# Special Issue \"Fuzzy Decision Making and Soft Computing Applications\"
###### Abstract  
Research on fuzzy logic [1] and soft computing for decision making has a long history. In many fields of application, rule-based fuzzy systems have been employed [2, 3, 4] for their unique properties in solving modelling problems. In particular, decision-making systems often deal with uncertain data. Moreover, in some fields of application, such as differential diagnosis in medicine, a meaningful confidence measure is required to be associated with the classification result in order to show all possible outcomes with the relative likelihood. Finally, semantically meaningful systems are often required, providing clear and logical interpretation of the inference process, in order to encapsulate them in interactive frameworks of cognitive systems, or to enable validation by domain experts. These issues can be accomplished, on the one hand, by encoding uncertain numerical data in terms of interpretable linguistic variables [5]. On the other hand, fuzzy rules show a clear and logical justification for each conclusion [6, 7]. Finally, if desired, fuzzy systems allow classification results to be presented associated with a confidence measure, such as the probability of different classes [8]. The remarkable progress made by these approaches in various fields underlines their benefits and is stimulating further research. In particular, despite the remarkable successes in different tasks, research on these approaches is a field of increasing interest [9], with regard to theoretical aspects, which are being deepened [10, 11, 12], as well as aspects regarding procedures for learning fuzzy systems optimizing accuracy and/or interpretability, or for solving mathematical tasks using fuzzy numbers and soft computing [13, 14, 15, 16, 17, 18]. Moreover, these approaches are prone to easily and proficiently be employed in different new fields of application [19, 20, 21]. This Special Issue collects original research articles discussing cutting-edge work as well as perspectives on future directions in the whole range of theoretical and practical aspects in this research area. In particular, there are 12 contributions selected for this Special Issue, representing progresses in the following areas specifically addressed. **Problem**: 1. **Theory of fuzzy systems and soft computing. ** The authors of [10] consider causal graphs and propose a procedure to explicitly understand underlying assumptions, the kind of data and methodology needed to understand a given relationship, and how to develop explicit assumptions with clear alternatives in order to apply a process of probabilistic elimination. In [11], the authors unambiguously define the relations \"greater than\", \"equal to\", and their combination, in the space of all ordered fuzzy numbers, to solve optimization tasks. Moreover, in [12], a problem of \"acceptance of an optimal solution\" is presented in the form of a vector problem of mathematical programming. The theory of vector optimization is proposed as a mathematical apparatus for the acceptance of optimal solutions of such a class of problems, and the analysis and problem definition of decision making under the conditions of certainty and uncertainty are presented. **Learning procedures. ** In [13], the authors propose two types (\"infimum type\" and \"supremum type\") of dual double fuzzy semi-metric, as well as different types oftriangle inequalities, which are used to investigate the convergence. Another contribution [14] proposes an adaptive-network-based fuzzy inference system (ANFIS) model for the accurate estimation of signal propagation. Results on benchmark data show that the proposed model outperforms nondeterministic models in terms of accuracy and presents flexibility, ease of use, robustness, generalization capability, and an alleviated training process for propagation prediction in complex scenarios. Some authors contributed with three different papers.