Fuzzy Logic: Advantage of Fuzzy Logic and Fuzzy Set Theory (Especially for GATE-Geospatial 2022)

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GIS, at present, has several limitations which make them inefficient tools for decision-making. Biggest limitation is that current commercial systems are based on an incorrect logical foundation. Current GIS are mainly based on Boolean logic.

Fuzzy logic is an alternative logical foundation coming from artificial intelligence (AI) technology with several useful implications for spatial data handling. Different to traditional logic, fuzzy logic accommodates the imprecision in information, human thought and perception. This is more suitable for dealing with real world problems, because most human reasoning is imprecise.

Advantage of fuzzy logic is that it allows the natural description, in linguistic terms, of problems that should be solved rather than in terms of relationships between precise numerical values.

This Figure Shows Results of Fuzzy Command Tool

Fuzzy set theory is an extension of the classical set theory. A fuzzy set A is defined mathematically as follows:

If denotes a space of objects, THEN the fuzzy set A in is the set of ordered pairs:

where the membership function is known as the โ€œdegree of membership of x in Aโ€ .

Usually, is a real number in the range , where 0 indicates no-membership and 1 indicates full membership. Here of x in A specifies the extent to which can be regarded as belonging to set A.

The standard operations of union, intersection, and complement of fuzzy sets A and B, defined in domain X, create a new fuzzy set whose membership function is defined as:

  • Union:
  • Intersection:
  • Complement:
Diagram Shows Standard Fuzzy Operations

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