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Hahn-Banach extension theorems over the space of fuzzy elements

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Abstract

The conventional Hahn-Banach extension theorem over a vector space has been widely used to derive many important and interesting results in nonlinear analysis, vector optimization and mathematical economics. Although the space of fuzzy elements is not a real vector space, the Hahn-Banach extension theorems over the space of fuzzy elements and the nonstandard normed space of fuzzy elements are presented in this paper. The work also shows the possible applications of the fuzzy-valued problems to nonlinear analysis, vector optimization and mathematical economics.

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Authors and Affiliations

  1. Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 802, Taiwan

    Hsien-Chung Wu

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  1. Hsien-Chung Wu
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Correspondence to Hsien-Chung Wu.

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Wu, HC. Hahn-Banach extension theorems over the space of fuzzy elements. Fuzzy Optim Decis Making 9, 143–168 (2010). https://doi.org/10.1007/s10700-010-9079-9

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  • DOI: https://doi.org/10.1007/s10700-010-9079-9

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