2021
DOI: 10.24996/ijs.2021.62.7.28
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Some Properties of Fuzzy Inner Product Space

Abstract: Our goal in the present paper is to introduce a new type of fuzzy inner product space. After that, to illustrate this notion, some examples are introduced. Then we prove that that every fuzzy inner product space is a fuzzy normed space. We also prove that the cross product of two fuzzy inner spaces is again a fuzzy inner product space. Next, we prove that the fuzzy inner product is a non decreasing function. Finally, if U is a fuzzy complete fuzzy inner product space and D is a fuzzy closed subspace of U, then… Show more

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Cited by 5 publications
(14 citation statements)
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“…is a nondecreasing function of t in the general fuzzy normed space (V, , ,⊗) for all u V this means when 0< t <s implies (u, t) < (u, s) . Remark 2.13: [28] Assume the general fuzzy normed space (V, , ,⊗). Then for any u V, s>0 ,0<n<1 .…”
Section: Lemma 212:[28]mentioning
confidence: 99%
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“…is a nondecreasing function of t in the general fuzzy normed space (V, , ,⊗) for all u V this means when 0< t <s implies (u, t) < (u, s) . Remark 2.13: [28] Assume the general fuzzy normed space (V, , ,⊗). Then for any u V, s>0 ,0<n<1 .…”
Section: Lemma 212:[28]mentioning
confidence: 99%
“…A subset W V is called a general fuzzy closed set if is a general fuzzy open. Definition 2.16: [28] Suppose that (V, , ,⊗) is a general fuzzy normed space. A sequence ( ) in V is said to be general fuzzy approaches to u if every 0 < < 1 and 0< s there is N such that ( u , s) > (1 ) for every n≥ N. If ( ) is general fuzzy approaches to the fuzzy limit u we write m = u or u.…”
Section: Lemma 212:[28]mentioning
confidence: 99%
“…Kider and Kadhum in 2017 [11] introduce the fuzzy norm for a fuzzy bounded operator on a fuzzy normed space and proved its basic properties then other properties was proved by Kadhum in 2017 [12]. Ali in 2018 [13] proved basic properties of complete fuzzy normed algebra.…”
mentioning
confidence: 99%
“…Ali in 2018 [13] proved basic properties of complete fuzzy normed algebra. Kider and Ali in 2018 [14] introduce the notion of fuzzy absolute value and study properties of finite dimensional fuzzy normed space.…”
mentioning
confidence: 99%
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