### How to determine mathematical membership functions and graphs?

How can we determine mathematical membership functions and graphs ? eg Fuzzy sets A, B and C defined on real numbers by the membership functions: $\mu_A(x)=\frac{1}{x+1}, \mu_B(x)=\frac{1}{x^2+10}, \mu_C(x)=\frac{1}{10^x}$ Determine mathematical membership functions and graphs of each of the following ? A $\cup$ B B $\cap$ C A $\cup$ B $\cup$ C A $\cap$ B $\cap$…

### What is exactly the role of commutative property in a Constraint Satisfaction Problem?

I have been looking into the backtracking search for CSPs, and understand that if we just plainly do a typical depth-limited search we have a vast tree with leaves size n!d^n where n is the # of variables and d the domain size. It can also be easily understood that there exists instead only d^n…

### Are there any strategies that would help me visualize the ‘behavior space’ and make a novelty function?

In “Abandoning Objectives: Evolution through the Search for Novelty Alone”, it is explained how the novelty search is a function that is domain specific, depending on the differing behaviors that can potentially emerge. The primary test is a deceptive maze and it seems like they define novelty as a function that is dependent on each…

### Why the error rates in table3 and table4 are differenct in the paper “deep residual learning for image recognition”

Why the error rates in table3 and table4 are differenct in the classifical paper “deep residual learning for image recognition” They are both error rates on the validation sets by single model. Why there are different rates for the same architecture?

### How would an AI learn the concept of the words “repeat twice”?

In a hypothetical conversation: Person A – “Repeat the word ‘cat’ twice”. Person B – “cat cat”. I’m thinking about how a human or AI can learn the concept of “repeat twice”. In reinforcment learning it would require that after the first sentence the AI would go through every random sentence until it got it…

### Is there a probabilistic version of minimax?

How would a probabilistic version of minimax work? For example we may choose a move that could result in a very bad outcome, but that outcome might just be extremely unlikely so we might think it would be worth the risk.

### SLAM versus “STAM” in vision

In the paper ‘Visual SLAM algorithms: a survey from $2010$ to $2016$‘ by Takafumi Taketomi, Hideaki Uchiyama and Sei Ikeda it is mentioned ‘It should be noted that tracking and mapping (TAM) is used instead of using localization and mapping. TAM was first used in Parallel Tracking and Mapping (PTAM)  because localization and mapping…

### How can I prove that all the a-cuts of any fuzzy set A defined on R^n are convex?

How can I prove that all the a-cuts of any fuzzy set A defined on Rn are convex if and only if $\mu_A(\lambda r + (1-\lambda)s) \geq min \{\mu_A(r), \mu_A(s)\}$ such that $r, s \in R^n$, $\lambda \in [0, 1]$ ? That’s a Fuzzy question on my assignment , any idea on how to start…