Fuzzy Logic Information Retrieval Model

Fuzzy Logic Information Retrieval Model Ferddie Quiroz Canlas, ME-CoE

Fuzzy Logic and Information Retrieval. • Fuzzy sets, fuzzy reasoning, null values. • Fuzzy logic in information retrieval. • Fuzzy query, retrieval process. • Common objections to fuzzy logic. • Conclusion.

LotfiZadeh introduced the theory of Fuzzy Logic in his paper, Fuzzy Sets (1965). • Fuzzy Logic provides a method of reducing as well as explaining the system complexity Theory of Fuzzy Logic The Idea of Fuzzy Sets Fuzzy sets are functions that map a value, which might be a member of a set, to a number between zero and one, indicating its actual degree of membership A degree of zero means that the value is not in the set, and a degree of one means that the value is completely representative of the set.

Characteristic Function: Conventionally we can specify a set C by its characteristic function, Char C(x). If U is the universal set form which values of C are taken, then we can represent C as C = { x | x  U and Char C(x) = 1} This is the representation for a crisp or non-fuzzy set. For an ordinary set C, the characteristic function is of the form Char C(x): U  {0,1} However for a Fuzzy set A we have Char F(x): U  [0,1] That is, for a fuzzy set the characteristic function takes on all values between 0 and 1 and not just the discrete values 0 or 1. For a fuzzy set the characteristic function is often called the membership function and denoted by F(x)

An example: By using conventional method we can call a person “TALL” if the height is 7 feet and a person with height 5 feet is NOT TALL. That is we represent the person is either “TALL” or “NOT TALL” in Boolean Logic 1 or 0, 1 for “TALL” and 0 for “NOT TALL” Fuzzy sets may be used to show the relationship or degree of precision: If S is the set of all people in the Universe, a degree of membership is assigned to each person in set S to find the subset TALL. The membership function is based on the person’s height. TALL(x) = 0, if Height(x) < 5’, (Height(x) – 5’ )/ 2’ if 5’<= Height(x) <= 7’ 1, if height(x)> 7 feet

Degree of relationship

Benefits of Fuzzy System Modeling • Ability to Model Highly Complex Business Problems • Ability to Model System Involving Multiple Experts • Reduce Model Complexity • Improve Handling of Uncertain and Possibilities

Fuzzy Logic in IR Fuzzy Model Overview A fuzzy model, like traditional Expert and Decision Support System, is based on the input, process, output flow concept. A fuzzy model differs in two important properties: What flows into and out of the process, and the fundamental transformation activity embodied in the process itself

Information flow in Fuzzy System

Basic Fuzzy Databases Approaches Fuzzy Relation : A fuzzy relation is a subset of the set cross product P(D1) X P(D2) X …X P(Dm) Membership in a specific relation, r, is determined by the underlying semantics of the relation. Fuzzy Tuples and Interpretation A fuzzy tuple t, is any member of both r and P(D1) X P(D2)X…XP(Dm)

The simplest form for a fuzzy database is the attachment of a membership value ( numeric or linguistic ) to each tuple. For a query POLLUTED_SITE, the membership values denotes the degree to which the tuple belongs within the relation. Each tuple corresponds to a site and its particular major source of pollution

POLLUTED_SITE SITE_ID POLLUTATN ps L121 Dioxin 1.0 M555 Oil 0.7 By11 Wastewater 0.6 M441 Mercury .95 F65 Landfill 0.3

QUERY1: What are the opinion of the resident F on environmental effects of pollutant? R1 = (  ( POLLUTANT, EFFECT) ( ( NAME = F) (SURVEY) ) This yields the temporary relation R1: R1= { [ Oil Severe], [Dioxin Extreme], [Water Tolerable] }

SURVEY Querying Fuzzy Relational Databases In systems that are relationally structured and using fuzzy set concepts, nearly all developments have considered various extensions of the relations algebra. Pollutant Name Effect Type Oil A Limited Expert Oil B Extreme Resident Water C Moderate Resident

Data Storage and Retrieval Process When a query is made for the address of a Person the archived data is clustered according to the various criteria, e.g., by similar street names, within the same zip code or by similar last name It constructs and attaches to a window discription a set expression for which an example (Cluster1  Cluster3)  ( Cluster2  Cluster3) Several properties of clusters are relevant. Each Cluster entry is a key value followed by a set of archived record numbers.

Example: If the destination is city is unambiguous and if “Plz” is detected as part of a street name, There might exist a cluster classified among other destination city clusters and whose key entries are street names and abbreviations The contents of this cluster might appear as: Pizza / { 50873, 109234, 231709} Place / { 25670, 43831, 331992 } Plaza / { 12909, 234144}…. Given the “Plz” example just shown, each of the key match to a certain extent. One measure of how well each matches is based on the number of changes necessary to copy a prefix of the key in the cluster entry onto the detected street name.

Common Objections to Fuzzy Logic • Much of the opposition to fuzzy logic is based on the misconception • Fuzzy logic invites the belief that the modeling process generates imprecise answers

Conclusion • The exact directions and extent of future developments will be dictated by advancing technology and market forces • Fuzzy logic is a tool and can only useful and powerful when combined with Analytical Methodologies and Machine Reasoning Techniques

Thank you So MuCH!

Fuzzy Logic Information Retrieval Model