On Mon, 19 Apr 2004, Rich Shepard wrote:
> On Mon, 19 Apr 2004, Pablo Diaz-Gutierrez wrote:
> Here's an example from Hans Zimmerman's "Fuzzy Sets, Decision Making and
> Expert Systems", in the section on fuzzy game theory:
>
> "We will start with considering two-person games and specify what is meant
> by a classical two-person-nonzero-sum game. Let s_ik \in k=1,2 be the ith
> pure strategy of player k. For any pair {s_i1,s_j2} from S_1 \oplus S_2
> there exists a unique real number g_k(s_i1,S_j2) \in G_k which is called the
> gain of player k."
It looks like S_1 \oplus S_2 means the direct product/sum of the sets S_1
and S_2, i.e. elements in S_1 \oplus S_2 are members of the set
{ (x,y) : x \in S_1, y \in S_2 }
I've seen \oplus used in this way (although I'd say a \times has been more
common, but I'm used to working with vector spaces where the direct sum
and direct product are the same).
> Over the years I've learned a lot of mathematics on my own, but it
> helps to have a dictionary of symbolic usage to which I can refer.
Here's a page that "explains"(*) the direct product:
http://mathworld.wolfram.com/DirectProduct.html
the site also has other "explanations" (*). Have fun ;-)
/Christian
* The explanations usually assume you're a mathematician...
--
Christian Ridderström http://www.md.kth.se/~chr
