| With the development and popularization of network information technology,the Internet has become the most heterogeneous,dynamic and open distributed database in the world.There exists ordernal data widely in the Internet,such as warehousing and logistics,ecological agriculture,investment risk analysis,and so on.Multi-criteria ordernal decision-making has become an important research issue in web information knowledge discovery and decision analysis.Rough sets theory is an effective mathematical tool to describe the heterogeneity of categorical data and information entropy is an important measure of information uncertainty.Rough sets model and entropy-based method are discussed with respect to multi-criteria ordernal decision-making in this work.The main contributions of this work are listed as follows.First,multi-granulation preference relation rough sets model is constructed for ordernal decision system.Rough sets is an effective approach to handle preference analysis.In order to solve multi-criteria preference analysis problem,this paper improves the preference relation rough sets model and expand it to multi-granulation case.Cost is also an important issue in decision analysis.Taking the cost into consideration,we also expand the model to cost sensitive multi-granulation preference relation rough set.Granule structure selection based on approximation quality is investigated and the algorithm is designed.Second,multi-granulation fuzzy preference relation rough sets model is constructed for ordernal decision system.Additive consistent fuzzy preference relation is introduced and the fuzzy preference relation rough sets model is reconstructed with additive consistent fuzzy preference relation.In order to solve the multi-criteria preference analysis problem,multi-granulation fuzzy preference relation rough sets model is defined.Taking cost into consideration,we also expand the model to cost sensitive multi-granulation fuzzy preference relation rough sets.Classification and sample condensation algorithms based on our models are investigated.Third,the concepts of preference inconsistence set,preference inconsistence degree and Preference Inconsistence Entropy(PIE)are proposed.As available information is usually obtained from different evaluation criteria or experts,the derived preference decisions may be inconsistent and uncertain.Shannon information entropy is a suitable measurement of uncertainty.This work proposes the concepts of preference inconsistence set and preference inconsistence degree and then preference inconsistence entropy is introduced by combining preference inconsistence degree and Shannon entropy.A number of properties and theorems as well as two applications are discussed.Feature selection is used for attribute reduction and sample condensation aims to obtain a consistent preference system.Forward feature selection algorithm,backward feature selection algorithm and sample condensation algorithm are developed.Fourth,aiming at the problem of preference decision in multi-criteria ordernal decision-making system,according to the preference inconsistency of ordernal decision,a preference decision method based on preference inconsistent entropy is proposed.Firstly,the Preference Inconsistence Entropy of Object(PIEO)is defined and used to measure the degree of inconsistency of preference of a particular sample with respect to the sample set.Then,according to the different attributes of the decision-making importance of the different characteristics in the preference decision,the weighted Preference Inconsistence-based Entropy of Object(wPIEO)is proposed.Moreover,combing wPIEO with attribute preference inconsistency entropy in measuring attribute importance,a weighting method based on attribute preference inconsistent entropy is proposed.Finally,a preference decision algorithm based on sample preference inconsistent entropy is proposed.After global Preference Inconsistent Entropy(gPIE)classification,the preference inconsistent entropty of each attribute is generally smaller than the entropy based on the inconsistent entropy classification based on the upward and downward prefernces,and it is closer to the preference inconsistent entropy of the original decisipon,which indicates that the classification base gPIE is better than the other two cases.The classificatipon deviation is as low as 0.1282,indicating that the classification results are close to the original decision.Fifth,a novel algorithm,called Condensation rule based on Fuzzy Rough Sets(FRSC),based on the FCNN rule together with fuzzy rough sets theory,is introduced to compute training-set-consistent subset for the nearest neighbor decision rule.In combination with fuzzy rough sets theory,the FRSC rule improves the performance of FCNN rule.Two variants,named as FRSC1 and FRSC2,of the FRSC rule,are presented.The FRSC1 rule is suitable for small data set and the FRSC2 adapts to larger data sets.Compared with the FCNN rule,the FRSC1 rule requires much less time cost and gets smaller subset for small data set.For medium-size data set,less than 5000 samples,the FRSC2 rule has better time performance than FCNN rule.This work develop two multi-granulation rough sets models,multi-granulation preference relation rough sets(mPRS)model with symbolic data,and multi-granulation fuzzy preference relation rough sets(mPFRS)model with numerical data,as well as preference inconsistent entropy(PIE),for ordernal decision system.Based on multi-granulation preference relation rough sets model,granulation structure selection algorithm is designed.Classification and sample condensation algorithms are addressed based on fuzzy multi-granulation preference relation rough sets model.Feature selection is used for attribute reduction and sample condensation aims to obtain a preference consistent system based on PIE.Aiming at the problem of preference decision,preference inconsistent entropy of object is introduced and a preference decision method is proposed.In order to compute training-set-consistent subset for the nearest neighbor decision rule,FRSC is introduced,too. |
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