Introduction

G’day to everyone who is looking at the site.

My name is Owen, and I am an IT Officer for the ISE Department at the University of Canberra

Let me quickly outline the purpose of this blog to give you some idea about what you can expect to see on it…

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Happy New Year

 Well, it’s been a while since I’ve posted last. I have been rather busy for a variety of reasons (research, work, wedding)

So I thought it was about time that I posted an update to the blog summarising the research I’ve been doing up until the latter part of last year.

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Objectified 3D Fuzzy Sets

I thought I would continue my thoughts on 3 Dimensional Fuzzy Sets,

One of the problems that the model presented in my last blog post faces, as it was presented to me by Robert Cox this morning, is that the system would have trouble handing invalid or incorrect data. When the training is not a series perfect solutions, then our system could potentially build up a less than optimal solution…

How do we handle this?

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Dimensions of Fuzzy Sets

I was sitting at my desk today, and it hit me, why must our fuzzy sets be 2D?

Whilst it is less complex to rely on a 2D fuzzy set, the limitations of such sets are fairly big. For example, we could plot two fuzzy sets simultaneously to create a joint graph, but then the implication is that the two sets will be consistent across our 3D space. We could instead, have a series of fuzzy sets defined at intervals across our 3D domains… but that would require alot of extra work in order to create something of relative simplicity.

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Counteractive Rule Sets

I’ve been working on an artificial intelligence system of late which has proved rather insightful into the workings of various rule systems. Of particular note I began to realise the simplicity that can programmed when you begin to use counteractive rules.

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Genetic Algorithms: Harnessing Environmental Selection

I have been considering a problem that was posed to myself a few weeks back. A programmer wants to create a program that attempts to replicate a painted image using a genetic algorithm. For example, a tree.

As he builds his genetic algorithm, each generation is given a score based on its closeness to the original image. As the program runs, subsequent generations slowly build up until you get an image which somewhat resembles the tree. However, this is a slow and tedious process, depending on the complexity of the algorithm designed (and I watched one slowly attempt to get a good tree), the length of time and the closeness to the original image that is desired.

Surely there would be a way to optimize the program a bit more!

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Operations on Fuzzy Sets

I must admit, I was a rather bit confused by one of the diagrams that I came across in my readings.

This diagram was intended to demonstrate the Complement of a Fuzzy set (Figure 4.7, pg. 101, Negnevitsky)

As Negnevitsky presents it, a triangular set A, in a domain of 0 to X and the standard memberships of 0 to 1, the complement (as he shows) is the inverted set A on the domain. This is incorrect. The complement requires that  when x has a membership of 1 in A then its membership in NOT A is 0, and when its membership in A is 0 then its membership in A is 1. The complement, then, is everything NOT in the triangle that Negnevitsky has labeled “Not A”

So for anyone looking at that diagram going “huh?” I’m not surprised! In fact, his diagram of the complement completely equates to the diagram of A. Though the triangle is upside down, the percentage of membership would still be the same, though it seems like it should be quite different graphically.

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Looking at Certainty Factors

I’ve been taking some time to read through Michael Negnevitsky’s Artificial Intelligence – A Guide to Intelligent Systems (2nd Edition) and I must say, I was quite surprised at his presentation of certainty factors in Expert Systems.

The surprise came on pages 77 and 78, where he presents how an ES (Expert System) would handle conjunctive and disjunctive rules. To determine the certainty factor, he presents that, one takes the minimum of the antecedents (for conjunctive rules) or the maximum of the antecedents (for disjunctive rules) and then multiplies by the certainty factor of the end hypothesis.

I feel this approach is actually flawed.

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Benefits of a Cellular Design

 So what are the capabilities of a system using this design? (The Cellular Approach to building AI as outline in my previous post)

 Let’s start by taking a look at the the lookup tables.

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A Cellular approach to Intelligent Systems

I was driving to work this morning and was thinking about how one would go about designing an intelligent system and about the weaknesses  that are inherent in an expert system.

As I was pondering the concept, it dawned on me that a traditional rule based system would actually be quite silly for large sets of rules. For a small quantity of rules it would be easy to navigate through them to find the ones that apply to a given situation… but what about for larger problems with multiple domains of knowledge required, and many rules flowing on from each other? And what if the problem was not entirely concrete?

There has to be a way of navigating through rules such that it is efficient, can deal with degrees of plausibility, and can span large and diverse domains of knowledge… and to add further complication, what if we were to make it so that it could learn?

I believe it is possible to build such a system, and below I will begin to detail how.

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