Lecture 8 - Cognitive fuzzy maps

Question 1

FCM

Answer 1

It is the modeling and simulation of complex systems that allows experts in a given domain to explore the outcome of hypothetical scenarios before they are observed in reality. They answer what–if questions.
They deal with non-linear patterns.

Question 2

We could use regression, but 3 problems arise with it:

Answer 2

1. the coeff. that belog to different models are omputed separately; the analysis will be fragmented because they are not computed at the same time.
2. in certain expert knowledge systems it is not possible because we use some methods that are deterministic, which means that we only learn from historical data
3. regression is linear

Question 3

CM (not fuzzy yet)

Answer 3

A directed graph where nodes represent relevant factors, variables and entities from a decision making environment.
It is a graphical representation of a complex system.

Question 4

Arrows in CM

Answer 4

represent the causal relationship between the nodes, which can be + or -

Question 5

Complex system

Answer 5

Can be represented by using concepts + causal relations , which both need to be represented by the experts.

Question 6

CM cannot represent…

Answer 6

1. what-if simulations

2. the intensity of the relationship

Question 7

FCM

Answer 7

CM + numbers on the arrows

Question 8

These numbers represent…

Answer 8

the intensity of the causal relation ( a numerical representation of the causal relation)

Question 9

Causal relation

Answer 9

1. the weights are determined by experts
2. 2 types of CR:
   + : if we de/increase C1, then C2 also de/increases
   - : the opposite
3. they are recurrent NN devoted to modeling and simulating complex systems.

Question 10

In FCM, the concepts/neurons are activation values..

Answer 10

AV are the extent to which this concept is activated or present in the system (also determined by experts).

Question 11

In FCM, the reasoning mechanism is the process of…

Answer 11

updating the activation values we have in the map in each iteration.

Question 12

Given the formula for one of the transfer functions, what happens in the argument?

Answer 12

We want to aggregate all inputs impacting the concept

Question 13

Transfer function

Answer 13

1. Used to produce suitable activation values

2. Bounds value produced such that they are in the allowed interval

Question 14

Transfer function can be..

Answer 14

Discrete:
- bivalent –> values are 0 or 1
- trivalent –> values are -1, 0 or 1
They can be cyclic, but not chaotic

Question 15

Transfer function can be..

Answer 15

Continuous:

• hyperbolic function –> range -1 to 1, when we have 0, it produces 0
• sigmoid function –> range (0,1), not included.

Question 16

Convergence

Answer 16

The reasoning mechanism continues until a fixed point or a maximal point of iterations.

Question 17

Fixed point attractor

Answer 17

the map continues to produce the same AV

Question 18

Cyclic behaviour

Answer 18

the map will produce a limited number of outcomes after a number of iterations which will be replicated in time

Question 19

Chaos

Answer 19

different values as the number of iterations grows.

Question 20

Theoretical issues in FCM

Answer 20

1. if fixed unique point, the simulation is useless

2. Shrinking theorem (ST)

Question 21

ST

Answer 21

Considers a feasible activation interval and states that the values outside this interval won’t be reached by the network, no matter network structures or AVs.