Knowledge Acquisition On Multi-source Intuitionistic Fuzzy Information Systems

Artifieial intelligence is a hotspot in the theory and application of information sci-ence.With the rapid development of computer science and technology,especially the rapid development of computer networks,a large amount of data information has been generated in all fields of human production and life.The ty pes and scales of these data information are becoming more and more complex,forming a large amount of high-dimensional data information with complex types and heterogeneous formats.Among them,structured data is still one of the main expressions of data information in infor-mation systems,usually expressed by the structure of two-dimensional data tables.In order to study the uncertainty of information system deeply,many scholars put forward a series of data analysis theories including fuzzy set theory,intuitionistic fuzzy(IF)set theory,rough set theory,formal concept analysis(FCA)theory and evidence theory from different perspectives.These theories play an important role in the process of knowledge discovery and data processing.The organic combination of these theories is of great sig-nificance to the in-dep th mining of the hidden information behind the data and the more accurate knowledge representation in the data,system.As an important extension of the theory of fuzzy sets,by considering the member-ship,non-membership and hesitation of the three aspects of information,IF set model is more flexible and practical in dealing with ambiguity and uncertainty.In recent y ears,the combination of IF set theory with rough set theory and evidence theory has attracted wide attention.Based on the existing theories and models,this dissertation takes IF infor-mation system as the research object,uses rough set theory,IF set theory,multi-adjoint theory,evidence theory,concept lattice theory and so on as tools to study the attribute reduction,rule extraction,information fusion and multi-attribute decision-making.The main contents include:similarity neasurement of IF sets,multi-granulation IF decision rough sets based on it,attribute reduction and rule extraction of generalized dominant multi-granulation IF rough sets,IF rough sets based on multi-adjoint,theory,construction of IF group decision methods based on multi-adjoint theory,and generalized IF one-side concept lattice.The works are as follows:(1)In the theory of IF sets,similarity measure is a very important measurement of uncertainty.According to the atomic definition of IF similarity measure,many scholars have given different methods for calculating IF similarity.These methods often have some unreasonable aspects in practical calculation.A novel similarity measure is presented by the combination of the information carried by hesitancy degree and the endpoint distance of membership and nonmembership,respectably.Moreover,a numerical example is used to verify the reasonable of the proposed similarity measure.After that,the similarity measure is applied to construct the IF decision-theoretic rough set(IF-DTRS)model and multigranulation IF decision-theoretic rough set(MG-IF-DTRS)model.Some proper-ties of IF-DTRS and MG-IF-DTRS are also investigated.Thirdly,based on granular significance,a novel approach of optimal granulation selection is formulated.Finally,a heuristic algorithm is designed and the effectiveness of this algorithm is demonstrated by an illustrative example.(2)Decision-theoretic rough set(DTRS)was proposed by Yao in 1990.in which Bayesian risk analysis was introduced in classical rough set theory.It has strong the-oretical basis and reasonable semantic interpretation.Subsequently,DTRS was further extended to inulti-granulation decision-theoretic rough set model(MG-DTRS).Consider-ing that IF sets and MG-DTRSs have strong advant ages in information representation and information processing,respectively.Constructing MG-IF-DTRSs model in multi-source IF information systems is one of our research contents.According to the newly defined IF similarity,we construct similarity relations and similarity classes in IF information systems.The IF-DTRSs and the MG-IF-DTRSs models are defined.By selecting thresh-old values,the concept,s of optimistic and pessimistic approximate distribution reduction under ?-down and ?-up are introduced into the MG-IF-DTR.Ss model,and the optimal granularity selection problem in multi-granulation space is analyzed.The granular im-portance is defined based on multi-granulation optimistic and pessimistic ?-down and?-up approximate distribution quality.A granular reduction algorithm for approximate distribution reduction under a-down is proposed.(3)The dominance relation rough set model is the main method of data mining when researching order information systems.The traditional IF dominance relation only judges the size of two IF numbers by the absolute difference between membership de-gree and non-membership degree(score function)and the suin of membership degree and non-membership degree(accuracy function),and then obtains the dominance relation in IF information system.This method ignores the natural semantics expressed by IF sets.Therefore,the definition of new IF dominance relation is one of our research con-tents.Firstly,three kinds of dominance relations and three kinds of dominance classes are defined by using triangular norms and triangular conorms in IF decision informa-tion sy stem.Secondly,generalized dominance-based multigranulation intuitionistic fuzzy rough set model is proposed and the belief structure of this model is discussed under evi-dence theory.Then.attribute reduction is acquired by the importance of granularity and attribute.Finally,considering that the approximated set of decision attributes is an IF set.according to the idea of multi-granulation,a decision rule with the logical connector"or" in the IF decision information system is constructed.(4)Multi-adjoint triples are generalization of t-norms and their resituated implica-tions which satisfy the adjointness property.Since they preserve their main properties as well as they help to increase the flexibility of the operators used for computation in the considered framework.Combined with rough set theory,researchers introduced multi-adjoint fuzzy rough set,which increases the number of applications that rough set theory can be used.Furthermore,using the multi-adjoint triples,a relationship was established between two objects.constructs rnulti-adjoint IF rough sets by using a family of adjoint triples under IF information system.Finally,an approximate reduction method is given by defining a dependence of the positive region.(5)Decision-making(DM),as an important of human thinking and cognitive activity,widely exists in every field of human social life.With the rapid development of econo-my and society,a man's wisdom is often limited while facing with a large and complex decision problem.Therefore,group decision-making is especially necessary.The member-ship and the non-membership are used to describe the relationship between the objects and attributes,which makes the hesitant degree to be clearly described.IFSs depict more exquisite,and the membership degree,the non-membership degree and the degree of hesitation are implied in the decision-making behavior to accept,reject,and cannot be determined(hesitation).Dempster-Shafer evidence theory,as a general generaliza-tion of Bayesian theory,has a strong advantage in dealing with uncertain,incomplete and even ambiguous information without prior probability and conditional probability density.Therefore,the multi-adjoint theory and D-S theory are applied to intuitionistic fuzzy group decision,which can effectively enhance the ability of the model to deal with intuitionistic fuzzy decision-making problem.At the same time.different use of adjoint triples increases the flexibility to deal with fuzzy decision-making problems.(6)FCA is one of the effective mathematical tools for data analysis and knowledge discovery.No matter the classical or fuzzy formal context,the aequisition of information is often a single aspect.However,in the process of cognition,people tend to show pos-itive,negative or hesitant results.IF set as a naturally and intuitive generalization of fuzzy sethas a stronger ability to express the ambiguities of information in the real word.Two pairs of adjoint mappings were defined in intuitionistic fuzzy formal context by using triangular norms and triangular conorms.And we vitrified that both adjoint mappings formed Galois connection.After that,two types of generalized one-sided intuitionistic fuzzy conept lattices were constructed and the main theorems and propositions were also carefully checked.Finally,we propose a discernibility matrix based attribute reduc-tion algorithm and the effectiveness of this algorithm is demonstrated by an numerical example.