ABSTRACT
This chapter introduces the basic concept of fuzzy systems. Fuzzy concepts derive from fuzzy phenomena that commonly occur in the natural world. The chapter deals with definitions of fuzzy sets and fuzzy operators and provides some extension principles and theorems. The concepts formed in human brains for perceiving, recognizing, and categorizing natural phenomena are often fuzzy. The human brain has the incredible ability of processing fuzzy classification, fuzzy judgment, and fuzzy reasoning. One of the effective means of resolving the contradiction is fuzzy set theory, a bridge between high preciseness and high complexity. Set theory was founded in 1874 by G. Cantor, a German mathematician. Cantor’s set theory has made great contributions to the foundations of mathematics. However, due to fuzziness, classical mathematics can encounter substantial difficulties. The polarity between fuzziness and preciseness is quite a striking contradiction for the development of science.
