Keywords. Ontology, mechanism theories, content theories, t-norm, t-conorm, multiinformation systems, Boolean aggregation.

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1 Intelligent Information Systems Morteza Anvari Computer Science Division University of California Berkeley CA Keywords. Ontology, mechanism theories, content theories, t-norm, t-conorm, multiinformation systems, Boolean aggregation. Abstract. In this article, we will discuss certain specific aspects of information systems that lend themselves to infusion of artificial intelligence methods and techniques. We recognize three information layers in an information/knowledge base system, i.e. the ontology (or ontic) layer, the metadata layer, and the data layer. The word ontology refers to a branch of metaphysics that explores the nature of Being. Following Martin Heidegger (German philosopher ), we use the word ontic to refer to being in the restricted sense, in this case an information system. The three layers represent a conceptual hierarchy from higher to lower levels of abstraction (or from lower to higher levels of specificity.) The ontic layer may be domainindependent, comprising generic organizing concepts of any knowledge base or may be domainspecific, e.g. ontology of a tourist information system. The Ontic Layer. This normally refers to the layer, which contains high-level concepts that organize the upper parts of a generic knowledge base. But it may also refer to the organizing elements of a domain-specific knowledge area such as a tourist knowledge base. Thus, the distinction between the ontic layer and the domain knowledge layer is that the former contains the vocabulary and the conceptual building blocks in the knowledge base and the latter contains the knowledge itself. For instance, in medicine the ontic layer of a patient knowledge base may contain the definition of such terms as "malaria" and "meningitis". At the data layer, a patient knowledge base contains patient-specific data, such as test results or timeline of diagnosis and treatment. By the same token, in a tourist information system, such terms as "vertical drop" and "cultural events" must be described in the ontic layer. But specific ski resorts or art festivals are included in the data layer. The importance of the ontic layer lies in its role as conceptualizer as well as agent/ facilitator for sharing ontologies among knowledge bases. As conceptualizer, the ontic layer describes and clarifies both domain-dependent and domain-independent terms that are used in a knowledge base. There is often no sharp division between domain-dependent and domain-independent terms, but rather, there is a spectrum of decreasing abstractness from the domain-independent to the domain-dependent terms. For instance, terms like space, time, event, object, attribute (or feature), and relation (among objects) are quite generic. They can appear in any ontology. The ontic layer also defines the context in which linguistic terms express approximate values for attributes and relations. For instance, the attribute price may take on a fuzzy value like inexpensive which means two different things when applied to a meal and to an airline ticket. In addition, as conceptualizer, the ontic layer can make a distinction between a role that an object plays and its conceptual relationship with other objects. In a university database, there are several classes of people including students, professors, employees, males and females. While males and females are always subclasses of the class humans, the types students and employees are roles that certain humans play. This distinction, between roles

2 and subclasses, is necessary since some students may be employees sometimes, or they may cease to be students at some other point in time. But students always constitute a subclass of the class humans. The lexicon of the ontic layer should include the term, its synonyms, its conceptual parent (superclass) as well as its siblings and its ancestor. Related terms, which act as operators on the object, are also listed. For example, in the entry for class hotel the following terms are listed. Lexicon and Lexical Links ID Type Set Size Sample Entries for Hotel R1 synonym 4 Motel, Inn, Lodge R2 ancestor 2 Accommodation term R3 parent term 1 Lodging R4 sibling term 1 Bed and Breakfast R5 related term 4 Reservation, Booking, Billing, operators Check-in, Check-out Fig. 1 In AI, mechanism theories refer to the set of theories concerned with algorithmic, heuristic, and other methodologies including neural nets, fuzzy logic, genetic algorithms, frame languages, and rule-based systems. Mechanisms are designed to enhance machine intelligence quota (MIQ). Content theories, on the other hand, concern the classes of objects, their properties, and the interrelationships that characterize the objects in a specific knowledge domain. The ontologies are content theories even when they relate to domain-independent concepts. The ontic layer may be described by means of augmented predicate calculi, semantic nets, fuzzy hypergraphs or other knowledge representation schemes or a combination thereof. The advantage of predicate calculus is that it allows dealing with propositional attitudes such as believe, think, hypothesize, and expect. Thus the ontic layer contends with facts, rules, beliefs, hypotheses, and predictions. When an ontology is domain-dependent, it is often task-dependent as well. This results from the fact that different tasks, as defined by different users, often require different aspects of reality. For this reason it would be prudent to consider, to the extent possible, different tasks that users may expect the knowledge base to perform. In summary, we need ontology for the following functions: To enable a platform to use the knowledge in some application. To enable multiple platforms to share their knowledge. To help oneself understand some area of knowledge better. To help other people understand some area of knowledge. To help people reach a consensus in their understanding of some area of knowledge. If semantic net is used to represent ontology, then for each term in the lexicon a link is established between the term and the relation that contains the data corresponding to the concept. 2

