Fuzzy Logic

Fuzzy logic is a mathematical approach to problem solving. Fuzzy logic bridges the gap between precise valuations done with classical logic, such as that typically implemented with computer systems, and a logic that reasons on uncertainties, vagueness, and judgments. These logical extensions are used in GIS to allow for a wider coverage of uncertainty than is generally available in standard software.

The term fuzzy logic itself has been a source of misunderstanding and has provoked discussions ever since it was created. Fuzzy logic is a formal, logical approach to imprecision rather than an imprecise logic. Fuzzy logic differs from classical logic in that statements are not simply black or white, or true or false. In traditional logic, a statement takes on a value of either 0 or 1 (i.e., false or true); in fuzzy logic, a statement can assume any real value between 0 and 1.

Fuzzy logic in general is a multivalued logic utilizing fuzzy set theory. Given the problem of designing increasingly complex systems in an engineering context, Lotfi Asker Zadeh proposed fuzzy sets in a seminal paper in 1965. Due to their ability to handle partial truth in making decisions in real-world situations, fuzzy sets and fuzzy logic have drawn much attention in a variety of disciplines. Fuzzy logic has become the core methodology in what is now called “soft computing,” a collection of tools for handling uncertainty as well as imprecise data and facts.

Within this context, it is important to note some subtle distinctions between the concepts of data, facts, information, and knowledge. Data are what you measure and collect. Facts presume an understanding of your data and a certain reasoning used to collect them. Information is what you understand from the data and facts, and knowledge is the result of searching for meaningful patterns within that understanding. All of these interact with or depend on each other throughout any analysis.

Uncertainty handled by means of fuzzy sets and fuzzy logic is perceived to be different from that arising from a mere lack of data or error of measurement. It is concerned with imprecision, ambiguity, and vagueness of information and knowledge. Fuzzy sets and fuzzy logic are argued to provide a more flexible approach to modeling variables and processes and to making decisions, thus producing precise results from imprecise and uncertain data and facts. Fuzzy logic therefore attempts to mimic humans who are expert in utilizing uncertain and imperfect data, information, and knowledge.

Geographical analysis is prone to uncertainty and imprecision. For example,

• Most geographical objects in the real world do not have precise boundaries. It is difficult to model natural boundaries by imposing precise borderlines (e.g., the location of coastlines or the transition between vegetation types). Even administrative boundaries may be uncertain for legal or statistical issues.
• Geographical concepts are vague. This is caused mainly by cognitive and linguistic processes involved with conceptualizing spatial phenomena.
• Geographical data have qualities that may be known only to the experienced expert in a certain field and may not be communicated completely on a map. Lack of communicating uncertainty in a map for use by different experts often causes problems. For example, the phenomenon of “noise” shown as high, medium, and low decibel levels on a map may not be easily comprehended by planners, technicians, politicians, or others who are making decisions on where to build a new street.
• Even measured data may be incomplete and uncertain due to use of inappropriate measurement tools or simply lack of time and money to measure thoroughly.

Fuzzy logic has great potential to address these forms of uncertainty and imprecision by extending beyond the binary representation of uncertainty.

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