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NPN Fuzzy Sets and NPN Qualitative Algebra: A Computational Framework for Bipolar Cognitive Modeling and Multiagent Decision Analysis
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics (1996)
  • Wen-Ran Zhang, Lamar University
Abstract
An NPN (Negative-Positive-Neutral) fuzzy set theory and an NPN qualitative algebra (Q-algebra) are proposed which form a computational framework for bipolar cognitive modeling and multiagent decision analysis. First a 6-valued NPN logic is introduced which extends the usual 4-valued Q-algebra (S,≈,⊕,⊗) and S={+,-,0,?} by adding one more level of specification; and then a real-valued NPN fuzzy logic is introduced which extends the 6-valued model to the real space {∀(x,y)|(x,y)∈[-1,0]×[0,1]} and adds infinite levels of specifications, As a generalization, a fuzzy set theory is presented that allows β-level fuzzy number-based NPN variables (x,y) to be substituted into (S,≈,⊕,⊗) where ⊗ stands for any NPN T-norm; ⊕ stands for disjunction (V) or union (∪), and β is the number of α-cuts.
Keywords
  • NPN fuzzy sets,
  • NPN qualitative algebra,
  • Bipolar cognitive modeling,
  • Multiagent decision analysis,
  • NPN logic
Disciplines
Publication Date
August, 1996
DOI
10.1109/3477.517031
Citation Information
Wen-Ran Zhang. "NPN Fuzzy Sets and NPN Qualitative Algebra: A Computational Framework for Bipolar Cognitive Modeling and Multiagent Decision Analysis" IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics Vol. 26 Iss. 4 (1996) p. 561 - 574
Available at: http://works.bepress.com/wen-ran_zhang/15/