## 1 Introduction
He notes the difference in arithmetic operations performed by classical and fuzzy arithmetic: \"a major problem in solving FEs: some basic operations we use to solve crisp equations do not hold for FEs. Actually, this comes as no great surprise because this also happens in probability theory\". Analyzing the history of research on IEs, it can be stated that the authors of subsequent articles always analyzed the methods of their predecessors, detected their weaknesses and tried to improve them in their methods. In this way, they realized scientific progress. They also introduced new definitions and concepts regarding IEs. For example, [PERSON] and [PERSON] in [16] introduced the concept of'set of solutions' and the optimal interval enclosure of the IEs system \([A]x=[c]\). An important item in the solving interval equations is the article [9] by [PERSON] and [PERSON]. They draw attention to the fact that \"almost from the start of fuzzy linear system research, various anomalies arose, which in our opinion, are from an incomplete or lack of understanding of interval linear equations\". They add that the resultant intervals are sometimes improper, and therefore unrealizable, and in the case of fuzzy equations, the solutions provided include at some \(\alpha\)-levels intervals, which are not nested. [PERSON] and [PERSON] have proposed their own method for solving linear IEs that returns either an empty interval or a proper interval, and never an improper one. In [10] [PERSON] at al. emphasize the need to find algebraic (equality type) solutions of IEs: \"Usually interval type computation packages deliver united, tolerance and control solutions of interval equations. But the practical need exists for algebraic solutions (both sides of equations are equal)\". Sometimes the interval system does not have an algebraic (equality type) solution. What is then to do? The authors of the article provide specific advice. In [17], [PERSON] and [PERSON] draw attention to anomalies arising when solving quadratic interval equations (QIE) and quadratic fuzzy equations (QFE) with known methods, e.g., excess width effect or too wide intervals or fuzzy values representing final solutions and achieving inverted (improper) intervals as solutions. They propose an approach of 'interval extended zero' for alleviating observed problems. In [17] this method was used to solve the QIE (2) where \([-y,y]\) means an 'extended zero' introduced instead of crisp 0. \[[\underline{a},\overline{a}][\underline{x},\overline{x}]^{2}+[\underline{b}, \overline{b}][\underline{x},\overline{x}]+[\underline{c},\overline{c}]=[-y,y] \tag{2}\]  
They also show an example of solving the equation which, according to authors of the article [12], did not have a negative root. The method of 'interval extended zero' showed the existence of such a root. It should be noted here that the authors of [17] assume in advance that the solution of a QIE is a 1-dimensional interval \([\underline{y},\overline{x}]\). In [18] [PERSON] and [PERSON] provide the solution method of the full fuzzy quadratic equation \(AX^{2}+BX+C=D\), based on the optimization theory. The method finds roots of equations. Its advantage is that the complexity level of the solution does not depend on whether the coefficients \(A\), \(B\) are positive or negative. [PERSON] and [PERSON] in [19] propose an analytical method of obtaining algebraic solutions of fuzzy linear systems based on the concept of 'interval inclusion linear system'. They show examples of solving of FE with 3 variables. The solutions are 2D fuzzy numbers (FN). In [20] [PERSON] et al. show with a counterexample that the weak solution of a fuzzy linear system defined by [PERSON] et al. in the paper [21] is not always a fuzzy number vector because one of its components can be a non-realizable fuzzy number. This article is one of the many pieces of evidence of difficulties in solving systems of FEs found in the scientific literature.