# Generator of Fuzzy Implications
## 1 Introduction
### Literature Review-Related Work
[27] presented the optimal designs of type-1 and interval type-2 fuzzy systems for the classification of heart rate level. The contribution of this work is a proposed approach for achieving the optimal design of interval type-2 fuzzy systems for the classification of heart rate in patients. The fuzzy rule base was designed based on the knowledge of experts. Optimization of the membership functions of the fuzzy systems was performed in order to improve the classification rate and provide a more accurate diagnosis, and for this goal the Bird Swarm Algorithm was used. Two different type-1 fuzzy systems were designed and optimized, the first one with trapezoidal membership functions and the second with Gaussian membership functions. [PERSON] et al. [28] proposed an interval type-2 fuzzy risk analysis model (IT2 FRAM) in order to determine the contingency reserve. In IT2 FRAM, the membership functions for the linguistic terms used to describe the probability, impact of risk and the opportunity events are developed, optimized, and aggregated using interval type-2 fuzzy sets and the principle of justifiable granularity. The contribution of IT2 FRAM is that it considers the opinions of several experts to develop the membership functions of linguistic terms. Moreover, the effects of outlier opinions in developing the membership functions of linguistic terms are reduced. IT2 FRAM also enables the aggregation of non-linear membership functions into trapezoidal membership functions. [PERSON] et al. [29] investigated the design of fuzzy logic-based solar power using maximum power point tracking (MPPT) algorithms using different fuzzy input variables. MPPT is one of the key functions of the solar power management system in solar energy deployment. Six fuzzy MPPT algorithms, based on different input variables, were considered in this study. Four algorithms had two input variables each, while two algorithms had a single input variable. [PERSON] et al. [30] proposed a novel model-based fault detection (FD) approach combined with an interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy system for fault detection in the drilling process. The system uncertainty is considered to prevail during the process, and the type-2 fuzzy methodology is utilized to deal with these uncertainties in an effective way. Two theorems are developed: Theorem 1, which proves the stability of the fuzzy modeling, and Theorem 2, which establishes the fault detector algorithm's stability. [PERSON] et al. [31] developed a fuzzy dissolved oxygen controller, taking into account a decision tree algorithm presented in the literature, and implemented in the supervision software SUPERSYS_HCDC. The algorithm was coded in MATLAB with its membership function parameters being determined using an Adaptive Network-Based Fuzzy Inference System tool. The controller was composed of three independent fuzzy inference systems: Princ1 and Princ2 assessed whether there would be an increment or a reduction in air and oxygen flow rates (respectively), whilst Delta estimated the sizes of these variations. To test the controller, simulations with a neural network model and _E. coli_ cultivations were conducted. When investigating the international literature, it was found that there is no similar work proposing a methodology. The motivation of this paper is that there is no family that defines the value of \(m\), and changes values of \(m\) to create a new family of fuzzy implication, combining the methods and techniques of fuzzy logic.