Handbook of Granular Computing

The arithmetical and topological structures of fuzzy numbers have been developed in the 1980s and this enabled to design the elements of fuzzy calculus (see [6, 7]); Dubois and Prade stated the exact analytical fuzzy mathematics and introduced the well-known LR model and the corresponding formulas for the fuzzy operations. For the basic concepts see, e.g., [8–12]. More recently, the literature on fuzzy numbers has grown in terms of contributions to fuzzy arithmetic operations and to the use of simple formulas to approximate them; an extensive recent survey and bibliography on fuzzy intervals is in [13]. Zadeh’s extension principle (with some generalizations) plays a very important role in fuzzy set theory as…