Fuzzy BDI Modeling For Intelligent Agent
JONG YIH KUO
Department of Computer Science and Information Engineering
Fu JenCatholicUniversity
HsinChuang, Taipei 242
TAIWAN
Abstract: -This paper presents fuzzy belief, desire and intension architecture as a useful framework for modeling intelligent agents in virtual market. The paper show the integration of fuzzy modeling and ontological reasoning may make significant impact on the use of ontology ability to extend agent to more effectively perform tasks for users with less human intervention. A goal-driven approach is employed to constructthe goal model, and the belief and plan model are derived through the goal model by means of ontology and fuzzy reasoning. Moreover, we show how an agent can dynamically adjust its bidding behavior to respond effectively to changes in the marketplace.
Key-Words:Intelligent agent, Fuzzy modeling, Ontology reasoning
1 Introduction
The intelligent agents act on behalf of customers to carry outdelegated tasks automatically. They have demonstrated tremendouspotential in conducting various e-commerce activities, such ascomparison-shopping, auction, sales promotion, and etc [8,15]. Whenagents are initially created, they have little knowledge andexperiences with relatively lower capability. In a dynamic market where external conditions can be changedunexpectedly, where agents are required to act rationally in responseto imprecise and unpredictable events, and where strategies can be continuously modified, it is extremely difficult to define a priorithe best strategies to be used by agents. A key feature of thisrationality is the ability of agents to adapt their coordinating andbidding strategies that are suitable to their prevailing circumstances[5]. Thus, a suitable mental structure of agents is one ofthe basic concerns.
An agent’s decision making about bidding involves uncertainty, multiple factors, and non-determinism that are affected by the attitudes toward risk of its opponents, the nature of the market supply (demand), and the preferences of the other bidders [9]. Since no agent can have all this information in advance, the best that can be achieved is a satisfying strategy.
In this paper, we present a formal framework for fuzzy modeling mentalstructure of agents by means of ontological and fuzzy reasoning mechanism. Section 2 describes the goal-driven BDImodeling approach. Section 3explains how to build the goal model based on ontology reasoning. The belief and plane model is derived in Section 4 and 5. We propose the heuristic fuzzy rules and fuzzy reasoning mechanisms in order to determine the best bid to make given the state of the marketplace. Our conclusion is summarized in Section 6.
2The MentalModelof Agent
This paper addresses fuzzy modeling of intelligent agents about the mentalskills, so that they could striveto adapt themselves to the changing environment.Obviously, there is no limit to what one would like to includeunder what we call mental skills. We agree that BDI model [4,14] provides a simple but powerful formalism for the representation,the specification and the analysis of the mental attributes ofintelligent agent: belief, desire and intention.
2.1 The BDI Model
In the BDI architecture, an agent can be completely specified by theevents that it can perceive, the actions it may perform, the beliefsit may hold, the goals it may adopt, and the plans that give rise toits intentions [2]. Figure 1 represents therelationships of BDI model.
A goal model (desires) describes the goals that an agent may possiblyadopt, and the events to which it can respond. It consists of a goalset which specifies the goal and event domain and one or more goalstates - sets of ground goals - used to specify an agent's initialmental state. A belief model describes the information about theenvironment and internal state that an agent of that class may hold,and the strategies and tactics it may perform. A plan model(intensions) describes the plans that an agent may possibly employ toachieve its goals. A plan is a sequence of strategies throughreasoning mechanism (mental skills of the agent). The strategy is thecombination of tactics with various weights.
Figure 1. The BDI Model for Agent
2.2 Architecture
To construct the BDI model, we build the goal model based on ourgoal-driven approach [11, 13] and ontological reasoning.The belief and plan model are derived through the goal model bymeans of and extension of Sugeno model [17]. The BDI architecture of agent is described as follow.
1. Goal model: There are two types of ontology which provide the domain and issue specific knowledge. Based on domain and issue specific ontology, we propose a goal structure to analyze the user’s requirement, and to construct the goals hierarchy.
2. Belief model: According to the environmental information and the goals hierarchy of the goal model, we can construct the belief model by defining some facts and fuzzy rules. Some fuzzy rules can constraint the usage of strategies of the plan model. Some facts or reasoning consequences will refine the goal model.
3. Plane model: By using the goals hierarchy of the goal model and the fuzzy rules of the belief model, the intelligent agent can plan some useful strategies for bidding goods. These strategies constitute a serial of active actions which will try to satisfy these goals of the goal model. If some successful or failed results return, these messages will be passed to the belief model. The belief model uses the feedback information to adapt the related fuzzy rules.
3. The Ontology Reasoning Goal Model
To build the goals model, we apply ontological reasoning and fuzzymodeling to get a set of soft and rigid goals. To achieve these goals, agents must use particularstrategies to change their mental states. We can continuously changethe mental state of agents to achieve the goal state.
