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# Discussion of Soft Shopping Agent Use Case

===From Straccia===== Kathy, that's more or less the approch to be followed. I would like to highlight the fact that, both buyer and seller have their own utility function, thus, the overal utility has to be combined, that we are not looking to the best utility, but rather the top-k utilities, there is background knoledge (an ontology on the domain), and more importantly, some attribute values, such as the price of the car may be negotiated. The optimal solution for each car is a so-called Nash-Equilibrium. ===END Straccia=====

===From Kathy===

My inclination would be to use a multi-attribute utility function to model this problem. The car has several attributes, including:

• Price
• Color
• et cetera

Now, for each of these attributes, I have a utility function, which measures my degree of satisfaction with the attribute. If I assign utility zero to a "reasonable worst case" and 100 to a "reasonable best case," then intermediate numbers reflect my relative satisfaction with levels in between reasonable worst and reasonable best. (In utility theory, the utilities assigned to the endpoints are arbitrary because utility is well-defined only up to a linear transformation, so any convenient assignment of utility to the endpoints will do.)

Then I need a combination rule to assign utilities to cars, which combines the single-attribute utility functions into a multi-attribute utility function.

The best car for me is the one with the highest utility.

I would not use the label uncertainty for what Umberto is calling "fuzzy constraints". We are not uncertain about the number of kilometers on the odometer or the color of the car. I might in fact be uncertain about the price for which I could obtain the car. I might be uncertain about the condition of the engine, or the cost of repairs over the next year. Those uncertainties I would model with probability.

===from Peter Vojtas === First, three use cases, Discovery, User preference modeling and Soft shopping agent have a lot in common, maybe we can discuss them together? Next, concerning Kathy's remarks. We work with Mitch and Vipul on a "uncertainty ontology" and it seems that here it is a problem of terminology - I think that utility functions are part of uncertainty modeling, degree of satisfiability is also a fuzzy function and decompose the global source ranking "g" into a combination function "t" and particular attribute preferences "u_i" is a nontrivial task to get

• "g = t(u_1, ...,u_n)"
• ===end Peter Vojtas ===

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