In the manual of a smart fan, the following rules about its operation are given:

A. If the temperature is comfortable and the humidity is low, then the speed is slow

The manual defines the following fuzzy sets:

The user wants to know, for a temperature of 25 ºC and a humidity of 50%, what the speed of the fan will be.

In the manual of a smart fan, the following rules about its operation are given:

A. If the temperature is comfortable and the humidity is low, then the speed is slow

The manual defines the following fuzzy sets:

The user wants to know, for a temperature of 25 ºC and a humidity of 50%, what the speed of the fan will be.

The evaluation of the antecedent of rule A results in an adequacy (or strength) value of:

Which of the following corresponds to the value for the state C at iteration 3 (starting at iteration 0)?

A mountain route agency has a defined trip to travel from village A to village B, separated by summit C.

According to the agency's experience:

• It takes 18 hours to reach village B from A by going around summit C.

• It takes 3 hours to climb from village A to reach summit C.

• It takes 6 hours to ascend by trekking from village A to summit C.

• It takes 2 hours to descend by rappelling from summit C to village B.

• It takes 5 hours to descend by trekking from summit C to village B. 

A group of clients who have booked the route from village A to B prefer to arrive as quickly as possible, and according to the agency's experience, based on the people in the group:

• There is a 100% probability of reaching the destination by going around the summit.

• There is a 30% probability of successfully reaching the summit by climbing and a 70% probability of doing so by trekking (ascending).

• Once at the summit, there is a 20% probability of descending by rappelling to village B and a 70% probability of reaching village B by trekking (descending).

The group of clients prioritizes reaching village B as quickly as possible.

Meteorologists from a regional office want to analyze, in a simplified way, the weather behavior in a coastal city to study how it influences whether residents carry umbrellas in the morning. After collecting preliminary data and conducting street interviews, they decided to model the situation with a Hidden Markov Model (HMM) considering whether the day will be sunny, rainy, or cloudy.

On the first day, based on historical city data and the date measurements begin, meteorologists estimate:

• 50% probability of being sunny.

• 30% probability of being rainy.

• 20% probability of being cloudy.

For subsequent days, experts believe the weather retains a "memory" of one day (first-order property), meaning that knowing the weather on one day defines the probabilities for the next day:

• If a day is Sunny:

• 30% of the time it transitions to rainy the next day.

• 10% of the time it transitions to cloudy.

• If a day is Rainy:

• 20% of the time it becomes sunny the next day.

• 30% of the time it transitions to cloudy.

• If a day is Cloudy:

• 30% of the time it clears to sunny the next day.

• 30% of the time it intensifies into rain.

Additionally, a research group conducts surveys each morning to determine how many people carry umbrellas. In a pilot survey, they interviewed 100 people for each type of day (Sunny, Rainy, Cloudy) and obtained the following results:

• Sunny day: 10 out of 100 people carried umbrellas for precaution; the other 90 did not.

• Rainy day: 90 out of 100 people carried umbrellas, and only 10 did not.

• Cloudy day: 60 out of 100 people carried umbrellas, while 40 did not.

These probabilities are considered representative of the observed behavior in this coastal city.

Meteorologists from a regional office want to analyze, in a simplified way, the weather behavior in a coastal city to study how it influences whether residents carry umbrellas in the morning. After collecting preliminary data and conducting street interviews, they decided to model the situation with a Hidden Markov Model (HMM) considering whether the day will be sunny, rainy, or cloudy.

On the first day, based on historical city data and the date measurements begin, meteorologists estimate:

• 50% probability of being sunny.

• 30% probability of being rainy.

• 20% probability of being cloudy.

For subsequent days, experts believe the weather retains a "memory" of one day (first-order property), meaning that knowing the weather on one day defines the probabilities for the next day:

• If a day is Sunny:

• 30% of the time it transitions to rainy the next day.

• 10% of the time it transitions to cloudy.

• If a day is Rainy:

• 20% of the time it becomes sunny the next day.

• 30% of the time it transitions to cloudy.

• If a day is Cloudy:

• 30% of the time it clears to sunny the next day.

• 30% of the time it intensifies into rain.

Additionally, a research group conducts surveys each morning to determine how many people carry umbrellas. In a pilot survey, they interviewed 100 people for each type of day (Sunny, Rainy, Cloudy) and obtained the following results:

• Sunny day: 10 out of 100 people carried umbrellas for precaution; the other 90 did not.

• Rainy day: 90 out of 100 people carried umbrellas, and only 10 did not.

• Cloudy day: 60 out of 100 people carried umbrellas, while 40 did not.

These probabilities are considered representative of the observed behavior in this coastal city.

Given the following Bayesian Network for autism diagnosis:

Clinical observations indicate that 15% of patients experience social interaction problems, particularly difficulties relating to other children and adults. Of this group, 70% also exhibit limited nonverbal communication, characterised by minimal or no gestures and facial expressions. If they do not suffer from social interaction problems, the likelihood of having limited nonverbal communication drops to 20%. Furthermore, patients with social interaction problems also experience motor stereotypies (the constant repetition of movements or sounds) 65% of the time; this number drops to 20% if they do not have social interaction problems.

Finally, if a child presents limited nonverbal communication and motor stereotypies, the probability of being diagnosed with autism is estimated at 99%. If only one of these two factors is present, autism is present in 85% of cases. In the absence of both, only 5% of children have autism.

Early diagnosis of autism spectrum disorders (ASD) is crucial for improving interventions and support (and, therefore, the quality of life) for individuals with this condition. Healthcare professionals use various observed manifestations and behaviours to support their diagnosis. This exercise proposes the development of a Bayesian network to aid in diagnosing autism in children, utilising various clinical observations and data.

Clinical observations indicate that 15% of patients experience social interaction problems, particularly difficulties relating to other children and adults. Of this group, 70% also exhibit limited nonverbal communication, characterised by minimal or no gestures and facial expressions. If they do not suffer from social interaction problems, the likelihood of having limited nonverbal communication drops to 20%. Furthermore, patients with social interaction problems also experience motor stereotypies (the constant repetition of movements or sounds) 65% of the time; this number drops to 20% if they do not have social interaction problems.

Finally, if a child presents limited nonverbal communication and motor stereotypies, the probability of being diagnosed with autism is estimated at 99%. If only one of these two factors is present, autism is present in 85% of cases. In the absence of both, only 5% of children have autism.