Methodology Study On Multi-attribute Decision Making With Preference Dependence

The traditional multi-attribute decision making model(TMADMM)assumes that all the attribute are preference independent,and then it is not suitable to handle the decision problem with attributes that are preference dependent.For this reason,Grabisch substitutes attribute-set for attribute weight in TMADMM,and provides Choquet integral model(CIM)to deal with alternative's preference value in multi-attribute decision making with preference dependence(MADM-PD).Due to the ability to handle the preference dependence between attributes,the CIM is attracting wide attention from foreign and domestic scholars,and is being used to solve decision making problem with and without hierarchy structure.However,the CIM have some drawbacks in theory and practice.First,the CIM in MADM can't reflect the point-dependence preference relationship depend on attribute preference value.Second,the decision maker is required to estimate too many attribute-set capacities,which is also called the exponential complexity problem of attribute-set capacity determination.Third,the Cumulative Prospect Theory(CPT)is incapable to explaining both the Allias behavior and the strong choice behavior,and the current academic on value functions is inconsistent.If we could solve the drawbacks mentioned above,it has important meaning to improve the ability to deal with complex decision making problems.Our work is focus on the following.At first,this paper analyse the current situation of the decision making method with preference dependence facing to simple system structure and to hierarchical system structure,and makes a comment on the theory basis of the research.For simple system structure,both the CIM for MADM(CIM-MADM)and the multiple factor decision-making method based on variable weights(MFDMM-VW)have serious technical shortcomings on reflecting reasonably the decision-maker's point-dependence preference in multiple attribute decision-making.To overcome the current approaches' shortcomings,a new MADM approach to evaluation and decision making,i.e.,the MADM model with relative variable weights(MADMM-RVW),and its corresponding method are presented based on two techniques,i.e.,the swing-weighting and the analytic network process,and the relative evaluation thought embodied in data envelopment analysis.Applied in a case study,the MADMM-RVW is showed to give decision conclusions well consistent with objective existence and the decision-maker's qualitative opinions on preference dependence,and thus to be capable of better and more reasonably reflecting the decision-maker's specific preference behaviors.For the drawback of CPT which is used to determine the preference value on attribute,i.e.,incapability of explaining both the Allias behavior and the strong choice behavior,and solve current academic inconsistence on value functions,this paper provide an inclusive value function(IVF)which is more general than every kind of value functions known in literature and an evaluation model for the prospect value,called prospect value model approximate to CPT(shorted as PVM-CPT),is constructed.For the attribute value corresponding to CIM,the CPT is incapable to explaining both the Allias behavior and the strong choice behavior,and the current academic on value functions is inconsistent.To overcome the drawbacks mentioned above,an(IVF)is firstly presented with reference to Need-Hierarchy Theory and especially through integrating CPT with Range-Frequency Theory(RFT).Note that,the IVF is more general than every kind of value functions known in literature.Then,with the CPT value function(CPTVF)taken as an approximation to the IVF,an attribute value model is constructed and a value function(called approximate CPTVF)endogenously dependent on the model is given.Finally,based on the approximate CPTVF,an evaluation model for the prospect value,called prospect value model approximate to CPT(shorted as PVM-CPT),is constructed.Data analysis shows that the PVM-CPT can not only explain both the Allias behavior and the strong choice behavior,but also under comparable conditions of input information draw evaluation conclusions highly consistent in those given by CPT.These analysis results have directly verified the rationality of the PVM-CPT w.r.t.the original model and indirectly verified that of the IVF w.r.t.the CPTVF.For the judgment of attribute-set capacity,the capacity judgment pattern which is based on the definition of attribute-set importance can not reflect decision makers' real preference due to the ambiguous definition of importance.For this problem,a capacity judgment pattern,called MGL judgment pattern has been presented in which the decision makers' preference on special alternative corresponding to an attribute-set capacity is expressed