Why Lattice-Valued Fuzzy Values? A Mathematical Justification

To take into account that expert\u27s degrees of certainty are not always comparable, researchers have used partially ordered set of degrees instead of the more traditional linearly (totally) ordered interval [0,1]. In most cases, it is assumed that this partially ordered set is a lattice, i.e., every two elements have the greatest lower bound and the least upper bound. In this paper, we prove a theorem explaining why it is reasonable to require that the set of degrees is a lattice

How to Estimate Forecasting Quality: A System-Motivated Derivation of Symmetric Mean Absolute Percentage Error (SMAPE) and Other Similar Characteristics

When comparing how well different algorithms forecast time series, researchers use an average value of the ratio |x-y|/(|x|+|y|)/2), known as the Symmetric Mean Absolute Percentage Error (SMAPE). In this paper, we provide a system-motivated explanation for this formula. We also explain how this formula explains the use of geometric mean to combine different forecasts

50 Years of Fuzzy: from Discrete to Continuous to -- Where?

While many objects and processes in the real world are discrete, from the computational viewpoint, discrete objects and processes are much more difficult to handle than continuous ones. As a result, a continuous approximation is often a useful way to describe discrete objects and processes. We show that the need for such an approximation explains many features of fuzzy techniques, and we speculate on to which promising future directions of fuzzy research this need can lead us

What is the Right Context for an Engineering Problem: Finding Such a Context is NP-Hard

Abstract—In the general case, most computational engineering problems are NP-hard. So, to make the problem feasible, it is important to restrict this problem. Ideally, we should use the most general context in which the problem is still feasible. In this paper, we start with a simple proof that finding such most general context is itself an NP-hard problem. Since it is not possible to find the appropriate context by utilizing a general algorithm, it is therefore necessary to be creative – i.e., in effect, to use computational intelligence techniques. On three examples, we show how such techniques can help us come up with the appropriate context. These examples explain why it is beneficial to take knowledge about causality into account when processing data, why sometimes long-term predictions are easier than short-term ones, and why often for small deviations, a straightforward application of a seemingly optimal control only makes the situation worse