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Fuzzy cognitive maps (FCMs) are recurrent neural networks comprised of well-defined concepts and causal relations. While the literature about real-world FCM applications is prolific, the studies devoted to understanding the foundations behind these neural networks are rather scant. In this article, we introduce several definitions and theorems that unveil the dynamic behavior of FCM-based models equipped with transfer $F$ -functions. These analytical expressions allow estimating bounds for the activation value of each neuron and analyzing the covering and proximity of feasible activation spaces. The main theoretical findings suggest that the state space of any FCM model equipped with transfer $F$ -functions shrinks infinitely with no guarantee for the FCM to converge to a fixed point but to its limit state space. This result in conjunction with the covering and proximity values of FCM-based models helps understand their poor performance when solving complex simulation problems.

IRBASIR is a recently proposed algorithm that, inspired on one of the extensions of classical Rough Set Theory, employs similarity relations to learn classification rules. By using similarity relations as its underlying building blocks, IRBASIR is able to process datasets with both nominal and numerical features. In this paper we propose IRBASIR-Bayes, a modification to the IRBASIR method that relies on Bayesian Networks to construct the reference vector used to generate the rules. This scheme has demonstrated satisfactory performance compared to other rule induction algorithms.

Recently, a learning procedure to improve the overall convergence of sigmoid fuzzy cognitive maps used in pattern classification was proposed. The algorithm estimates the slope of each sigmoid neuron while preserving the causal weights. This paper proposes a more realistic error function for this algorithm, which is based on 1) the dissimilarity between two consecutive responses, and 2) the dissimilarity between the current output and the expected one. As a second contribution, we introduce sufficient conditions to arrive at stability features. These conditions allow assessing the accuracy–convergence tradeoff attached to the proposed learning procedure.

In this paper, we survey different granular computing (GrC) applications to the field of cognitive mapping by highlighting how fuzzy cognitive maps (FCMs) have been augmented with different types of information granules such as intervals, fuzzy sets, fuzzy clustering, rough sets, and grey sets. These information granules have been integrated into core FCM components such as their set of concept nodes, the causal links among these concepts or their underlying inference mechanisms. We discuss the advantages and limitations brought forth by these granular cognitive maps (GCMs) as well as their reported applications, with especial emphasis on time series analysis and pattern classification scenarios. To the best of our knowledge, this is the first time that GCMs stemming from a variety of granular constructs are systematically reviewed. We hope this survey inspires further research endeavors in the exciting interplay between GrC and intelligent systems.

Liner shipping is vulnerable to many disruptive factors such as port congestion or harsh weather, which could result to delay in arriving at the ports. It could result in both financial and reputation losses. The vessel schedule recovery problem (VSRP) is concerned with different possible actions to reduce the effect of disruption. In this work, we are concerned with speeding up strategy in VSRP, which is called the speed-based vessel schedule recovery problem (S-VSRP). We model S-VSRP as a multiobjective optimization (MOO) problem and resort to several multiobjective evolutionary algorithms (MOEAs) to approximate the optimal Pareto set, which provides vessel route-based speed profiles. It gives the stakeholders the ability to tradeoff between two conflictive objectives: total delay and financial loss. We evaluate the problem in three scenarios (i.e., scalability analysis, vessel steaming policies, and voyage distance analysis) and statistically validate their performance significance. According to experiments, the problem complexity varies in different scenarios, and NSGAII performs better than other MOEAs in all scenarios.

Rough Cognitive Networks (RCNs) are a kind of granular neural network that augments the reasoning rule present in Fuzzy Cognitive Maps with crisp information granules coming from Rough Set Theory. While RCNs have shown promise in solving different classification problems, this model is still very sensitive to the similarity threshold upon which the rough information granules are built. In this paper, we cast the RCN model within the framework of fuzzy rough sets in an attempt to eliminate the need for a user-specified similarity threshold while retaining the model's discriminatory power. As far as we know, this is the first study that brings fuzzy sets into the domain of rough cognitive mapping. Numerical results in the presence of 140 well-known pattern classification problems reveal that our approach, referred to as Fuzzy-Rough Cognitive Networks, is capable of outperforming most traditional classifiers used for benchmarking purposes. Furthermore, we explore the impact of using different heterogeneous distance functions and fuzzy operators over the performance of our granular neural network.