3 In Fig. 2, the lower half of the Figure depicts the ontology of Hotel represented by a semantic net. The upper half of the Figure is the relation Hotel that contains the data about individual hotels. The hotel ontology points to the relation Hotel by a link. Relation Hotel Name address rating etc Fig. 2 accomodation lodging hotel operators motel inn lodge B&B Boolean Combinations By an atomic query we mean a query in which only one attribute participates. In traditional databases an atomic query may result in more than one set of attribute values, but the query refers to a single attribute. When two or more attributes are involved in a query, then the query will consist of a Boolean aggregation of two or more atomic queries. If a fuzzy atomic query is issued to a database, then the outcome will be a fuzzy set. For instance, if the query is find restaurants near Soda Hall then the set (r, µ near (r)) is returned, where r represents a restaurant and µ near (r) represents the degree to which r is located near Soda Hall. If the query is find inexpensive restaurants near Soda Hall, then a set (r, µ near (r) µ inexpensive (r)) is returned, where denotes the Boolean and. In fuzzy logic there are several ways of defining and in terms of its binary parts, the most common being min [ µ near (r), µ inexpensive (r)]. The Boolean or, denoted by, is defined as max of the two membership functions that comprise the binary parts of. Generally speaking, if x is an object and q is a query, let µ q (x) denote the grade of x under the query q. If q is an atomic query, then the following rules allow us to extend this definition to non-atomic queries. Conjunction rule: µ A B (x) = min {µ A (x), µ B (x)} Disjunction rule: µ A B (x) = max {µ A (x), µ B (x)} Negation rule: µ A (x) = 1- µ A (x) In general, a triangular norm is a 2-ary aggregation function t, called t-norm, that generalizes the conjunction rule and satisfies the following properties: 1. and-conservation: t(0,0) = 0; t(x,1) = t(1,x) = x. 2. Monotonicity: t(x 1, x 2 ) t(x 1, x 2 ) if x 1 x 1 and x 2 x Commutativity: t(x 1, x 2 ) = t(x 2, x 1 ). 4. Associativity: t (t(x 1, x 2 ), x 3 ) = t(x 1, t(x 2, x 3 )). Similarly, a triangular co-norm is a 2-ary aggregation function s that generalizes the disjunction rule with the following properties: 3

