Science Fair Project

Uncertainty Management in Rule Based ESMuhammad Ridwan Andi Purnomo, ST, MSc, PhD

Department of Industrial EngineeringFaculty of Industrial TechnologyUniversitas Islam Indonesia2013

What is uncertainty ?

One of the common characteristics of information is its imperfection.Information can be incomplete, inconsistent, uncertain, or all three. Information is often unsuitable for solving a problem.An expert can cope with these defects and can usually make correct judgements and right decisions. Expert systems also have to be able to handle uncertainty and draw valid conclusions.

Uncertainty in ESUncertainty can be defined as the lack of the exact knowledge.It disables us to reach a perfectly reliable conclusion.Example:IF A is trueTHEN B is true B is not always true when A is true.IF today is rainTHEN tomorrow is rain tomorrow can be dry even though today is rain.

Sources of uncertain knowledgeWeak implications put degree of correlations as numerical certainty factors.Imprecise languagenatural language is inherently ambiguous and imprecise sometime, terms like often and sometimes, frequently and hardly ever are preferably than IF THEN term.Unknown dataif the info is missing, then the only solution is to accept unknown and proceed to approximation reasoning.Combining the views of different expertsOccurred when there are different opinions.

Quantification of ambiguous and imprecise term

Cont

How can we define probability?The probability of an event is the proportion of cases in which the event occurs (Good, 1959).

Probability can also be defined as a scientific measure of chance.

Probability can be expressed mathematically as a numerical index with a range between zero (an absolute impossibility) to unity (an absolute certainty).

How can we define probability?

Example: dice throwing eventProbability to get side 6 is: (this is mutually exclusive case)

Probability formulaProbability that A occurred if B occurred is: (this is not mutually exclusive)

Probability that both A and B are occurred, is called joint probability.

Bayesian formula

Bayesian formulaIn rule based ES, there are several rules, hence:

Bayesian formulaIf the occurrence of event A depends on only two mutually exclusive events, B and NOT B, then:

Bayesian reasoningIF E is trueTHEN H is true {with probability p} event E occurs, then the probability that event H will occur is p.

Example: Weather forecastThe expert system should give us two possible outcomes tomorrow is rain and tomorrow is dry and provide their likelihood the expert system must determine the conditional probabilities of the two hypotheses tomorrow is rain and tomorrow is dry.The Rules:Rule: 1IF today is rain THEN tomorrow is rainRule: 2IF today is dry THEN tomorrow is dry

Example: Weather forecastRewrite the rules based on the probability:Rule: 1IF today is rain {LS 2.5 LN .6} THEN tomorrow is rain {prior .5}Rule: 2IF today is dry {LS 1.6 LN .4} THEN tomorrow is dry {prior .5}

Example: Weather forecast

Example: Weather forecast

Example: Weather forecast

Example: Weather forecastRules 1 produces:

Rules 2 produces:

Example: Weather forecastConclusion:If it is raining today there is a 71 per cent chance of it raining and a 29 per cent chance of it being dry tomorrow.Check !How is user input today is dry ? Compute probability tomorrow is dry and rain probability.

Complete example of weather forecast

Complete example of weather forecast

Complete example of weather forecast

Complete example of weather forecast

Complete example of weather forecast

Complete example of weather forecast

Complete example of weather forecast

Complete example of weather forecast

Complete example of weather forecast

Thank You !