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- 한국지능시스템학회 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS Vol.5 No.2
- 발행연도
- 2005.6
- 수록면
- 175 - 178 (4page)
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In the present paper, we observe a relation between fuzzy norms and induced crisp norms on a linear space. We first prove that if ρ₁, ρ₂ are equivalent fuzzy norms on a linear space, then for every ε∈ ( 0, 1 ) , the induced crisp norms P¹<SUB>ε</SUB> and P²<SUB>ε</SUB> respectively are equivalent. Since the converse does not hold, we prove it under some strict conditions. And consider the following theorem proved in [8]: Let ρ be a lower semicontinuous fuzzy norm on a normed linear space X , and have the bounded support. Then ρ is equivalent to the fuzzy norm χ <SUB>B</SUB> where B is the closed unit ball of X. The lower semi-continuity of ρ is an essential condition which guarantees the continuity of P<SUB>ε</SUB> where 0 < ε < 1 . As the last result, we prove that : if ρ is a fuzzy norm on a finite dimensional vector space, then ρ is equivalent to χ<SUB>B</SUB> if and only if the support of ρ is bounded.
목차
Abstract
1. Introduction
2. Preliminaries
3. Main results
References
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