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Applications for Rule-Based Type-2 Fuzzy Logic Systems

Fuzzy logic systems expert Jerry Mendel describes some applications for rule-based type-2 fuzzy logic systems.
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To date, type-2 fuzzy sets and FLSs have been used for the following applications:

  • Classification of coded video streams

  • Co-channel interference elimination from nonlinear time-varying communication channels

  • Connection admission control

  • Control of mobile robots

  • Decision making

  • Equalization of nonlinear fading channels

  • Extraction of knowledge from questionnaire surveys

  • Forecasting of time series

  • Function approximation

  • Preprocessing of radiographic images

  • Handling of relational databases

  • Solving of fuzzy relation equations

  • Transport scheduling

It is important to have some guidance about the kinds of situations that seem to be most appropriate for using type-2 FLSs. So far, in applications of them, they have been found to be very suitable in these cases:

  1. Measurement noise is nonstationary, but the nature of the nonstationarity cannot be expressed beforehand mathematically (as in variable SNR measurements).

  2. A data-generating mechanism is time-varying, but the nature of the time variations cannot be expressed beforehand mathematically (as in equalization of nonlinear and time-varying digital communication channels, or reduction of co-channel interference for nonlinear and time-varying digital communication channels).

  3. Features are described by statistical attributes that are nonstationary, but the nature of the nonstationarity cannot be expressed beforehand mathematically (as in rule-based classification of video traffic).

  4. Knowledge is mined from experts using IF-THEN questionnaires (as in connection admission control for ATM networks).

  5. Linguistic terms are used that have a nonmeasurable domain (as in diagnostic medicine and patient care by nurses).

Here I will focus on the fourth application, knowledge mining using surveys. I interpret knowledge mining (also known as knowledge engineering) as extracting information in the form of IF-THEN rules from people. These rules can be modeled using a fuzzy logic system (FLS), which can then be used as a fuzzy logic advisor (FLA) to make decisions or judgments. By "judgment," I mean an assessment of the level of a variable of interest. For example, in everyday social interactions, each of us is called upon to make judgments about the meaning of another's behavior (kindness, generosity, flirtation, and harassment). Such judgments are far from trivial because they often affect the nature and direction of the subsequent social interaction and communications. Although a variety of factors may enter into our decision, behavior (such as touching and eye contact) is apt to play a critical role in assessing the level of the variable of interest.

In developing an FLA for engineering or social variables, I have adopted the following methodology:

  1. Identify the behavior of interest.

  2. Determine the indicators of the behavior of interest.

  3. Establish scales for each indicator and the behavior of interest.

  4. Establish names and interval information for each of the indicator's fuzzy sets and the behavior of interest's fuzzy sets.

  5. Establish the rules.

  6. Survey people (experts) to provide consequents for the rules.

Uncertainty occurs about the names used for the indicators and behavior of interest, as reflected by their interval information when that information is obtained from people using surveys. It also occurs in the consequents for the rules because a group of experts will not all agree on the consequents; hence, each rule can have a histogram of consequents associated with it. A type-2 FLA can account for these kinds of uncertainties, whereas a type-1 FLA cannot. Making use of surveys, we can design type-1 and type-2 consensus FLAs (for example, an FLA obtained by combining the surveys from a group of people).

Figure 1 depicts one way to use an FLA to advise an individual about a social judgment. It assumes that an individual is given the same questionnaire that was used in Step 6 of the knowledge-mining process, which led to the consensus FLA.

Figure 1 One way to use the FLA for a social judgment.

The completed questionnaire can be interpreted as the individual's FLA, and its output can be plotted on the same plot as the output of the consensus FLA. These outputs can then be compared. If some or all of the individual's outputs are far from those of the consensus FLA, then some action could be taken to sensitize the individual about these differences. Figure 2 depicts this for a type-1 consensus FLA, and Figure 3 depicts this for a type-2 consensus FLA.

Figure 2 Comparison of a type-1 consensus FLA [yc1(x)] behavior level and an individual's FLA behavior [yI(x)] level.

Figure 3 Comparison of a type-2 consensus FLA behavior level and an individual's FLA behavior level.

We immediately see a problem with the type-1 comparisons—namely, how far must the differences be between the individual FLA and the consensus FLA before some action (such as sensitivity training) is taken? This can be difficult to establish when we are comparing two functions, especially because "far" is itself a fuzzy term.

This problem is handled directly with the type-2 comparisons in Figure 3. Note that the individual's FLA is still type-1 and has not changed from Figure 2 to Figure 3. It is treated as type-1 because the individual takes the survey only one time; hence, there is no uncertainty associated with his consequents. The type-2 consensus FLA is represented on Figure 3 by two curves, yc2,L (x) and yc2,R (x). These represent the left and right curves, respectively, for the type-reduced sets of the type-2 consensus FLA. The difference between these curves represents a measure of the uncertainties due to the words used in the surveys as well as the consensus consequents.

Observe from Figure 3 that the individual's FLA curve falls within the bounds of the type-reduced set; hence, no actions need to be taken. This conclusion is quite different from the one that might have been reached by examining the curves in Figure 2, where it appears that there is a significant difference between the individual's behavior level and the consensus FLA's behavior level for larger values of x.

The potential applicability for type-2 FLSs is enormous. At a very high level, rule-based type-2 FLSs should be applicable to every area where type-1 rule-based FLSs have been applied and where some uncertainty is present. Type-2 fuzzy sets should also be applicable to non—rule-based applications of fuzzy sets, again if uncertainty is present.

Let's focus on a small number of specific areas in which there is no doubt that lots of uncertainties are present and in which the payoffs for accounting for them could be very substantial.

  • FL control—To date, no journal articles have appeared on the applications of type-2 FLSs to FL control. Because FL control is today by far the most widely used application of FL, we can expect to see type-2 FL controllers in the not-so-distant future. They will account for system or input uncertainties in an analogous way that stochastic optimal control or robust control does, all within the framework of FL. By modeling uncertainties using appropriate footprints of uncertainty (FOUs), it should be possible to design for robustness using type-2 FL controllers.

  • Diagnostic medicine—FL methods are already being used in medicine, a field in which uncertainties abound. Rule-based FLSs (FLAs) that account for all kinds of uncertainties should be able to provide diagnosticians with decision-making flexibilities. Diagnostic medicine is an application in which both linguistic and numerical rules will need to be developed. One of the challenges will be to design hierarchical type-2 FLSs to let low-level decisions be combined in a proper way for making a top-level decision.

  • Financial applications: Financial models contain many sources of uncertainties because financial markets change in an unknown manner with time. It will be very interesting to model such changes within the framework of type-2 fuzzy sets—determining appropriate FOUs—for important market indicators and variables, and then developing rule-based FLSs for forecasting and making decisions. This is another application in which linguistic and numerical rules will need to be developed.

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