Fuzzy Logic

Fuzzy logic is a totally different approach to representing uncertainty:

• It focuses on ambiguities in describing events rather the uncertainty about the occurrence of an event.
• Changes the definitions of set theory and logic to allow this.
• Traditional set theory defines set memberships as a boolean predicate.

Fuzzy Set Theory

• Fuzzy set theory defines set membership as a possibility distribution.The general rule for this can expressed as:
  
  
  where n some number of possibilities.
  This basically states that we can take n possible events and us f to generate as single possible outcome.
  This extends set membership since we could have varying definitions of, say, hot curries. One person might declare that only curries of Vindaloo strength or above are hot whilst another might say madras and above are hot. We could allow for these variations definition by allowing both possibilities in fuzzy definitions.
• Once set membership has been redefined we can develop new logics based on combining of sets etc. and reason effectively.