Minimum and maximum fuzziness generalized operators

✍ Scribed by I.J. Rudas; M.O. Kaynak

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 547 KB
• Volume: 98
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(96)00381-8

✦ Synopsis

New methods for constructing generalized triangular operators, using a minimum and maximum fuzziness approach are outlined. Based on the entropy of a fuzzy subset, defined by using the equilibrium of the generalized fuzzy complement, the concept of elementary entropy function and its generalizations are introduced. These functions assign a value to each element of a fuzzy subset that characterizes its degree of fuzziness. It is shown that these functions can be used to construct the entropy of a fuzzy subset. The new generalized T-norm and generalized T-conorms are defined as minimum and maximum entropy operations. They are commutative semigroup operations on [0, 1] with identity elements but they are not monotonic. (~) 1998 Elsevier Science B.V. All rights reserved.