28-09-2016, 11:22 AM
1456549565-FinalPaper250216.docx (Size: 53.2 KB / Downloads: 4)
ABSTRACT
All real world knowledge is characterized by incompleteness, imprecision and inconsistency fuzzy set theory provides the possibility of defining inexact medical entities as fuzzy sets. It offers a linguistic concept with excellence approximation to texts. In addition, fuzzy logic presents powerful reasoning methods capable of handling approximate inferences. These facts make fuzzy set theory highly suitable for the development of computer based diagnostic and treatment recommendation systems. The query processing Information retrieval systems based on fuzzy sets theory have been proposed as an improvement of Boolean logic models to handle uncertain information. In this paper, the knowledge based fuzzy information retrieval method based on concept networks by using concept matrix for knowledge representation in which elements in a concept matrix represents relevant values between the concepts .The implicit relevant value between the concepts can be inferred by the transitive closure of the concept matrix based on fuzzy logic and also used a document retrieval based on extended concept networks with four kinds of fuzzy relationships between concepts, that is fuzzy positive association, fuzzy negative association, fuzzy generalization and fuzzy specification. This provides evidence for fuzzy Matrix Theory as an inference tool to formalize Medical Processes.
0 INTRODUCTION
Uncertainty of knowledge about the patient and about medical relationships is generally accepted and considered to be an inherent concept in medicine. The physician, however, is capable of drawing conclusions from this information .Naturally, these conclusions are approximate rather than precise
In medicine, the principle of “Measuring everything measurable and trying to make measurable that which has not been measurable so far” (G.GALILEI) still exists but its limitations have become obvious in the century.
In fact, all real world knowledge is characterized by
Incompleteness hence the human process of cognition is infinite.
Imprecision as indicated by HEISENBERG’s Uncertainty Principle.
Inconsistency anticipated by GODEL’s Theorem.
Fuzzy Set Theory developed by ZADEH[1] provides the possibility of defining inexact medical entities as fuzzy sets .it offers a linguistic concept (ZADEH[2], ZADEH[3]) with excellent approximation to medical texts. In addition, fuzzy logic (ZADEH [4], BELLMAN and ZADEH [5]) presents powerful reasoning methods that can handle approximate inferences.
These facts make fuzzy set theory highly suitable for the development of computer based diagnostic and treatment recommendation system [6].
The Medical expert system CADIAG-2 {7, 8, 9] provides evidence for fuzzy set theory as a mathematical tool to formalize medical processes.
The query processing Information retrieval systems based on fuzzy sets theory have been proposed as an improvement of Boolean logic models to handle uncertain information. In this paper, the knowledge based fuzzy information retrieval method based on concept networks by using concept matrix for knowledge representation in which elements in a concept matrix represents relevant values between the concepts .The implicit relevant value between the concepts can be inferred by the transitive closure of the concept matrix based on fuzzy logic.we present a method in detail for concept networks with only one kind of fuzzy relationship between concepts and illustrate with suitable examples. We discuss a method for document retrieval based on extended concept networks with four kinds of fuzzy relationships between concepts, that is fuzzy positive association, fuzzy negative association, fuzzy generalization and fuzzy specification.
2.0 EXPERIMENTAL METHODS
2.1 Concept Networks
A concept network includes nodes and directed links .Each node represents a concept (or) a document. Each directed links connects two concepts (or) directs from one concept to a document. Let us consider a network with n concepts {c_1,c_2,….c_n} and m documents {d_(1 ) ,d_2….,d_m }. if c_i □(→┴µ c_j ) , ,then it indicates that the degree of the relevance from concept c_i to concept c_j is µ where µ ∈[0,1]. if c_i □(→┴µ d_j ) ,then it indicates that the degree of relevance of document d_j with respect to the concept c_i is µ,where µ ∈[0,1].Let F(c_i,c_j ) denotes the relevant value from concept c_i to c_j .The relevant value from concept c_ito concept c_j and the relevant value from concept c_j to c_k are given, that is F(c_i,c_j ) and F(c_j,c_k )are known ,then F(c_i,c_k ) is defined as follows F(c_i,c_k )= min { F(c_i,c_j )F(c_j,c_k )} ….. 1.1
Similarly if F(c_1,c_2 ),F(c_2,c_3 ))….and F(c_(n-1),c_n ),then
F(c_1,c_n )=min{F(c_1,c_2 ),F(c_2,c_3 )…F(c_(n-1),c_n )} ….. 1.2
Definition 1.1
Let {c_1,c_2,….c_n} be a set of n concepts. A concept matrix C=(c_(ij )) is an n x n fuzzy matrix, where c_(ij )=F(c_i,c_j ) is the relevant value from the concept c_i to the concept c_j and〖 c〗_ij∈[0,1] satisfying the following properties:
i. Reflexive : F(c_i,c_j )=1 for each i= 1 to n
ii. Non- symmetric : F(c_i,c_j )≠F(c_j,c_i )
iii. Transitivity: F(c_i,c_k )≥max〖min{F(c_i,c_j )F(c_j,c_k )〗}
Note 1.1
For A∈∱_n,A^(k+d)=A^k holds some positive integers k and d, under the max-min product of fuzzy matrices. This property leads to the following definition.
Definition 1.2
Let M be a concept matrix of order n .Then there exists an integer p≤ n-1,such that under the max-min product of fuzzy matrices, M^(P )=M^(P +1 ) =M^(P+2 ) and T= M^p is called the transitive closure of concept matrix M.
Note 1.2
In case, the relevant value between concepts are represented by real intervals in [0, 1], instead of crisp real number in [0, 1] then the concept matrix is an interval valued fuzzy matrix .The transitive closure is also an interval value fuzzy matrix.
A query is an expression of one (or) more factors combined by disjunctive (or) conjunctive Boolean operation. For instance “More or Less “ big and not “ very” heavy is an example of query. Here ‘big ‘ is an abbreviation of the term ( size = big ) in a relation having a domain called size .Likewise the value ‘heavy’ is an abbreviation .Each user’s query ‘Q’ can be represented by a query descriptor vector (q ) ̅=(x_1,x_2,…x_n ) , that is Q={(c_1,x_1 ),(c_2,x_2 )…(c_n,x_n ) } where x_i∈[0,1] for i = 1 to n , indicates the degree of strength that the desired documents contains concept c_i .In a query descriptor vector (q ) ̅ if x_i=0 then documents desired by the user must not contain the concept c_i. Further if the user feels that certain concepts may be neglected in the query processing ,then the user need not have to assign the degrees of strength with respect to such concepts in the query descriptor vector (q ) ̅.The symbol ‘-’ is used to label a neglected concept. Therefore if x_i=‘-’,then it indicates that concept c_i is a neglected concept that is c_iwould not be considered in the document retrieval process.
Definition 1.3
Let {d_(1 ) ,d_2….,d_m }be the set of documents and {c_1,c_2,….c_n} be the set of concepts in a concept network with m documents and n concepts .A document descriptor matrix D = (d_ij) is an m x n matrix ,where d_ij is the degree of relevance of document d_i with respect to concept c_j.
The document descriptor matrix D* = DT where D is the document descriptor of the network and T is the transitive closure of the concept matrix indicates the degree of the relevance of each document with respect to specific concepts and is used as a basis for similarity measures between queries and documents . We shall illustrate the above basic concepts in a concept network with suitable examples.