Generalized arithmetic operations in interval-valued fuzzy set theory

Authors:
Glad Deschrijver;Annelies Vroman
Affiliations:
Fuzziness and Uncertainty Modelling Research Unit, Department of Mathematics and Computer Science, Ghent University, Belgium;Fuzziness and Uncertainty Modelling Research Unit, Department of Mathematics and Computer Science, Ghent University, Belgium
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology - Dedicated to the 60th birthday of Etienne E. Kerre
Year:
2005

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Abstract

We generalize the addition, subtraction, multiplication and division on L^{I} defined in [4], where L^I is the underlying lattice of both interval-valued fuzzy set theory [14] and intuitionistic fuzzy set theory [1]. We investigate some algebraic properties of these operations. We show that using these operations some important t-norms on L^I and some related operations can be written in a similar way as their counterparts on ([0,1], ≤).