Abstract The objective of this study is to analyze the numerical intervals of the Human Immunodeficiency Virus (HIV) using the solution of a dynamics model at each time iteration, considering the infection rate of C D 4 + T lymphocytes and the production rate of the virus as outputs of an interval type-2 Fuzzy Rule-Based System (FRBS). The mathematical model consists of a system of ordinary differential equations in the case of the HIV-seropositive individuals who are under antiretroviral treatment. The input variables of FRBS are adherence to treatment and medication potency, which are important factors in the treatment of HIV-seropositive individuals. If the infection rate of C D 4 + T lymphocytes and the production rate of the virus are output variables of a type-1 FRBS, then we obtain curves for the solution of the HIV dynamic model. When the rates are outputs obtained through the interval type-2 FRBS, we can obtain ranges. This means that a type-2 FRBS provides more information about the behavior of the uninfected and infected C D 4 + T lymphocytes, free virus particles, and virus-specific cytotoxic T lymphocytes (CTL) that attack infected cells in the bloodstream of a HIV-seropositive individual. The theory of the single level constraint interval arithmetic allows us to obtain a single interval that containing the intervals of all iterations for uninfected and infected C D 4 + T lymphocytes, free virus particles, and CTL. Thus, the novel contribution of this research is twofold. Firstly, the use of interval type-2 fuzzy rule-base analysis to obtain more informative and robust results not possible with standard approaches is new. Secondly, the use of the fuzzy constraint interval representation for fuzzy type-2 intervals in the context of the type-2 fuzzy rule base is new. Moreover, constraint intervals unifies the theory and its use in single-level constraint representations simplifies the calculations, though this aspect is not pursued in detail here.

中文翻译：

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使用类型 2 模糊集的 HIV 动力学模型解的区间分析

摘要 本研究的目的是在每次迭代时使用动力学模型的解来分析人类免疫缺陷病毒 (HIV) 的数值区间，考虑 CD 4 + T 淋巴细胞的感染率和病毒的产生率为区间类型 2 基于模糊规则的系统 (FRBS) 的输出。在接受抗逆转录病毒治疗的 HIV 血清阳性个体的情况下，数学模型由常微分方程系统组成。FRBS 的输入变量是对治疗的依从性和药物效力，这是治疗 HIV 血清阳性个体的重要因素。如果 CD 4 + T 淋巴细胞的感染率和病毒的产生率是 1 型 FRBS 的输出变量，那么我们得到 HIV 动态模型解的曲线。当速率是通过区间类型 2 FRBS 获得的输出时，我们可以获得范围。这意味着 2 型 FRBS 提供了更多关于未感染和感染的 CD 4 + T 淋巴细胞、游离病毒颗粒和病毒特异性细胞毒性 T 淋巴细胞 (CTL) 行为的信息，这些细胞攻击 HIV- 血流中的受感染细胞。血清阳性个体。单级约束区间算法的理论使我们能够获得包含未感染和感染 CD 4 + T 淋巴细胞、游离病毒颗粒和 CTL 的所有迭代间隔的单个区间。因此，这项研究的新贡献是双重的。首先，使用区间类型 2 模糊规则库分析来获得标准方法无法实现的更多信息和稳健结果是新的。第二，在类型 2 模糊规则库的上下文中，模糊类型 2 区间的模糊约束区间表示的使用是新的。此外，约束区间统一了理论，它在单层约束表示中的使用简化了计算，尽管这里不详细讨论这方面。