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Integrations of q-Rung Orthopair Fuzzy Continuous Information
IEEE Transactions on Fuzzy Systems ( IF 11.9 ) Pub Date : 2019-10-01 , DOI: 10.1109/tfuzz.2019.2893205
Xiaoqin Shu , Zhenghai Ai , Zeshui Xu , Jianmei Ye

Yager's q-rung orthopair fuzzy sets (q-ROFSs), which extend Zadeh's fuzzy sets, use the membership and nonmembership functions to describe things’ vague characteristics, and the sum of the qth-power for the membership and nonmembership functions is less than or equal to 1. More recently, some scholars have proposed a series of aggregation operators to fuse q-rung orthopair fuzzy discrete information. However, so far, there is no research on aggregating q-rung orthopair fuzzy continuous information. Thus, we proposed q-rung orthopair fuzzy definite integrals (q-ROFDIs) to fill this vacancy. First, we further study the operations of q-rung orthopair fuzzy numbers (q-ROFNs) that are the core of q-ROFSs. We also introduce the limit of a q-ROFN sequence. Subsequently, we construct the q-ROFDIs step-by-step, give their concrete values, and discuss their integrability criteria from two perspectives. From the perspectives of modern analysis and the operational laws of q-ROFNs, we investigate the q-ROFDIs in detail, which are concise and considerably different from the investigative techniques of the previous research on aggregating continuous information. Finally, a practical example is provided to show the effectiveness, elasticity, and superiority of the q-ROFDIs via comparing them with the existing methods.

中文翻译:

q-Rung Orthopair 模糊连续信息的集成

Yager 的 q-rung orthopair 模糊集 (q-ROFSs),它扩展了 Zadeh 的模糊集,使用隶属和非隶属函数来描述事物的模糊特征,隶属函数和非隶属函数的 q 次幂之和小于或等于1。最近,一些学者提出了一系列聚合算子来融合q-rung orthopair模糊离散信息。然而,到目前为止,还没有关于聚合q-rung orthopair模糊连续信息的研究。因此,我们提出了 q-rung orthopair 模糊定积分 (q-ROFDI) 来填补这个空缺。首先,我们进一步研究作为 q-ROFS 核心的 q-rung orthopair 模糊数 (q-ROFN) 的运算。我们还介绍了 q-ROFN 序列的极限。随后,我们逐步构建 q-ROFDI,给出它们的具体值,并从两个角度讨论它们的可集成性标准。我们从现代分析的角度和 q-ROFN 的运行规律,详细研究了 q-ROFDI,它们简洁明了,与以往关于聚合连续信息的研究的调查技术有很大不同。最后,提供了一个实例,通过与现有方法进行比较,展示了 q-ROFDI 的有效性、弹性和优越性。
更新日期:2019-10-01
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