This paper presents two models that use interval type-2 fuzzy sets (IT2 FSs) for representing the meaning of words that refer to emotions. In the first model, the meaning of an emotion word is represented by IT2 FSs on valence, activation, and dominance scales. In the second model, the meaning of an emotion word is represented by answers to an open-ended set of questions from the game of Emotion Twenty Questions (EMO20Q). The notion of meaning in the two proposed models is made explicit using the Frege an framework of extensional and intensional components of meaning. Inter- and intra-subject uncertainty is captured by using IT2 FSs learned from interval approach surveys. Similarity and subsethood operators are used for comparing the meaning of pairs of words. For the first model, we apply similarity and subsethood operators for the task of translating one emotional vocabulary, represented as a computing with words (CWW) codebook, to another. This act of translation is shown to be an example of CWW that is extended to use the three scales of valence, activation, and dominance to represent a single variable. We experimentally evaluate the use of the first model for translations and mappings between vocabularies. Accuracy is high when using a small emotion vocabulary as an output, but performance decreases when the output vocabulary is larger. The second model was devised to deal with larger emotion vocabularies, but presents interesting technical challenges in that the set of scales underlying two different emotion words may not be the same. We evaluate the second model by comparing it with results from a single-slider survey. We discuss the theoretical insights that the two models allow and the advantages and disadvantages of each.