3.1The Formal Representation of Goals
There are soft and rigid goals specified by the users. We can applythe soft requirement [11] to formally represent the usergoals. A user goal, g, is specified by the properties of agent's mentalstate-transition b, g, a, where b is thestate before a plan, and a is the state after invoking the plan. Aplan or strategy can thus be specified using a pair precondition, post-condition. The precondition and thepost-condition describe properties that should be held by the stateb and a. A rigid goal describes state properties that must besatisfied. The soft goal describes state properties that can besatisfied to a degree. We use Zadeh's test-score semantic [16]to represent the user goals. A basic idea underlies test-scoresemantics is that a proposition p in a natural language may be viewedas a collection of elastic constraints, C1, … ,Ck, whichrestricts the values of a collection of variables X = (X1, . . .,Xn). In fuzzy logic, this is accomplished by representing p in thecanonical form: G R(P) IS A
in which A is a fuzzy predicate. The canonical form of G impliesthat the possibility distribution of R(P) is equivalent of themembership function of A, namely, R(P) = A. For ourexample, the agent helps a user to buy high quality camera and can berepresented using the canonical form below:
G1Quality(camera) IS HIGH
Where HIGH is a fuzzy predicate. The rigid goal is thespecialization of the soft goal, which membership function of fuzzypredicate is 1.0. For our example:
G2 MaxPrice(camera) IS Pr
G3 Deadline(camera) IS tmax
Where Pr is maximum price which user will pay, and tmax isthe deadline which user wants it.
3.2The Goal Structure
Firstly, we extended the goals structure [13] to analyze the user’s goals. A faceted classification is proposed for identifying goalsfrom domain descriptions and user requirements.
Figure 2. Extended Goal Structure
Each goal can beclassified along the following two dimensions: (1) classifying the verb with different viewpoints: content and competence, (2) three types of parameters: view, target, andconstraints. The content describes whether the requirements represented by this goal are functional or non-functional. A functional goal can be achieved, ceased, or impaired. As for non-functional goal, it usually refers to the goals that need to be satisfied, such as to optimize or maintain. The facet of competence is related to whether a goal iscompletely satisfied or only to a degree. A rigid goal describes aminimum requirement for the user, which is required to be satisfiedutterly. A soft goal describes a desirable property for the user, andcan be satisfied to a degree. The view concerns whether agoal is user-specific or agent-specific. User-specific goals areobjectives of a user in using an agent system; meanwhile,agent-specific goals are requirements on services that the agentsystem provides. Targets are entities affected by the goal. Two types of targets are distinguished, object and result. An object is supposed to exist before the goal is achieved. Result can be of two kinds: (1) entities which do not exist before the goal is achieved; and (2) abstract entities which exist but are made concrete as a result of achieving the goal. Constraints represent the pre-/post-condition thatmust be satisfied before or after the achievement of a goal. We then usethe fuzzy and ontological reasoning to structure the goals hierarchy.
Figure 3: Camera Ontology
(from
Figure 4: The ontology of camera via DAML+OIL
3.3The Goal-driven Ontology Reasoning
To fulfill the goal model, we have modified our previous work onPPN-ASDL by means of DAML-based ontology. The ontology defines a common vocabulary for users who need to share information in a domain. The foundation of the goalmodel is made up of two types of ontology: the domain specific and issue specific ontology (see Figure5) [12]. All domainspecific concepts are defined in domain specific ontology.
In thevirtual market, the domain specific ontology means goods required byuser, for our example, the camera. The issue specific ontologydescribes the elastic constraints or bidding issue, for our example,the quality or price of product. In Figure 3 and 4, DAML+OIL is used to annotate its ontology because camera semantics varies in different domains. In Figure 4, we know that the class camera is a subclass of purchasable item and it disjoint from the class Body and Lens, and its primary properties are to have lens, body, and viewFinder.
(a) A Class Hierarchy of Camera
(b) A Class Hierarchy of Quality
Figure 5: Class Hierarchy
In practical terms, developing ontology not only includes using ontology markup language but also arranging the classes in a taxonomic hierarchy. For our example, the class hierarchiesof domain specific ontology and the issue specificontology shown as Figure 5. The ontology also contain othersemantic relations [3, 6], for examples parts/whole orrelatedness, used by the DAML+OIL inference engine to calculate thesimilarity between these concepts. To compare resource and requirement based on their semantics, the inference mechanism quantifies the confidence level of matching two classes by computing a similarity between two classes in a class hierarchy [12].
A goal hierarchy can be builtdynamically by reasoning the concepts defined in the domain and issuespecific ontology. If sub goals are generated, a goal confirmation formcan be generated for user to get the feedback. Meanwhile, the DAML+OILinference engine use the domain and issue specific ontology toderive the similarity between concepts. The inference engine isimplemented by DAMLJessKB [10]. Relations between concepts aregiven the pre-defined relevance value. And the semantic relation pathis a directed path composed by the same type of relations from oneconcept to the other one. The calculation of similarity between twoconcepts is the product of relevance values of the relations whichconstitute the semantic relation path.
4The Fuzzy Reasoning Belief Model
The inference mechanism of fuzzy reasoning on a rule base employed inthis paper is extended from the Sugeno controllers [17] to derive the belief model. Thestrategy is based on some heuristic rules and the fuzzy reasoningmechanism.
