首页|Fuzzy variational calculus in linearly correlated space: Part I
Fuzzy variational calculus in linearly correlated space: Part I
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NETL
NSTL
Elsevier
This article is the first part of series of articles that aim to present the foundations for fuzzy variational calculus for functions taking values in the space of linearly correlated fuzzy numbers RT(A). Recall that the space RT(A) is composed by all sums of a real number r and a fuzzy number qA, where A is a given asymmetric fuzzy number and q is an arbitrary real number. Two advantages of this space are that it can be equipped with a Banach space structure and, similar to additive models in Statistics, its elements can be interpreted as the sum of a deterministic expected/predictable value with an uncertain/noise component. The foundation of variational calculus theory requires the definition and establishment of many concepts and results. This article presents a total order relation on RT(A) for which the notions of local minimal and maximal of a RT(A)-valued function f can be derived. We present a fuzzy version of the first and second optimality conditions in terms of derivatives off. Finally, we present a generalized fuzzy version of du Bois-Reymond lemma which is essential in variational calculus theory.
NETL
NSTL
Elsevier
