• Got Speakers

Use Case Title: Got Speakers?

/Discussion

Purpose/Goals (Summarize what the use case is to accomplish, e.g. story, real world example)

Customer needs to make a decision on (1) whether to go to a store today or wait until tomorrow to buy speakers, (2) which speakers to buy and (3) at which store. Customer is interested in two speaker features: wattage and price. Customer has a valuation formula that combines the likelihood of availability of speakers on a particular day in a particular store, as well as the two features. The features of wattage and price are fuzzy. Optionally, Customer gets the formulas from CustomerService, a Web based service that collects information about products, stores, statistics, evaluations.

Issues and Relevance to Uncertainty (Summarize how relevant to uncertainty (vagueness, ambiguity, imprecision,…) reasoning)

1. There is known probability distribution on the availability of particular speaker type in particular stores on a particular day in the future. Say there are two stores (not too close to each other) and the probability that speakers of type X will be available in stores A and B tomorrow are Pr(X, A)=0.4 and Pr(X, B)=0.6. The probabilities for all types of speakers are represented in the same way.

• The uncertainty annotation process (UncAnn) was used.

• The agent issues a query (a sentence): Sentence. It is a complex sentence consisting of three basic sentences. One related to the availability, one to the wattage and one to the price of speakers.

• Each of these sub-sentences will have uncertainty Uncertainty associated with it.

• The uncertainty type related to the availability of particular speaker type in the stores is of type UncertaintyType: Empirical.

• The uncertainty nature is UncertaintyNature: Aleatory.

• The uncertainty model is UncertaintyModel: Probability.

2. The customer has (or obtains from CustomerService) definitions of features of wattage and price in terms of fuzzy membership functions. For wattage, Customer has three such functions: weak, medium and strong. These are of "trapezoid shaped" membership functions. Similarly, for price Customer has three such membership functions: cheap, reasonable and expensive.

• The uncertainty type related to the features of wattage and price is of type UncertaintyType: Vagueness.

• The uncertainty nature is UncertaintyNature: Epistemic.

• The uncertainty model is UncertaintyModel: FuzzySets.

3. The valuation has three possible outcomes, all are expressed as fuzzy membership functions: bad, fair, good and super.

4. Customer knows the probabilistic information, since the probabilities are provided by CustomerService. CustomerService uses the Uncertainty Ontology for this purpose.

5. Customer has (or selects) fuzzy definitions of the features of wattage and price. Again, the six membership functions that define these features are annotated with the Uncertainty Ontology.

6. Customer has (or uses one suggested by CustomerService) a combination function that computes the decision, d, based upon those types of input. This function can be modified by each customer, however the stores need to give input to CustomerService - the probabilities and the (crisp) values of wattage and price for their products. The features are fuzzified by the customer's client software. Customer uses the Uncertainty Ontology to annotate the fuzziness of particular preferences.

Assumptions/Preconditions (List the preconditions necessary for this use case to occur, including description of necessary context)

• Customer either relies on the definitions provided by CustomerService or is knowledgeable in both probability and fuzzy sets

• Stores provide information to CustomerService. CustomerService keeps information on both probabilistic models and fuzzy models

• Customer has the capability of either obtaining or defining a combination function for combining probabilistic information with fuzzy

Required Resources (List the general resources, such as data sources, ontologies, needed for scenario)

1. Data collected by CustomerService on the availability of items, which in turn depends on restocking and rate of selling

2. Ontology of uncertainty that covers both probability and fuzziness

Successful End (Describe what happens if this use case is successful)

Customer gets necessary information about the availability and types of speakers from stores. This information is sufficient for customer to compute the required metric.

Failed End (Describe what happens if this use case fails)

• Customer does not get necessary information and thus needs to go to multiple stores, wasting in this way a lot of time.

Main Scenario (List the sequence of events for the basic course (numbered))

1. Customer formulates query about availability of speakers in the stores within some radius.

2. Customer sends the query to the CustomerService.

3. CustomerService replies with information about the availability of speakers. CustomerService cannot say for sure whether a given type of speaker will be available in a store tomorrow or not. It all depends on delivery and rate of sell. Thus CustomerService provides the customer only with probabilistic information.

4. Since part of the query involves requests that cannot be answered in crisp terms (vagueness), CustomerService annotates its replies with fuzzy numbers.

5. CustomerService uses the uncertainty annotated information to compute a metric.

6. Customer uses the resulting values of the metric for particular stores and for particular types of speaker to decide whether to buy speakers, what type and which store.

Existing software or other resources (Summarize/provide references to existing tools that may be relevant to the use case problem, including examples of Required Resources noted above)

Additional background information or references (Summarize/provide references to information to further describe or characterize use case)

This use case was inspired by the following paper: "sMart - A Semantic Matchmaking Portal for Electronic Markets", by Sudir Agarwal and Steffen Lamparter. In: Proceedings of the 7th International IEEE Conference on E-Commerce Technology 2005, Munich, Germany, IEEE Computer Society (2005).