Fuzzy-valued integrals based on a constructive methodology

Hsien-Chung Wu

Applications of Mathematics (2007)

  • Volume: 52, Issue: 1, page 1-23
  • ISSN: 0862-7940

Abstract

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The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued integral of fuzzy-valued function with respect to fuzzy-valued measure. Finally, we provide a Dominated Convergence Theorem for fuzzy-valued integrals.

How to cite

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Wu, Hsien-Chung. "Fuzzy-valued integrals based on a constructive methodology." Applications of Mathematics 52.1 (2007): 1-23. <http://eudml.org/doc/33274>.

@article{Wu2007,
abstract = {The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued integral of fuzzy-valued function with respect to fuzzy-valued measure. Finally, we provide a Dominated Convergence Theorem for fuzzy-valued integrals.},
author = {Wu, Hsien-Chung},
journal = {Applications of Mathematics},
keywords = {dominated convergence theorem; fuzzy number; fuzzy-valued function; fuzzy-valued integral; resolution identity; dominated convergence theorem; fuzzy number; fuzzy-valued function; fuzzy-valued integral; resolution identity},
language = {eng},
number = {1},
pages = {1-23},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Fuzzy-valued integrals based on a constructive methodology},
url = {http://eudml.org/doc/33274},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Wu, Hsien-Chung
TI - Fuzzy-valued integrals based on a constructive methodology
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 1
SP - 1
EP - 23
AB - The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued integral of fuzzy-valued function with respect to fuzzy-valued measure. Finally, we provide a Dominated Convergence Theorem for fuzzy-valued integrals.
LA - eng
KW - dominated convergence theorem; fuzzy number; fuzzy-valued function; fuzzy-valued integral; resolution identity; dominated convergence theorem; fuzzy number; fuzzy-valued function; fuzzy-valued integral; resolution identity
UR - http://eudml.org/doc/33274
ER -

References

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