Abstract
Hernández et al. [9] established the axioms that an operation must fulfill in order to be a negation on a bounded poset (partially ordered set), and they also established in [14] the conditions that an operation must satisfy to be an aggregation operator on a bounded poset. In this work, we focus on the set of the membership degrees of the type-2 fuzzy sets, and therefore, the set M of functions from [0, 1] to [0, 1]. In this sense, the negations on M respect to each of the two partial orders defined in this set are presented for the first time. In addition, the authors show new negations on L (set of the normal and convex functions of M) that are different from the negations presented in [9] applying the Zadeh’s Extension Principle. In particular, negations on M and on L are obtained from aggregation operators and negations. As results to highlight, a characterization of the strong negations that leave the constant function 1 fixed is given, and a new family of strong negations on L is presented.
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This paper was partially supported by Universidad Politécnica de Madrid (Spain) and Universidad Mayor (Chile).
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Torres-Blanc, C., Cubillo, S., Hernández-Varela, P. (2018). New Negations on the Type-2 Membership Degrees. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_61
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