Certainty Factors

Rules may represent either guidelines based on experience, or compact descriptions of events, processes, and behaviors with the details and assumptions omitted. In either case, there is a degree of uncertainty associated with the appHcation of the rule to a given situation. Rule-based systems allow for expHcit ways of representing and dealing with uncertainty. This includes the representation of the uncertainty of individual rules, as weU as the computation of the uncertainty of a final conclusion based on the uncertainty of individual rules, and uncertainty in the data. There are numerous approaches to uncertainty within the rule-based paradigm (2,35,36). One of these approaches is based on what are called certainty factors. In this approach, a certainty factor (CF) can be associated with variable—value pairs, and with individual rules. The certainty of conclusions is then computed based on the CF of the preconditions and the CF for the rule. For example, consider the foUowing example. 

Thus certainty factors express the intuitive notion that the certainty of a conclusion should be lower than the certainty of the data and knowledge involved in arriving at the conclusion. Certainty factor theory also allows for combining the CFs of conjunctions, disjunctions, and negations ... 

The certainty factor approach has been among the more popular rule-based approaches to uncertainty. However, although it is easy to apply given the individual CFs, acquiring the raw CFs from the experts is often quite difficult. Further, although the formulas for CF combination are mathematically appealing, they often have no relation to the ways in which experts combine evidence to arrive at conclusions. Some of the task-specific approaches discussed later address uncertainty combination in a more intuitive way (35). 

That is why systems that can handle this kind of uncertainty are mandatory elements of an expert system. Uncertainty in expert systems can be handled in a variety of approaches certainty factors, fuzzy logic, and Bayesian theroy. 

Certainty theory is an approach to inexact reasoning that describes uncertain information in a certainty factor [28]. Certainty factors are used as a degree of confirmation of a piece of evidence. Mathematically, a certainty factor is the measure of belief minus the measure of disbelief. Again, using an example with John, an uncertainty could be the following ... 

FIGURE 2.4 Simple mathematical functions can be used to relate certainty factors with a corresponding outcome. Each outcome — early, on time, late — is associated with a function. Early arrival is defined for a time frame between 8 20 and 8 30, with certainty factors between 0 and 1. An input time of 8 25 with a certainty factor of 1 would result in an early arrival. The smaller the certainty factor, the wider the time frame for arrival. The same applies to the other functions. 

The rule says that if John leaves the house at 8 00, the certainty that he will reach the bus in time and attend to the meeting is 80%. Depending on the time frame, we can create functions that relate certainty factors with the time of arrival. Figure 2.4 show how the aforementioned example of John s arrival can be described by means of a transfer function. 

Even the concept of certainty factors is not derived from a formal mathematical basis it is the most commonly used method to describe uncertainty in expert systems. This is mainly due to the fact that certainty factors are easy to compute and can be used to effectively reduce search by eliminating branches with low certainty. However, it is difficult to produce a consistent and accurate set of certainty factors. In addition, they are not consistently reliable a certainty factor may produce results opposite to probability theory. 

Certainty Factors are used as a degree of conhrmation of a piece of evidence. Mathematically, a certainty factor is the measure of belief minus the measure of disbelief. 

Prediction Simulation Fuzzy Logic Certainty Factors... 

Each if statement includes a parameter considered in a certain context that is tested for a value based on the operation. The then statement has the same syntax but provides a certainty factor. This construction basically makes no difference between the structure of the question and the answer and allows for the application of other rules as a result of a rule — although at the cost of losing modularity and clarity of the rule base. An example for a MYCIN rule is as follows ... 

The 0.7 is the certainty that the conclusion will be true given the evidence. MYCIN uses certainty factors to rank the rules or outcomes it will abandon a search once the certainty factor is less than 0.2. If the evidence is uncertain the certainties of the bits of evidence are combined with the certainty of the rule to give the certainty of the conclusion. 

These rules are used to reason backward that is, MYCIN starts with a hypothesis that needs to be validated and then works backward, searching the rules in the rule base that match the hypothesis. The hypothesis can be either verified with a certainty factor or can be proven wrong. 

Whereas expert system languages for reasoning like PROLOG are universally qualified (all/all not) and nonquantitative, MYCIN allows an aspect of existential qualification (some, some not) and is quantified. The rules have both a rule form as above, and a certainty factor (CF). For those of a mathematical bent, the MYCIN certainty factor is defined by the following equation ... 

Certainty factor The confidence the scientist has in a given piece of information. Usually a value in a range of numbers (e.g. 0 to 1 or -1 to 1). They may or may not have a statistical basis. They may apply to the confidence the expert has in the conclusion in a rule, or to the input supplied by the end-user during a problem solving session. 

Figure 5 shows several representative rules generated by the system automatically. Each rule has a probability associated with it. These are called certainty factors (CFs). CFs are a measure of how certain the system can be of that particular rule. Here, CFs take on values between -100 and 100. Another scale frequently used is 0 to 100. The CFs are a product of three terms the first is the grid value, the second is the importance of the trait, and the last is dependant on which CF scale the inference engine utilizes. 

These rules are ready to be run by an inference engine. The inference engine is a separate entity from the KEY system. In the present work, a rudimentary inference engine was written in Prolog to test the knowledge base that KEY generated. Each answer the inference engine provides is a result of the combination of certainty factors from several rules. 

Reaction Surface Type Temp. (K) 7 Un- certainty Factor... 

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