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Fuzzy Sets and Systems
Volume 145, Issue 2, 16 July 2004, Pages 253-266
A characterization of truth-functions in the nilpotent minimum logic*1
S.-M.San-Min WangCorresponding Author Contact Information, E-mail The Corresponding Author, E-mail The Corresponding Author, a, Bao-Shu Wanga and Xiang-Yun Wangb
a School of Computer Science and Engineering, XiDian University, No. 2 South Taibai Road, Xi'an 710071, People's Republic of China
b Department of Automatic Control, BeiHang University, Beijing 100083, People's Republic of China
Received 30 May 2002; Revised 25 February 2003; accepted 27 March 2003. Available online 23 April 2003.
Abstract
By introducing a new family of partitions into the n-cubenext term [0,1]previous termnnext term, the problem of characterizing truth tables of formulas in the nilpotent minimum logic is solved and their normal forms are presented. So far, only this kind of previous termfuzzynext term truth functions have normal forms among all previous termfuzzynext term propositional calculi which are based on left-continuous but discontinuous t-norm.
Author Keywords: previous termFuzzynext term logic; previous termFuzzynext term logic function; NM-algebra; NM-function; Normal forms
The Article