NPN fuzzy sets and NPN qualitative algebra: a computational framework for bipolar cognitive modeling and multiagent decision analysis

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