Abstract
Recently, Al-Fhaid and Mohiuddine (Adv. Differ. Equ. 2013:203, 2013) and Mohiuddine and Alghamdi (Adv. Differ. 2012:141, 2012) got some results in intuitionistic fuzzy normed spaces using ideas of intuitionistic fuzzy sets due to Atanassov and fuzzy normed spaces due to Saadati and Vaezpour. In this note, we show that the mentioned results follow directly from well-known theorems in fuzzy normed spaces.
Highlights
1 Introduction Intuitionistic fuzzy normed spaces were investigated by Saadati and Park [ ]
They introduced and studied intuitionistic fuzzy normed spaces based both on the idea of intuitionistic fuzzy sets due to Atanassov [ ] and the concept of fuzzy normed spaces given by Saadati and Vaezpour in [ ]
In this note we prove that the topology τ(μ,ν) generated by an intuitionistic fuzzy normed space (X, μ, ν, ∗, ) coincides with the topology τμ generated by the generalized fuzzy normed space (X, μ, ∗), and the results obtained in [ ] and [ ] are immediate consequences of the corresponding results for fuzzy normed spaces
Summary
Introduction Intuitionistic fuzzy normed spaces were investigated by Saadati and Park [ ]. Preliminaries A binary operation ∗ : [ , ] × [ , ] → [ , ] is a continuous t-norm if it satisfies the following conditions: (a) ∗ is associative and commutative, (b) ∗ is continuous, (c) a ∗ = a for all a ∈ [ , ], (d) a ∗ b ≤ c ∗ d whenever a ≤ c and b ≤ d, for each a, b, c, d ∈ [ , ].
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