4.1 The Fuzzy Reasoning Mechanism
We have modified the auction model [7] as:
MAi = <gi, ci, t0i, tendi, pricei, Si
Where i is the identity of auction, g is the goods to beauctioned, c is the unit cost, t0 and tend is the startand end time, pricei is the minimum price step requiredin the auction, and the S={s1, .., sm} is the finite set ofspecifications of goods, where m is the number of specifications.
We construct the belief model by means of the goals model. Firstly, weanalyze the virtual market environment to extract the basicinformation for the agent. The information includes how many auctionsare, where agent can go, what the start and end time of auctions are,how many product brands satisfy these constraints of goals, and whatthe specifications or functionalities of those brands are,etc. Secondly, we identify the users and their preferences to buildthe specific user-defined ontology. The knowledge can be built into ageneral common ontology. The ontology hierarchy is stored into theknowledge base of the belief model. Finally, we derive some strategiesfor building plan model. By means of the goal and belief model, we canderive the plans to achieve these goals. We also evaluate the degreesof satisfaction for the planes. Inthe first two cases, we use some heuristic rules described below:
HR1 IF tendi much_bigger than tmax
AND Si little_bigger than qg
THEN include Ai
HR2 IF Experience(user) IS much
THEN SiIS more_professional
HR3 IF Experience(user) IS little
THEN Si IS less_professional
The bidding issue in the last case, which is more complicated, ishandled through a fuzzy reasoning on a rule based. If we have onlylittle information about the value of the auctioned goods, the planmay be as watch/modify/bid. In contrast, the plan may be aswait/bid. If the bid deadline is coming soon, the agent may tend touse the time-dependent tactics. If agent does the best to buy thegoods, it may tend to use the desire-dependent tactics. Some fuzzy rules are described below:
HR4 IF tendi close_to tmax
THEN Weigth(time_tactics) IS large
HR5 IF Preference(goods) IS much
THEN Weigth(desire_tactics) IS large
5.The Strategiesof Plan Model
Based on the fuzzy rules of the belief model, the intelligent agent monitors and collections information from the ongoing auctions and determines which auction it wishes to participate in. The decision on how much to bid in the selected auction is made based on a serial of tactics and strategies.
A bidding strategy which is the combination of tactics with various weights determines the bidding price at time t. A tacticgenerates a value for a single bidding issue based upon a singlecriterion (e.g. time remaining). As biddingproceeds, the goals of agent may become relevant and the relativeimportance of existing criteria may vary. To reflect this fact, anagent has a strategy that varies the weights of the different tactics over time in response to various environments. We extended the researchin [1] to four types of tactics:
1. Time-dependent tactics：These tactics model the fact that the agent is likely to concede morerapidly as the bidding deadline approaches. The bidding must havecompleted at the pre-established deadlinetmax. The maximum price is Pr. When the deadline is nearly up, and the price approachesthe Pr. The function:
ft =t(t) Pr,
0t(t)1, t(0)=kt, t(tmax)=1,
0kt1, 1/200t1000
2 Resources-dependent tactics: These tactics generate offers depending on how a particular resourceis being consumed; they become progressively more conciliatory as his quantity of resource diminishes. Here, we use the bidder tactics. Theequation is:
fr =r(t) P,r
0kr1, 1/200r1000
Where c(t) is the number of web at 0~t, |A| is the number of active bidding web at 0~tmax.
3. Price-dependent tactics: Agent uses these tactics to maintain the goal of minimum price. Agentmust get the biding prices of all active bidding webs. The equation:
fp =p(t)+p(t)( Pr-p(t))
0.1kp0.3, 1/200p0.5
Where|L(t)| is the number of active bidding webs at time t. Thei represents the start time of the ith bidding web. Thei is the end time of the ith bidding web. The irepresents the highest price of the ith bidding web at time t.
4.Desire-dependent tacticsAgent does the best to buy the high quality goods to achieve the userdesired. The curve of the price will quickly approach the Pr.
fd =d(t)+d(t)( Pr-d(t))
0.7kd(t)0.9, 1.67d1000
The equation of a strategy describes below:
S(t)= wtft+ wrfr + wpfp + wdfd,
0wt, wr, wp, wd1,wt+wr+wp+ wd=1
Wherewt, wr, wp, wdare the weight of the related tactics.
6Conclusion
In this paper, we present a new approach to modeling intelligentagents in e-commerce. The proposed BDI modelrepresents the mental skills of the intelligent agent, includingbelief, desire, intension, and strategy.A goal-driven approach is proposed to construct the user'ssoft and rigid goals based on fuzzy set theory and ontological reasoning. It explain how the intelligent agent to use the ontology to retrieve semantic information and to build the belief and plan model. We propose the heuristic fuzzy rules and fuzzy reasoning mechanisms in order to determine the best bid to make given the state of the marketplace.
Acknowledgment
This research is partially sponsored by the National Science Councilunder grant NSC 92-2213-E-030-016 and Ministry of Education undergrant EX-92-E-FA06-4-4.
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