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,/spl ap/,/spl oplus/,/spl otimes/) 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 {/spl forall/(x,y)|(x,y)/spl isin/[-1,0]/spl times/[0,1]} and adds infinite levels of specifications, As a generalization, a fuzzy set theory is presented that allows /spl beta/-level fuzzy number-based NPN variables (x,y) to be substituted into (S,/spl ap/,/spl oplus/,/spl otimes/) where /spl otimes/ stands for any NPN T-norm; /spl oplus/ stands for disjunction (V) or union (/spl cup/), and /spl beta/ is the number of /spl alpha/-cuts.