Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 1
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Abstract
The inequality \mu^{\frac{1}{\nu}} + \nu^{\frac{1}{\mu}} \leq 1 is introduced and proved, where \mu and \nu are real numbers, for which \mu, \nu \in [0, 1] and \mu + \nu \leq 1. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E. Also, a generalization of the above inequality for arbitrary n \geq 2 is proposed and proved.一个不等式及其在直觉模糊集理论中的应用。第1部分
引入并证明了不等式\mu ^ {\frac{1}{\nu}} + \nu ^ {\frac{1}{\mu}}\leq 1，其中\mu和\nu为实数，其中\mu、\nu\in[0,1]和\mu + \nu\leq 1。同样的不等式也适用于\mu = \mu ＿A(x)， \nu = \nu ＿A(x)，其中\mu ＿A和\nu ＿A是任意直觉模糊集A在固定宇宙E和x \in E上的隶属函数和非隶属函数。此外，对任意n \geq 2提出并证明了上述不等式的推广。
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