Wireless sensor and actuator networks (WSANs) are heterogeneous networks composed of many different nodes that can cooperatively sense the environment, determine an appropriate action to take, then change the environment’s state after acting on it. As a natural extension of wireless sensor networks (WSNs), WSANs inherit from them a variety of research challenges and bring forth many new ones. These challenges are related to dealing with imprecise and vague information, solving complicated optimization problems or collecting and processing data from multiple sources. Computational intelligence (CI) is an overarching term denoting a conglomerate of biologically and linguistically inspired techniques that provide robust solutions to NP-hard problems, reason in imprecise terms and yield high-quality yet computationally tractable approximate solutions to real-world problems. Many researchers have consequently turned to CI in hope of finding answers to a plethora of WSAN-related challenges. This paper reviews the application of several methodologies under the CI umbrella to the WSAN field. We describe and categorize existing works leaning on fuzzy systems , neural networks , evolutionary computation , swarm intelligence , learning systems , and their hybridizations to well-known or emerging WSAN problems along five major axes: 1) actuation; 2) communication; 3) sink mobility; 4) topology control; and 5) localization. The survey offers informative discussions to help reason through all the studies under consideration. Finally, we point to future research avenues by: 1) suggesting suitable CI techniques to specific problems; 2) borrowing concepts from WSNs that have yet to be applied to WSANs; or 3) describing the shortcomings of current methods in order to spark interest on the development of more refined models.

The aggregation of preferences (expressed in the form of rankings) from multiple experts is a well-studied topic in a number of fields. The Kemeny ranking problem aims at computing an aggregated ranking having minimal distance to the global consensus. However, it assumes that these rankings will be complete, i.e., all elements are explicitly ranked by the expert. This assumption may not simply hold when, for instance, an expert ranks only the top-K items of interest, thus creating a partial ranking. In this paper we formalize the weighted Kemeny ranking problem for partial rankings, an extension of the Kemeny ranking problem that is able to aggregate partial rankings from multiple experts when only a limited number of relevant elements are explicitly ranked (top-K), and this number may vary from one expert to another (top-Ki). Moreover, we introduce two strategies to quantify the weight of each partial ranking. We cast this problem within the realm of combinatorial optimization and lean on the successful Ant Colony Optimization (ACO) metaheuristic algorithm to arrive at high-quality solutions. The proposed approach is evaluated through a real-world scenario and 190 synthetic datasets from www.PrefLib.org. The experimental evidence indicates that the proposed ACO-based solution is capable of significantly outperforming several evolutionary approaches that proved to be very effective when dealing with the Kemeny ranking problem. The authors would like to thank Ph.D. Student Isel Grau from Vrije Universiteit Brussel, Belgium, for her valuable support on designing the membership measure and running the algorithms. This work was supported by the Research Council of Hasselt University.

Rough Cognitive Networks are granular classifiers stemming from the hybridization of Fuzzy Cognitive Maps and Rough Set Theory. Such cognitive neural networks attempt to quantify the impact of rough granular constructs (i.e., the positive, negative and boundary regions of a target concept) over each decision class for the problem at hand. In rough classifiers, determining the precise granularity level is crucial to compute high prediction rates. Regrettably, learning the similarity threshold parameter requires reconstructing the information granules, which may be time-consuming. In this paper, we put forth a new multiclassifier system classifier named Rough Cognitive Ensembles. The proposed ensemble employs a collection of Rough Cognitive Networks as base classifiers, each operating at a different granularity level. This allows suppressing the requirement of learning a similarity threshold. We evaluate the granular ensemble with 140 traditional classification datasets using different heterogeneous distance functions. After comparing the proposed model to 15 well-known classifiers, the experimental evidence confirms that our scheme yields very promising classification rates. This work was supported by the Research Council of Hasselt University. The authors would like to thank the anonymous reviewers for their constructive remarks throughout the revision process.