Calculus for interval-valued functions using generalized Hukuhara derivative and applications

DOI10.1016/j.fss.2012.12.004zbMath1278.26025OpenAlexW1986928005MaRDI QIDQ385364

Antonio Rufián-Lizana, Heriberto Román-Flores, Yurilev Chalco-Cano, M. Dolores Jiménez-Gamero

Publication date: 2 December 2013

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10533/130361

zbMATH Keywords

differentiabilityintegrabilityfuzzy functionsgeneralized Hukuhara differenceinterval-valued functions

Mathematics Subject Classification ID

Fuzzy real analysis (26E50) Fuzzy ordinary differential equations (34A07)

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Cites Work

• Unnamed Item
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• Generalized derivative and \(\pi \)-derivative for set-valued functions
• Elementary fuzzy calculus
• Fixed points, fixed sets, and \(m\)-retracts
• Goal programming problems with interval coefficients and target intervals
• Multiple objective linear programming models with interval coefficients -- an illustrated overview
• First order linear fuzzy differential equations under generalized differentiability
• On new solutions of fuzzy differential equations
• A generalization of Hukuhara difference and division for interval and fuzzy arithmetic
• Solutions of fuzzy differential equations based on generalized differentiability
• Nonlinear variation of parameters formula for set differential equations in a metric space
• Generalized Hukuhara differentiability of interval-valued functions and interval differential equations
• Stability of set differential equations and applications
• The optimality conditions for optimization problems with convex constraints and multiple fuzzy-valued objective functions
• Comparation between some approaches to solve fuzzy differential equations
• On the differentiability of multifunctions
• Calculus for interval functions of a real variable
• Multiobjective programming in optimization of interval objective functions -- a generalized approach
• A non-stochastic approach for modeling uncertainty in population dynamics
• The Cauchy problem for continuous fuzzy differential equations
• Minimax regret solution to linear programming problems with an interval objective function
• Existence and interrelation between set and fuzzy differential equations.
• Introduction: Set-valued analysis in control theory
• Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations
• Set valued functions in Fréchet spaces: continuity, Hukuhara differentiability and applications to set differential equations
• Multiobjective transportation problem with interval cost, source and destination parameters
• Embedding of level-continuous fuzzy sets on Banach spaces
• On the differentiability of set-valued functions defined on a Banach space and mean value theorem
• Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem
• The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions
• The Karush--Kuhn--Tucker optimality conditions in an optimization problem with interval-valued objective function
• A nonlinear interval number programming method for uncertain optimization problems
• A note on fuzzy differential equations
• A differential calculus for multifunctions
• Impulsive functional differential inclusions and fuzzy population models
• Multiobjective programming in optimization of the interval objective function
• Linear Multiple Objective Problems with Interval Coefficients
• An application of the central limit theorem for banach-space-valued random variables to the theory of random sets
• Set Differential Equations and Flow Invariance
• Limit theorems for random compact sets in Banach space
• Testing Statistical Hypotheses
• Set-valued analysis

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