| Intelligent information processing is an important research content of computer science and technology.In the intelligent information processing,there exist many uncertain information.As a kind of typical uncertain information,2-dimension fuzzy linguistic information can not only describe the assessment of objects,but also describe the reliable judgment about the evaluation of objects.There are comparable and incomparable relations among 2-dimension fuzzy linguisitic information,while lattice implication algebra can simultaneously describe the comparable and incomparable relations of uncertain information.This dissertation mainly focus on the theory of 2-dimension fuzzy linguistic information,then considers its application.By connecting the structures of 2-dimension fuzzy linguistic information and lattice implication algebra,2-dimension linguistic lattice implication algebra is founded;Then the derivation structure of 2-dimension linguistic lattice implication algebra is discussed;Further the representation models and computational models of 2-dimension fuzzy linguistic information are investigated;After that,the different measurement notions of 2-dimension fuzzy linguistic information are defined;Finally,the measurement theory of 2-dimension fuzzy linguistic information is given to application.The main contents of this dissertation include the following parts:Part 1,2-dimension linguistic lattice implication algebra is founded,then the derivations of 2-dimension linguistic lattice implication algebra are investigated.After 2-dimension linguistic lattice implication algebra is founded,the comparable and incomparable relations among 2-dimension fuzzy linguisitic information can be described by using of 2-dimension linguistic lattice implication algebra;Then the notion of derivation is introduced to 2-dimension linguistic lattice implication algebra,the characteristics of derivation in 2-dimension linguistic lattice implication algebra are investigated,some special derivations including isotone derivation,embedding derivation,isomorphism derivation and regular derivation,are discussed in 2-dimension linguistic lattice implication algebra,finally the derivations of some algebraic substructures which include ideals,sl-ideals and LI-ideals,are investigated in 2-dimension linguistic lattice implication algebra.Part 2,the concept and operations of 2-dimension fuzzy linguistic set are given,and the distance and similarity measures of 2-dimension fuzzy linguistic set are investigated.Firstly,the notion of 2-dimension fuzzy linguistic set is defined by extending fuzzy linguistic set,then the operations of 2-dimension fuzzy linguistic set including intersection,union,complement and implication,are discussed along with the properties of these operations;Then the distance measures of 2-dimension linguistic label are given,which include general distance measure,general similarity measure,Hausdorff distance measure,Hausdorff similarity measure and hybrid distance measure;Based on the distance and similarity measures of 2-dimension linguistic label,the distance and similarity measures of 2-dimension fuzzy linguistic set are defined,and the simple applicaitons of these measures are discussed.Part 3,the 2-tuple representation model and computational model of 2-dimension fuzzy linguistic information are founded,and the expection,variance,correlation,correlation coefficent and entropy measures of 2-dimension fuzzy linguistic information are discussed.Firstly,by extending the linguistic 2-tuple from one dimension to 2-dimension,we found the 2-tuple representation model and computational model of 2-dimension fuzzy linguistic information,then investigate the properties of aggregation operators of 2-dimension fuzzy linguistic information;Then the expection of 2-dimension linguistic label is defined,and the properties of the expection are investigated;By using of the expection of 2-dimension linguistic label,some measures of 2-dimension fuzzy linguistic set,which include expection,variance,correlation and correlation coefficent,are researched along with the characteristics of these measures;Finally,the entropy measures of 2-dimension linguistic label and 2-dimension fuzzy linguistic set are investigated.Part 4,the representation model and computational model of 2-dimension hesitant fuzzy linguistic information are founded,and the expection,variance,correlation,correlation coefficent and entropy measures of 2-dimension hesitant fuzzy linguistic information are discussed.Firstly,hesitant fuzzy linguistic set is redfined,then the score founction and hesitant fuzzy degree function of hesitant fuzzy linguistic set are given;The representation model and computational model of 2-dimension hesitant fuzzy linguistic information are founded by extending hesitant fuzzy linguistic label to 2-dimension hesitant fuzzy linguistic label;Next,the expection of 2-dimension hesitant fuzzy linguistic label is defined,and the properties of the expection are investigated;Based on the expection of 2-dimension hesitant fuzzy linguistic label,some measures of 2-dimension hesitant fuzzy linguistic set including expection,variance,correlation and correlation coefficent,are investigated along with the characteristics of these measures;Finally,the entropy measures of 2-dimension hesitant fuzzy linguistic label and 2-dimension hesitant fuzzy linguistic set are given.Part 5,the measure theory of 2-dimension fuzzy linguistic information is given to application.At first,the aggregation operators of 2-dimension fuzzy linguistic information with 2-tuple are applied to aggregate 2-dimension fuzzy linguistic information with 2-tuple,then compared with the existing aggregation methods of 2-dimension fuzzy linguistic information;Then the distance measures of 2-dimension fuzzy linguistic information with 2-tuple are applied to pattern recognition;Further,the distance measures and entropy measures of 2-dimension fuzzy linguistic information are used to determine the attribute weight vector;Next,the aggregation operators of 2-dimension hesitant fuzzy linguistic information are discussed to aggregate 2-dimension hesitant fuzzy linguistic information;Then the entropy measures of 2-dimension fuzzy linguistic information are used to determine the attribute weight vector;Finally,the correlation coefficent measures of 2-dimension hesitant fuzzy linguistic information are applied to pattern recognition.All the above applications to pattern recognition are supplied with the concrete algorithms along with the corresponding R software programs. |
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