Optimisation of a non linear fuzzy function

Facchinetti, Gisella; Giove, Silvio; Pacchiarotti, Nicoletta

doi:10.1007/s00500-002-0164-z

Cited by 7 publications

(4 citation statements)

References 11 publications

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“…Then for any a ∈ F the set of -cut of fuzzy number a the interval a = [L a ( ), R a ( )], ∈ [0, 1], is defined [14]. Let a ∈ F, b ∈ F and…”

Section: The Space Of the Pairs Of Fuzzy Numbersmentioning

confidence: 99%

“…Then to provide the solution of the closed-loop system (14) x(t) →∞, one has to make additional investigations.…”

Section: Remarkmentioning

confidence: 99%

“…Let us define by F the class of convex normal fuzzy numbers. Then for any a ∈ F the set of α‐cut of fuzzy number a the interval a α = [ L a (α), R a (α)], α∈[0, 1], is defined 14. Let a ∈ F , b ∈ F and a α = [ L a (α), R a (α)], b α = [ L b (α), R b (α)].…”

Section: The Space Of the Pairs Of Fuzzy Numbersmentioning

confidence: 99%

See 2 more Smart Citations

Optimal synthesis problem for the fuzzy systems

Aliev

Niftiyev

Zeynalov

2010

Optim Control Appl Methods

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In this paper, first a space of fuzzy numbers is constructed and a scalar product is introduced. The derivative of fuzzy function in this space is defined. Further, a synthesis problem for fuzzy systems is considered. A formula for optimal control is obtained.From (20) we see that P( , s; t) is positive homogeneous on s ∈ R. It is known that [18] this function is either convex or concave with respect to s ∈ R. First, let P( , s; t) be convex. Then P( , 0; t) 1 2 [P( , −1; t)+ p( , 1; t)].

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“…Then for any a ∈ F the set of -cut of fuzzy number a the interval a = [L a ( ), R a ( )], ∈ [0, 1], is defined [14]. Let a ∈ F, b ∈ F and…”

Section: The Space Of the Pairs Of Fuzzy Numbersmentioning

confidence: 99%

“…Then to provide the solution of the closed-loop system (14) x(t) →∞, one has to make additional investigations.…”

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

Optimal synthesis problem for the fuzzy systems

Aliev

Niftiyev

Zeynalov

2010

Optim Control Appl Methods

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“…The control problems containing indeterminacies have been studied, for example, in papers [1][2][3][4][5]. To investigate fuzzy optimal control problems, one has to define the notion of a derivative of fuzzy functions.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Optimal Control Problem with Non-linear Functional

Niftiyev

Zeynalov

Poormanuchehri

2011

Fuzzy Information and Engineering

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In this paper, we introduce a new space of fuzzy numbers equipped with a scalar product defined in this space. The notion of a derivative of a fuzzy function in this space is defined. By employing these notions, an optimal control problem with non-linear functional is formulated and an optimality condition is obtained in the form of maximum principle. Using this result, the numerical algorithm is offered for the solution of such problems.

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