rankingnumber of compare between various attribute values. On this basis, generalizedprecedence ordering method of multi-attribute decision making is proposed.Meanwhile, the concept of time degree is introduced according to the model of timeseries-based multi-attribute decision making. The optimization model of the timeweight vector is proposed by means of the idea of closeness degree. On this basis, thenew approach for time series-based multi-attribute decision making is provided.Moreover, the method of dynamic multi-attribute decision making is given byanalyzing the dynamic weight method based on TOPSIS. The time weight and therelated attribute weight are dynamic, reflecting the dynamics of decision makinginformation, more conforming to the law of development.In chapter six, an appropriate partial order relation is established based on theformula of possibility degree according to the multi-attribute decision makingproblem in the case of interval number. Then the expression of generalizedprecedence ordering number is introduced, and on this basis, the optimization modelof the attribute weight and time weight is proposed based on the idea of variancemaximization. Finally, the approach for solving the interval multi-attribute decisionmaking problem is proposed.In chapter seven, in the2-tuple linguistic sense, the generalized precedenceordering number for linguistic multi-attribute group decision making is provided bytransforming the linguistic assessment into2-tuple linguistic. In this sense, the optimization model of the attribute weight is constructed, thereby, the generalizedprecedence ordering method of linguistic multi-attribute group decision making isproposed.In chapter eight, the choice and ranking problem of chemotherapy regimen forfour kinds of non-small cell lung cancer (NSCLC) is considered by using the idea ofmulti-attribute decision making based on fractional differential operator. There arethree decision attributes (clinical efficacy, adverse reaction, survival rate) areinvestigated by means of the data of medical case of illness surveyed. The threeattributes are analyzed by using the generalized precedence ordering number andfractional differential operator. The best chemotherapy regimen of NSCLC isobtained with the help of calculating the generalized precedence ordering number ofeach regimen.Chapter nine sums up the main contents, processes, and conclusions in thisdissertation, and puts forward the aspects needing refinement and in-depth researchdirections in the future.