We point to several persistent misconceptions and wrong beliefs in the field of fuzzy logic and enounce propositions that clarify and, hopefully, will contribute to eliminating those misapprehensions. That may improve many engineering designs and reduce confusion for those learning fuzzy logic systems. In their paper of 2015, Reshma and John state that “Fuzzy is the logic of approximations. It can be used . . . to describe vague and imprecise information” [1]. Such statements are frequently heard at conferences and read in publications. As a first remark, there is no single fuzzy logic. How to choose one version of the infinite number of infinite-valued logics (sometimes named fuzzy logics) for a given application is not an issue solved in the frame of these (fuzzy) logics. This problem of what kind of fuzzy logic to use for building a fuzzy logic system suitable for a specific application rather pertains to metalogics and has not yet been addressed in any significant manner; we are not discussing it. Some glimpses of this issue are found in [2]. In their popular volume on Fuzzy Logic and Control, Jamshidi, Vadiee, and Ross [3] describe the state of the art in 1993 as “Among many new technologies based on AI, fuzzy logic is now perhaps the most popular area. . . fuzzy logic is enjoying an unprecedented popularity in the technological and engineering fields including manufacturing.” Interestingly, after 30 years from this book and almost 60 years from Zadeh’s seminal papers, the domain of fuzzy logic is still very much alive and popular. One may ask what contributes to its continuous popularity. One explanation is summarized by Jamshidi et al. [3]: “Fuzzy logic offers design rules that are relatively easy to use in a wide range of applications, including nonlinear robotic equations”. . . “Fuzzy logic also allows for design in cases where models are incomplete, unlike most design techniques.” (Section 14.1 in [3]). It is not clear from that volume what are those design rules that fuzzy logic offers, but the popular interpretation of the above is that fuzzy logic is based on IfThen rules that are easy to enunciate in an intuitive manner and that always work more or less well. Unfortunately, the misconceptions about fuzzy logic include: Misconception #1. “Fuzzy logic offers design rules that are relatively easy to use.“ Fuzzy logic is not providing any indication of how to choose the rules for a fuzzy logic system, even less “design rules”. While it is easy to enunciate If-Then rules, there is no indication inside fuzzy logic theory to estimate the quality and suitability of those rules. The easiness of enunciating fuzzy If-Then rules does not mean the easiness of finding a “good enough” set of rules for a specific application. The latter was implicitly recognized by the need to develop myriads of intricated, combined techniques (many based on genetic algorithms or other biology-inspired methods) for the optimization of the rule systems. In addition, fuzzy logic and fuzzy logic systems (FLS) theories are related, yet distinct. Among others, fuzzy logic says nothing about how to choose a defuzzifier, which is an essential part of a FLS. Another vastly popular misconception is implied by (and well summarized in) Ngo and Tran [4], who say “The membership functions of the fuzzy sets are triangles and trapezoids due to simple and effective programming.“ The implied delusion is Misconception #2. Using simple, triangular, or trapezoidal membership functions (m.f.s) is suitable in virtually all applications of FLSs. The fallacy here is more subtle, involving (i) the disconnection of the issue of choosing the set of rules from the issue of choosing the membership functions; (ii) avoiding discussing the choice of the membership functions as an approximation problem (which would need also the consideration of the set of rules). In addition, saying that the triangular or trapezoidal membership functions are simpler to include in programs than, say, Gaussian m.f.s is possibly unjustified. Further on, saying that the program is more effective using triangles and trapezoids is unjustified: the duration or running a program achieving a specified error is often larger for this choice of m.f.s. Jamshidi et al. in the cited volume [3] are not falling into the same type of error; they are saying “. . . determining the optimum shape of a membership function may not always be easy and can sometimes be obtained empirically at best. To avoid these ‘black art’ approaches to membership functions . . . ”. However, several other issues are illustrated by the above quotation, including: Misconception #3. There is an “optimum shape of a membership” function for any application. In the first place, this is an ill-posed problem, because the optimality criterion is not stated. In addition, again, the issue of m.f.s is disconnected from the issue of the rule system, which is not possible. Assuming that the optimality means that the system approximated with a specified error a given function on a specified interval of the input variable(s), the “optimum shape of a membership function” does not exist. It can be easily proved that there is an infinity of m.f.s that, for a specified set of rules, a specified defuzzifier, a specified interval of the input variable(s), and a specified error satisfy the approximation error (at least if the function to approximate has no discontinuity in the interval). Misconception #4. The design of membership functions and in general of FLSs is much of a “black art” or should necessarily be done using some adaptive or learning system, such as a neural network (see Jamshidi et al. [3] and many other texts). In fact, when there is a well-defined problem, with a given inputoutput function and a criterion of approximation, there are several mathematically sound solutions to the design, either by interpolation or approximation, as presented first in a series of volume sections in [58], and in a series of papers as in the reference list of [9], with additional details in [10-15]. The main part of the presentation will focus on this issue: the optimization of the design of membership functions, for a specified approximation or interpolation problem. During the development of methods for solving this type of problems it becomes apparent that some of the simplest m.f.s, the polynomial ones, face difficulties with analytic representations of the solutions because fuzzy logic systems’ input-output functions cannot be represented by algebraic operations (a result from [12]). As said, there are several other issues related to FLS design, such as choosing the fuzzy logic [2], deciding on the problem approximation or interpolation and choosing the type of FLS for it, and choosing the right optimization criterion [10-15]. These are not problems pertaining to fuzzy logic systems or to proper FLSs theory and these problems should be addressed apart for completing the well-posed problem of design. However, these problems will also be briefly discussed during the presentation. Concluding, the theory of FLSs is a mature domain, which reality is not always reflected in the published articles and books, even those published by the most respected publishers. Improving the understanding of engineers of the underlaying FLS theory could improve the design results, decdecrease the design time, and largely reduce the waste of resources.