Banach spaces generated by strongly linearly independent fuzzy numbers

Esmi, Estevão; Barros, Laécio Carvalho de; Pedro, Francielle Santo; Laiate, Beatriz

doi:10.1016/j.fss.2020.09.010

Cited by 15 publications

(4 citation statements)

References 15 publications

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“…where + and q i A i stand for the usual sum and scalar multiplication in the class of fuzzy numbers [13].…”

Section: Mathematical Backgroundmentioning

confidence: 99%

Bidimensional Fuzzy Initial Value Problem of Autocorrelated Fuzzy Processes via Cross Product: The Prey-Predator Model

Laiate¹,

Barros²,

Pedro³

et al. 2021

Atlantis Studies in Uncertainty Modelling

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This paper introduces the notion of a bidimensional fuzzy initial value problem for a special class of fuzzy functions. These functions, also called A-linearly correlated fuzzy processes, are a particular case of the socalled S-linearly correlated fuzzy processes, whose range is embedded in Banach spaces of fuzzy numbers. To this end, it recalls the notion of cross product and proves that this operation is the Zadeh's extension of the linearization of the real-valued function given by the product of two real numbers. The equivalence between the bidimensional FIVP under the Fréchet derivative and a nonlinear classical initial value problem is provided. Lastly, an application on the preypredator is presented.

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“…where + and q i A i stand for the usual sum and scalar multiplication in the class of fuzzy numbers [13].…”

Section: Mathematical Backgroundmentioning

confidence: 99%

Bidimensional Fuzzy Initial Value Problem of Autocorrelated Fuzzy Processes via Cross Product: The Prey-Predator Model

Laiate¹,

Barros²,

Pedro³

et al. 2021

Atlantis Studies in Uncertainty Modelling

Self Cite

View full text Add to dashboard Cite

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“…where L A , U A : [0, 1] → R represent the lower and upper endpoints of the α−cuts, respectively, ∀α ∈ [0, 1] [9]. A fuzzy number is uniquely determined by its levels sets [15].…”

Section: Mathematical Backgroundmentioning

confidence: 99%

“…Theorem 2. [9] Let A = (a; b; c; d) be a non-symmetric trapezoidal fuzzy number. The set {χ {1} , A, A 2 , .…”

Section: Definition 2 [9]mentioning

confidence: 99%

“…This procedure can be extended to sets of fuzzy numbers whenever they have the property of strongly linearly independence. In this case, the Minkowski combinations of the fuzzy numbers involved turns to be Banach spaces of arbitrary dimension when endowed with induced operations of sum and scalar multiplication [9]. This fact was used to establish a calculus theory based on the Fréchet derivative of fuzzy functions called S-linearly independent fuzzy processes, whose range are embedded in Banach spaces of fuzzy numbers [10,18].…”

Section: Introductionmentioning

confidence: 99%

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Solutions of Systems of Linear Fuzzy Differential Equations for a Special Class of Fuzzy Processes

Laiate

Esmi

Pedro

et al. 2021

Lecture Notes in Networks and Systems

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This paper introduces the concept of first-order systems of linear fuzzy differential equations for S-linearly correlated fuzzy processes. These fuzzy processes have range embedded in Banach spaces of fuzzy numbers, and the fuzzy initial value problems studied are given in terms of the Fréchet derivative of these fuzzy functions. An equivalence between the first-order systems of linear fuzzy differential equations and a family of classical first-order systems of linear differential equations is established. Also, conditions on the existence and uniqueness of the solutions are presented. Lastly, an application on the multiple mass-spring system is provided.

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Differential and Integral Calculus for Fuzzy Number-Valued Functions with Interactivity

Barros

Pedro

Esmi

2021

Advances in Fuzzy Integral and Differential Equations

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Banach spaces generated by strongly linearly independent fuzzy numbers

Cited by 15 publications

References 15 publications

Bidimensional Fuzzy Initial Value Problem of Autocorrelated Fuzzy Processes via Cross Product: The Prey-Predator Model

Bidimensional Fuzzy Initial Value Problem of Autocorrelated Fuzzy Processes via Cross Product: The Prey-Predator Model

Solutions of Systems of Linear Fuzzy Differential Equations for a Special Class of Fuzzy Processes

Differential and Integral Calculus for Fuzzy Number-Valued Functions with Interactivity

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