Shi Xiangting, Al Ahmadi Ahmad Aziz, Khan Muhammad Bilal, Ciurdariu Loredana, Hakami Khalil Hadi
Industrial Engineering and Operations Research Department, Columbia University, 500 W. 120th Street, New York, NY, 10027, USA.
Department of Electrical Engineering, College of Engineering, Taif University, Taif, 21944, Saudi Arabia.
Heliyon. 2024 Nov 27;10(23):e40664. doi: 10.1016/j.heliyon.2024.e40664. eCollection 2024 Dec 15.
It is widely recognized that fuzzy number theory relies on the characteristic function. However, within the fuzzy realm, the characteristic function transforms into a membership function contingent upon the interval [0,1]. This implies that real numbers and intervals represent exceptional cases of fuzzy numbers. By considering this approach, this paper introduces a new space and novel refinements for integral variations of Hölder's inequality which is known as Hölder's-like inequality over fuzzy domain. Numerous prevailing inequalities associated with Hölder's-like inequality can be enhanced through the newly acquired inequalities, as demonstrated through an application. By using newly defined special means, some new versions of integral inequalities have obtained where differentiable mappings are real-valued convex-like (or convex fuzzy) mappings Lastly, nontrivial numerical examples are also included to validate the accuracy of the presented inequalities as they vary with the parameter .
人们普遍认识到模糊数论依赖于特征函数。然而，在模糊领域内，特征函数会根据区间[0,1]转变为隶属函数。这意味着实数和区间代表模糊数的特殊情况。通过考虑这种方法，本文引入了一个新的空间以及对赫尔德不等式积分变体的新颖改进，即在模糊域上的类赫尔德不等式。通过一个应用表明，许多与类赫尔德不等式相关的现有不等式可以通过新得到的不等式得到加强。通过使用新定义的特殊均值，得到了一些积分不等式的新版本，其中可微映射是实值类凸（或凸模糊）映射。最后，还包括非平凡的数值例子来验证所提出的不等式随参数变化时的准确性。
