Fuzzy Logic, Tues 4 Sept. 2007

This class extended the previous class and brought up combining fuzzy statements by composition. These can be visualized by a relational matrix or a saggital diagram. These compositions can be in the same or different product spaces (if different, the cartesian product is ussed. Eg's... same product space: "x is far away from y or x is close to y"; different product space "x is close to y and y is near z". Also, the composition of two fuzzy relations can also apply when one of the fuzzy relations is just a fuzzy set. This special case is important in the representation of rules.

Fuzzy Logic, Thursday 30 Aug. 2007

In this lecture we went over the transition from crisp sets to fuzzy sets. One key point is to translate the member conditions to a membership function, one can use max() for "or" or min() for "and". Also, 1 - mu_a(x) for ~A (complement). Actually, these functions are a subset of possible functions that have the necessary properties. This brought us into t-norms and t-conorms which seems to be a cool and wierd thru the looking glass type of mathematics.

Algorithms, Wednesday 29 Aug 2007

First we had the quiz-- I need to review sorting and data structures. we finished Dijkstra's algorithm. In particular we verified all the nitty gritty details to prove how/why it works. We ended w/ how to speed up Dijkstra's algorithm with priority queues/min-heaps.

Fuzzy Logic - 28 Aug 2007

In the first lecture we covered

-some of the history of fuzzy logic: how Zadeh thought it up and had trouble with Western academics/philosophy but it caught on in the east, like Japanese electronics.

- how prof. Mendel got into FL,

- philosophy behind FL

- type 1 and 2 fuzzy systems

- fuzzy sets

Algorithms, Monday 27 Aug 2007

Well, the first time I took the class I didn't pass the intro quiz so I dropped it. The first class was pretty similar to the last time: The questions of what is computer science, what is an algorithm and dijkstra's algorithm. We didn't finish the proof so I guess we'll continue wed after the quiz. Now I'm focusing on trying to pass the quiz by reading the first few chapters of the book (Algorithm Design by Kleinberg/Tardos) and the other book I've been studying over the summer (Discrete algorithmic mathematics)-- that book is a bit lower level but more detailed.

In the Kleinberg/Tardos book:
- overview: of the chapters' topics. possible paths through the book.
- chapter 1: stable matching algorithm (Gale-Shapley). 5 representative problems: (1) Interval scheduling, (2) Weighted interval scheduling, (3) Bipartite matching, (4) Independent set, and (5) Competitive facility location. The difference between finding solution and checking it. NP complete problems and PSPACE problems.
-chapter 2: