Modal intervals: reason and ground semantics
Proceedings of the International Symposium on interval mathematics on Interval mathematics 1985
Information Sciences: an International Journal
Stable embedding of ill-posted linear equality systems into fuzzified systems
Fuzzy Sets and Systems
t-Norm-based addition of fuzzy intervals
Fuzzy Sets and Systems
A note to the T-sum of L-R fuzzy numbers
Fuzzy Sets and Systems
Shape preserving additions of fuzzy intervals
Fuzzy Sets and Systems
Analytical expressions for the addition of fuzzy intervals
Fuzzy Sets and Systems - Special issue: fuzzy arithmetic
T-sum of bell-shaped fuzzy intervals
Fuzzy Sets and Systems
Inner and outer bounds for the solution set of parametric linear systems
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Algebraic structures for fuzzy numbers from categorial point of view
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations
Expert Systems with Applications: An International Journal
Solution of a system of linear equations with fuzzy numbers
Fuzzy Sets and Systems
Solutions of fuzzy equations based on Kaucher arithmetic and AE-solution sets
Fuzzy Sets and Systems
Triangular and parametric approximations of fuzzy numbers---inadvertences and corrections
Fuzzy Sets and Systems
A generalization of Hukuhara difference and division for interval and fuzzy arithmetic
Fuzzy Sets and Systems
Fuzzy interval cooperative games
Fuzzy Sets and Systems
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The construction of the membership function of fuzzy intervals is an important problem in vagueness modeling. The preservation of the shape of fuzzy sets during the addition is a natural requirement in practical computation. The LR-fuzzy intervals introduced by Dubois and Prade, satisfy this requirement if the addition is based on the nilpotent t-norm, generated by L or R shape functions. The shortcoming that not any LR-fuzzy interval has an opposite (inverse related to shape-preserving t-norm-based addition), can be solved, if the set of LR-fuzzy intervals is isomorphically included in an extended set, and this extended set forms a group with respect to shape-preserving t-norm-based addition. In this paper we construct the extended set of these LR-fuzzy intervals. We also show that the extended set is a real vector space with scalar product, and the modal intervals can be considered as the elements of this extended set. Finally, we present the algebraic form of LR-fuzzy intervals and the associated application.