Interpreting fuzzy set operations and Multi Level Agreement in a Computing with Words context

Computing with Words (CWW) aims to investigate the possibility of imitating the unique ability of humans for approximate reasoning on the basis of approximately defined classes and concepts in the form of words. Type-2 fuzzy sets have been used to provide an adequate modeling basis for words in a fuzzy logic context. In the context of type-2 fuzzy sets employed as part of CWW, a variety of research efforts have been made to investigate approaches to model the meaning of specific words using type-2 fuzzy sets. In this paper we start by focusing on the interpretation of classical set-theoretical operations (complement, union and intersection) for crisp and type-1 fuzzy sets. We proceed by extending the interpretations to the results of the union and intersection operations of interval type-2 fuzzy sets, specifically indicating their effect on the uncertainty representation in the sets. We note the impact of the choice of t-norms and t-conorms in particular in the context of CWW applications where the interpretation of the resulting sets and its resemblance to the human intuitive meaning of the concept or word is essential. Finally, we provide the interpretation and reasoning behind the Multi Level Agreement (MLA) operation based on zSlices which was previously introduced and discuss the requirement for the selection of the right operations for the amalgamation of individual fuzzy sets and the potential for investigating this choice in particular in a CWW context.