On the Semantics of Bipolarity and Fuzziness

Abstract

This paper analyzes the relationship between fuzziness and bipolarity, notions which were devised to address different kinds of uncertainty: linguistic imprecision, in the former, and knowledge relevance and character or polarity, in the latter. Although different types of fuzziness and bipolarity have been defined, these relations are not always clear. This paper proposes the use of four-valued extensions to provide a formal method to rigorously define and compare the semantics and logical structure of diverse combinations of fuzziness and bipolarity types. As a result, this paper claims that these notions and their different types are independent and not semantically equivalent despite its possible formal equivalence.

Paired structures in knowledge representation

“…The point of departure of this paper can be found in the above considerations, together with the bipolar approach proposed by Dubois and Prade in several papers (see [22], [23], [24]). Among other things, Dubois and Prade proposed a classification of bipolar models in three types of bipolarity that indeed shows similarities with our proposal below, but also essential differences: our approach, as it will be seen, follows from a constructive view of what we call paired structures, by focussing on how the semantic tension between two opposites generates certain types of neutrality (see [62] for a previous attempt). In this sense we emphasize the key role of certain neutralities in our knowledge representation models, as pointed out by Atanassov [4], Smarandache [70] and others.…”