About decydeWARE™

Why decydeWARE™ is Different

Existing computing technology displays a rudimentary intelligence that captures some of the ways that people reason. decydeWARE™ is based on a new algorithm that extends machine intelligence to include the intuitive reasoning people use when they make judgement calls.

• Existing Binary Computing Technology
People can draw precise yes/no conclusions. "The sun is shining." "The door is locked." "There are seven pebbles." Binary computing technology captures this process.

The language of binary computing technology is Boolean - yes/no, on/off, 0/1, true/false, black/white. As a result, binary technology can only process data that is precise, and/or quantifiable. And, there must be a specific rule for every contingency. In the real world this means an infinite number of rules.

If there is no rule to cover the situation at hand, binary computing technology cannot draw conclusions.

• Existing Fuzzy Computing Technology
People can draw conclusions that are not precise. "The car is travelling very fast." "The box feels kind of heavy." "The room seems to be cooling." Fuzzy computing technology captures this.

Because fuzzy technology uses fuzzy mathematics and the same linguistic variables that people use to summarize numerical data - "fast", "heavy", "cool" - it can, like people, compute with imprecise measurement-based information. And, it is beginning to be able to compute with concepts like "honesty", "reliability", and "risk", where the perception-based information cannot be quantified.

Fuzzy technology uses fuzzy logic to infer conclusions. Like people when they reason, it summarizes experience in words, "If the management is not very honest, then the investment risk is fairly high". This means fuzzy technology can get by with fewer rules than binary technology..

But existing fuzzy computing technology still needs a complete set of overlapping rules. Otherwise it cannot draw conclusions.

• New Fuzzy Computing Technology
Even though existing IT systems display a rudimentary intelligence, they are far from doing what people must do regularly in order to survive in an uncertain world. That is, make judgement calls without much experience or information.

People hypothesize. They use their wits to extrapolate from limited experience and sketchy information. They can draw conclusions based on one experience, then modify their impressions and opinions as they gain experience, or as more evidence comes in.

An algorithm has been invented that captures this cognitive process. A new fuzzy implication operator drives the inferencing process. The engine embodying the operator can extrapolate consistent and mathematically rigorous conclusions from one or two rules. And do it with minimum information.

decydeWARE™ is intelligent information technology (IIT) that uses the new fuzzy engine to reason - like people do - from one experience-based rule. And, modify or change the conclusions as more experience is gained, or new information comes in.

Why decydeWARE™ is Different - A More Technical Description.

1. When there is a mismatch between input and rule input:
Existing fuzzy logic implication operators do not generate outputs that correspond to intuitive ideas for the output when the input does not match the rule input exactly.

For example, in the case of mismatch between input and rule input, informal logic postulates that the output should be an envelope of possibility that spreads around the rule output, and spread wider as the input becomes less similar to the rule input. This spreading reflects the increased uncertainty about the range of possible outputs. If the input is "sort of" like the rule input, the output should be "sort of" like the rule output, where "sort of" means an increased degree of fuzziness, and/or a wider support set.

Existing fuzzy logic generates two basic types of outputs when there is a mismatch between data input and rule input. The envelope of possibility generated by the Zadeh implication operator has a core identical to the rule output and infinite flat tails whose height is proportional to the mismatch. The envelope of possibility generated by the Sugeno implication operator does not spread at all but becomes increasingly subnormal as the mismatch increases. Neither of these outputs corresponds to intuitive ideas about the mismatch.

This algorithm bridges the gap between non-matching rules and rule inputs by creating envelopes of possibility for an output that is closer to intuitive reasoning.
The desired shape of the envelope of possibility is a system parameter determined at set up by an expert. The similarity between the user input and the rule input may be measured by existing measures, or by a novel measure.
The rate of spread is a function of the dissimilarity between the user input and the expert determined rule input. It may also depend on the location of the input in the input space, or other parameters of the input and the rule input. In multidimensional inputs, a weight function makes it possible for one input dimension to "compensate" for another.

2. When there is not a complete set of overlapping rules:
Existing fuzzy logic requires a complete set of overlapping rules covering all possible combinations of inputs. Humans can reason from a very sparse set of rules or examples.

Currently, expert knowledge in fuzzy logic is formulated as a complete set of rules. However, in much of informal reasoning expert knowledge is represented by a sparse set of rules. Knowledge of how to deviate from those rules. And, a measure of how far to trust those deviations. None of this is represented by existing fuzzy logic.

This algorithm eliminates the requirement for a complete set of overlapping rules. It is possible to calculate the degrees of similarity between disjoint fuzzy sets using a distance function in order to interpolate or extrapolate from sparse rules. Fuzzy limits can be set on the vaguely known possible rate of change. It is possible to reconcile contradictory inputs, and choose the appropriate pattern from which to interpolate or extrapolate.

3. When there is a gap between examples and rules:
In current practice, a large number of discrete data points (examples) are sampled, clustering analysis or the application of neural nets follows. Then a complete fuzzy rule set is extracted. People, on the other hand, will start reasoning from one example, correct their reasoning on getting a second example, and with no switchover from one mathematical approach to another, continue formulating new rules from whatever examples are available.

This algorithm smoothly bridges the gap between examples and rules by calculating the degrees of similarity (or distance) between two fuzzy sets. Between two point data examples. Or between two fuzzy numbers.

4. When assessing degrees of continuity and chaos:
Existing fuzzy logic does not explicitly encode degrees of continuity and chaos. People assess certain environments as more chaotic than others. In chaotic environments it is just as possible that a small change in the input could lead to a large change in the output, as to a small change. Assessing the possibilities is an important survival skill.

This algorithm incorporates a new family of implication operators, of which the Zadeh implication operator is a special case, that explicitly encode degrees of continuity and chaos. If the inputs are multidimensional, an output can be continuous in one of the input dimensions but chaotic in another. This is equivalent to providing early warning of high risk.

5. When the concepts of belief and plausibility are applied to propositions:
In existing fuzzy measure theory, the concepts of belief and plausibility are applied only to assertions. Assertions are statements of fact.

People however apply belief and plausibility concepts to new rules entailed from established rules, or propositions. Any conclusions drawn from entailed rules should inherit the degrees of belief and plausibility derived from the entailment before they are used in decision-making.

This algorithm applies concepts of belief and plausibility to propositions as well as assertions. Using the kernel of the new fuzzy implication operator, one can arrive at a degree of plausibility for an entailed proposition and an envelope of possible conclusions for a given input.
Then using set intersection or other distance measures, the operator can calculate the strength of the chain of evidence linking the data to the conclusion, and obtain an envelope of belief.
The difference between the envelopes of belief and possibility measures all the vagueness, uncertainty gaps, contradiction, and probabilistic nature of the rules and the input data as well as the mismatch between the inputs and the rules inputs. The degree to which an assertion is proven and the degree to which it is merely possible can be quantified.

6. When simulating systems with fractal geometry:
Existing fuzzy logic expert systems do not explicitly simulate fractal systems.

This algorithm can use the fractal dimension, or other parameters, to calculate an envelope of possibility for fractal systems. Using the new implication operator with the appropriate kernel and the appropriate new distance measure, an envelope of possibility can be found for a system characterized by a vaguely specified fractal dimension.

In summary, existing fuzzy logic systems have limited decision-making capabilities and are, therefore, less likely to emulate a desired system requiring reasoning that is similar to informal human reasoning. As described above, the algorithm on which decydeWARE™ is based addresses these limitations. As a result decydeWARE™ can duplicate the intuitive reasoning that people use when they make judgement calls.

decydeWARE™
Lorna Strobel Stewart Ph.D.
4/8/03