4 5. or-conservation: s(1,1) = 1; s(x,0) = s(0,x) = x. 6. Monotonicity: s(x 1, x 2 ) s(x 1, x 2 ) if x 1 x 1 and x 2 x Commutativity: s(x 1, x 2 ) = s(x 2, x 1 ). 8. Associativity: s(s(x 1, x 2 ), x 3 ) = s(x 1, s(x 2, x 3 )). Triangular norm t and triangular co-norm s are dual functions, i.e. s(x 1, x 2 ) = 1 - t(1 - x 1, 1 - x 2 ). Below we list a few t-norms t and their corresponding t-co-norms s. Minimum: t(x 1, x 2 ) = min [x 1, x 2 ]. Maximum: s(x 1, x 2 ) = max[x 1, x 2 ]. Bounded difference: t(x 1, x 2 ) = max [0, x 1 + x 2-1]. Bounded sum: s(x 1, x 2 ) = min [ x 1 + x 2, 1]. Algebraic product: t(x 1, x 2 ) = x 1. x 2. Algebraic sum: s(x 1, x 2 ) = x 1 + x 2 - x 1. x 2. An m-ary aggregation can be generated by iterating a 2-ary aggregation. For instance, from a 2- ary conjunction t(x 1, x 2 ), a 3-ary conjunction can be defined as t(t(x 1, x 2 ), x 3 ). Similarity of Objects. We assume that each object in the knowledge base has a number of features. A hotel, for instance, has such features (attributes) as address, AAA rating, daily rate, etc. A restaurant has features such as location, atmosphere, type, price-range, etc. In order to compare two hotels or two restaurants, we must define a concept of similarity that would include all features that are relevant with respect to a given query. For instance, suppose the query is find an inexpensive Italian restaurant near Soda Hall at UC Berkeley. Then the relevant features are cost (inexpensive), type (Italian), and location (near Soda Hall). The features, cost (inexpensive) and location (near Soda Hall) are imprecisely stated. The feature, type, is crisp. We will define a similarity measure for objects, which would aggregate feature values of objects and would return the degree to which objects in the database are similar to the object defined by the query. We envisage two types of similarity: a) Set-theoretic similarity. This is based on presence or absence of features. Two instances of an object are compared by evaluating the number of their common and uncommon features. By assigning weights to the presence or absence of certain features a user can customize the measure of similarity that would best suit his application. For instance, the similarity of two campgrounds may be defined as a function of presence or absence of such features as swimming pool, shower, grocery store, and restaurant in the two campgrounds. In general, if A and B are two instances of an object, and a = {a1,, an} and b = {b1,, bm} are the corresponding features of A and B, then the function f (a b, a b, b a) can represent a measure of similarity of A and B. b) Metric similarity. Metric similarity is defined as a function over pairs of feature values for each feature of an object. For instance, distance and cost are two of the features of the object restaurant. In the example above, the feature distance represents the distance in miles measured between a restaurant and Soda Hall. The similarity S(R 1 (d), R 2 (d)) is a number in [0,1] that represents the similarity of the restaurants in terms of their respective distances, R 1 (d) and R 2 (d), to Soda Hall. Similarity of cost is defined the same way. Similarity of two restaurants is defined in terms of a function (aggregation) of similarities of features of restaurant. One such function is the weighted sum Σ α i S [R 1 (f i ), R 2 (f i )], where R 1 (f i ) and R 2 (f i ) are the values of feature f i (1 = < i = < n ) of restaurants R 1 and R 2, respectively, and α i is the weight ascribed to the feature f i. 4

