In the present paper, we investigate a connection between two fuzzy inner product one of which arises from Felbin's fuzzy norm and the other is based on Bag and Samanta's fuzzy norm. Also we show that, considering a fuzzy inner product space, how one can construct another kind of fuzzy inner product on this space.

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Let k be a field, T an algebraic k-torus, X smooth k-compactification of and PicX‾ the Picard group X‾=X×kk‾. Hoshi, Kanai Yamasaki [HKY22] determined H1(k,PicX‾) for norm one tori T=RK/k(1)(Gm) gave necessary sufficient condition Hasse principle extensions K/k number fields with [K:k]=n≤15 n≠12. In this paper, we determine 64 cases H1(k,PicX‾)≠0 give [K:k]=12.