on seven-semantic scale.However,there are inconsistencies between the judgment information provided by MGL capacity judgment pattern(shorted as inconsistency problem)due to the two drawbacks of its adopted seven-semantic scale.First,seven semantic scales is not enough to describe decision makers' preference.Second,the preference differences corresponding to seven semantic scales may not be of arithmetic progression as they fixed.Differently,in traditional multiple attribute decision making,the swing weighting pattern in which the decision maker is required to make ratio judgment on preference change of special alternative,can not only overcome the ambiguous definition of importance,but also can avoid the inconsistency problem causing by semantic scale.Based on the above considerations and to overcome the inconsistency problem in MGL capacity judgment pattern,a new capacity judgment pattern,called swing weighting capacity judgment pattern with multi-attribute,is presented through extending swing weighting pattern in traditional multi-attribute decision making to attribute-set swing weighting.Empirical analysis shows that swing weighting capacity judgment pattern is superior to MGL capacity judgment pattern,not only on the reliability of capacity judgment but also on the reliability of alternative rank.Thus,swing weighting capacity judgment pattern is more feasibility in practical application.For the exponential complexity problem of attribute-set capacity determination,the two fuzzy measures namely the ?-measure and the k-order measure,as well as attribute-set capacity calculation(ASCC)models based on these two measures,have been presented in literature.However,they are suffered from impracticality in many decision cases due to arbitrary hypotheses on preference dependence relationship.The impracticality embodies in two aspects.One is the unfeasibility of measurement pattern,the other is the inaccurateness in capacity calculation.To overcome the impracticality of the ?-measure and the k-order measure,a new measurement pattern on attribute-set capacity,called sandwich measurement pattern(SMP),is proposed based on such a strategy of balancing the feasibility of attribute-set capacity determination with the accurateness of ASCC.Then,a linear programming model for ASCC corresponding to SMP,shorted as LPM-SMP,is presented.In specific,the model determines an attribute-set capacity through restricting it between the minimum and maximum of attribute-set capacities of the same order,and squeezing it into a particular range by theoretical quantitative relationships of attribute-set capacities.Besides,the attribute-set capacity given by LPM-SMP satisfies other constraints built on the judgment information of the decision maker.The judgment information is of three types.The first is on the attribute-set capacity ranks,the second is on the numerical values of low-order attribute-set capacities,and the third is on the minimum and maximum attribute-set capacities within a high-order capacity rank.Data simulation analysis shows that SMP is not only more feasible than the k-order measure,but also greatly superior in calculation accurateness to the ?-measure and the k-order measure.As a result,SMP is more applicable to real-world decisions of MADMPDR.For the hierarchical system structure,there are two problems within the approach built on CIM for hierarchical MADM,called TOYLC-AHP.First,it does not in effect guarantee the satisfaction commensurability that CIM requires.Second,its adopted MACBETH-based method for determining the capacities of attribute sets,also suffers from making judgements on non-specific alternatives.To develop TOYLC-AHP,the prescriptive commensurable method(PCM)for alternatives' satisfaction values on multiple attributes,is proposed to measure the commensurable satisfaction values(CSV)of alternatives' performances on the specific attributes in a hierarchy.Based on PCM,a judgement mode for determining attribute-set capacities,similar to the swing weighting mode widely used in simple MADMs,is firstly presented to help DMs to make meaningful preference comparisons.Then,based on the new judgement mode and PCM,a new approach called targets-oriented analytic hierarchy process for ordinal preference dependence(ToAHPOPD)is given to substitute for TOYLC-AHP.A case study shows that ToAHPOPD is able to make better discriminations on alternatives than TOYLC-AHP,and thus verified to be superior to TOYLC-AHP.At last,through the cases of the investment risk assessment of project in T coal enterprise and the site selection of Y farmer specialized cooperative society,it is shows that the method of multiple attribute decision making with relative variable weights is more rationable than the CIM-MADM and the MFDMM-VW,and the To AHPOPD is more rationable than the TOYLC-AHP.