5 In many applications related to recognition, planning, and diagnosis, one cannot expect to find database objects that are identical with a given object. In these situations, one must search for similar objects instead. In a tourist information system, one might plan a vacation subject to certain fuzzy constraints. In the restaurant example, described above, there are two fuzzy constraints in the query, i.e. near Soda Hall and inexpensive. The criteria of near and inexpensive must be defined in the ontology. The restaurants that satisfy these criteria, to certain degree, should be retrieved as an outcome of the query. The list of retrieved restaurants {r} is ordered by the degree to which they satisfy the constraints. Conjunction of two fuzzy sets is treated as t- norm and the retrieved list is ordered by decreasing values of min (µ near (r), µ inexpensive (r)) or (µ near (r) times µ inexpensive (r). Multi-information Systems. We assume that the information system comprises a number of distinct and independent stand-alone systems. For instance, a tourist information system is assumed to utilize several systems including a hotel information system, a restaurant database, an airline flight schedule/reservation system, and so on, each of which is developed and managed independently of the others. It is the ontology of the tourist information system that provides the semantics of data (the mortar) among the stand-alone systems (the building blocks). The tourist information system is an example of a multi-platform system that aggregates knowledge from several systems to respond to multi-faceted queries. Besides, very often queries involve fuzziness. For instance, a tourist may require a hotel near the city center and a list of inexpensive restaurants in the city near the city center. To satisfy both requirements, the system must parse and generate two queries, one to the hotel database and the other to the restaurant database. The system must then combine the outcome of the two queries and rank the results based on closeness of hotels and restaurants to the city center and the inexpensive-ness of restaurant meals. The conjunction of these requirements can be formally stated as min [min (µ A (r), µ B (r)), µ C (h)], or (µ A (r)timeµ B (r)times µ C (h) which will be denoted by Q. Here A and C are the set of restaurants and hotels near the city center, respectively and B is the set of inexpensive restaurants. µ Y (t) represents the degree to which t belongs to the set Y. The higher the value of Q, the more the restaurant and/or the hotel will satisfy the query. The outcome of the query will be a set of r s and h s in decreasing order of Q values. The system can be made to stop after a desired number of (r, h) s have been retrieved or after a low threshold value of Q is reached. For the sake of completeness, let us assume that feature values of objects are stored on separate sub-systems that, together, constitute a multi-system. Let us also assume that feature values are represented by fuzzy sets. Below is a naïve algorithm for aggregation of feature values of an object. Let A and B be two feature values and x be an object. Algorithm 1. The sub-system that deals with the feature A outputs explicitly the graded set of all pairs (x,µ A (x)) for every object x. 2. The sub-system that deals with the feature B outputs explicitly the graded set of all pairs (x,µ B (x)) for every object x. 3. Use the information thus obtained to compute µ A B (x) = min (µ A (x), µ B (x)) for every object x. 5

6 4. For the objects with grades µ A B (x) > = α, where α is set by the user, output the objects along with their grades of membership. We may also output the top m µ A B (x) along with the corresponding objects. Fuzzy Databases. Imprecise information exists in many applications. In medical imaging, images inherently contain imprecision due to sensor inaccuracies. In medical diagnosis, the symptoms of a single illness often vary, in kind and in degree, from one patient to another. In a fuzzy database query, one seeks to find a set of instances that best satisfy the specifications stated in the query. In medical diagnosis, the set of instances is the set of illnesses that, more or less (to various degrees), exhibit those symptoms. In a tourist information system, the set of instances is the set of tour packages that satisfy the query, to different degrees. Let P denote a predicate and val(p) denote the truth value of P. In fuzzy logic, the law of the excluded middle [val(p P) = 1], and the law of non-contradiction [val(p P) = 0] do not hold. Therefore, these two laws cannot be employed to constrain query evaluations. Conclusion. We have presented a number of concepts and their implementation in the context of approximate reasoning. We assume that the knowledge base contains crisp data. We provide the mechanism in the form of fuzzy sets to translate the approximate queries into data base queries. The processing for this translation is carried out within the ontic layer. The aggregation of connectives is provided by min, max, and negation. Various forms of similarity function furnish a wide variety of methods to compare and contrast in recognition of objects and retrieval of similar objects. References 1. Bloch I, Maitre H, and Anvari M: Fuzzy Adjacency between Image Objects, the International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, Vol. 5, No. 6 (1997) pp Anvari M: A database model for medical consultation. J Am Soc Information Sci, September 19, 1991, 42 (8) pp Anvari M.: Tourist Information System. Technical report to British Telecom Dionisio J. and Cardenas A.: A Unified Data Model for Representing Multimedia, Timeline, and Simulation Data. IEEE Transactions on Knowledge and Data Engineering, Vol. 10, No.5,

INFORMATION RETRIEVAL SYSTEM USING FUZZY SET THEORY - THE BASIC CONCEPT

ABSTRACT INFORMATION RETRIEVAL SYSTEM USING FUZZY SET THEORY - THE BASIC CONCEPT BHASKAR KARN Assistant Professor Department of MIS Birla Institute of Technology Mesra, Ranchi The paper presents the basic