Implication functions in interval-valued fuzzy set theory

Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results pertaining to implications in interval-valued fuzzy set theory. In particular, we describe several possibilities to represent such implications using implications on the unit interval, we give a characterization of the implications in interval-valued fuzzy set theory which satisfy the Smets-Magrez axioms, we discuss the solutions of a particular distributivity equation involving strict t-norms, we extend monoidal logic to the interval-valued fuzzy case and we give a soundness and completeness theorem which is similar to the one existing for monoidal logic, and finally we discuss some other constructions of implications in interval-valued fuzzy set theory

FSL-BM: Fuzzy Supervised Learning with Binary Meta-Feature for Classification

This paper introduces a novel real-time Fuzzy Supervised Learning with Binary Meta-Feature (FSL-BM) for big data classification task. The study of real-time algorithms addresses several major concerns, which are namely: accuracy, memory consumption, and ability to stretch assumptions and time complexity. Attaining a fast computational model providing fuzzy logic and supervised learning is one of the main challenges in the machine learning. In this research paper, we present FSL-BM algorithm as an efficient solution of supervised learning with fuzzy logic processing using binary meta-feature representation using Hamming Distance and Hash function to relax assumptions. While many studies focused on reducing time complexity and increasing accuracy during the last decade, the novel contribution of this proposed solution comes through integration of Hamming Distance, Hash function, binary meta-features, binary classification to provide real time supervised method. Hash Tables (HT) component gives a fast access to existing indices; and therefore, the generation of new indices in a constant time complexity, which supersedes existing fuzzy supervised algorithms with better or comparable results. To summarize, the main contribution of this technique for real-time Fuzzy Supervised Learning is to represent hypothesis through binary input as meta-feature space and creating the Fuzzy Supervised Hash table to train and validate model.Comment: FICC201

Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences

Mathematical fuzzy logic (MFL) specifically targets many-valued logic and has significantly contributed to the logical foundations of fuzzy set theory (FST). It explores the computational and philosophical rationale behind the uncertainty due to imprecision in the backdrop of traditional mathematical logic. Since uncertainty is present in almost every real-world application, it is essential to develop novel approaches and tools for efficient processing. This book is the collection of the publications in the Special Issue “Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences”, which aims to cover theoretical and practical aspects of MFL and FST. Specifically, this book addresses several problems, such as:- Industrial optimization problems- Multi-criteria decision-making- Financial forecasting problems- Image processing- Educational data mining- Explainable artificial intelligence, etc

A Neutrosophic Description Logic

Description Logics (DLs) are appropriate, widely used, logics for managing structured knowledge. They allow reasoning about individuals and concepts, i.e. set of individuals with common properties. Typically, DLs are limited to dealing with crisp, well defined concepts. That is, concepts for which the problem whether an individual is an instance of it is yes/no question. More often than not, the concepts encountered in the real world do not have a precisely defined criteria of membership: we may say that an individual is an instance of a concept only to a certain degree, depending on the individual's properties. The DLs that deal with such fuzzy concepts are called fuzzy DLs. In order to deal with fuzzy, incomplete, indeterminate and inconsistent concepts, we need to extend the fuzzy DLs, combining the neutrosophic logic with a classical DL. In particular, concepts become neutrosophic (here neutrosophic means fuzzy, incomplete, indeterminate, and inconsistent), thus reasoning about neutrosophic concepts is supported. We'll define its syntax, its semantics, and describe its properties.Comment: 18 pages. Presented at the IEEE International Conference on Granular Computing, Georgia State University, Atlanta, USA, May 200

Aggregated fuzzy answer set programming

Fuzzy Answer Set programming (FASP) is an extension of answer set programming (ASP), based on fuzzy logic. It allows to encode continuous optimization problems in the same concise manner as ASP allows to model combinatorial problems. As a result of its inherent continuity, rules in FASP may be satisfied or violated to certain degrees. Rather than insisting that all rules are fully satisfied, we may only require that they are satisfied partially, to the best extent possible. However, most approaches that feature partial rule satisfaction limit themselves to attaching predefined weights to rules, which is not sufficiently flexible for most real-life applications. In this paper, we develop an alternative, based on aggregator functions that specify which (combination of) rules are most important to satisfy. We extend upon previous work by allowing aggregator expressions to define partially ordered preferences, and by the use of a fixpoint semantics

Comparing Defeasible Argumentation and Non-Monotonic Fuzzy Reasoning Methods for a Computational Trust Problem with Wikipedia

Computational trust is an ever-more present issue with the surge in autonomous agent development. Represented as a defeasible phenomenon, problems associated with computational trust may be solved by the appropriate reasoning methods. This paper compares two types of such methods, Defeasible Argumentation and Non-Monotonic Fuzzy Logic to assess which is more effective at solving a computational trust problem centred around Wikipedia editors. Through the application of these methods with real-data and a set of knowledge-bases, it was found that the Fuzzy Logic approach was statistically significantly better than the Argumentation approach in its inferential capacity

The Fuzziness in Molecular, Supramolecular, and Systems Chemistry

Fuzzy Logic is a good model for the human ability to compute words. It is based on the theory of fuzzy set. A fuzzy set is different from a classical set because it breaks the Law of the Excluded Middle. In fact, an item may belong to a fuzzy set and its complement at the same time and with the same or different degree of membership. The degree of membership of an item in a fuzzy set can be any real number included between 0 and 1. This property enables us to deal with all those statements of which truths are a matter of degree. Fuzzy logic plays a relevant role in the field of Artificial Intelligence because it enables decision-making in complex situations, where there are many intertwined variables involved. Traditionally, fuzzy logic is implemented through software on a computer or, even better, through analog electronic circuits. Recently, the idea of using molecules and chemical reactions to process fuzzy logic has been promoted. In fact, the molecular word is fuzzy in its essence. The overlapping of quantum states, on the one hand, and the conformational heterogeneity of large molecules, on the other, enable context-specific functions to emerge in response to changing environmental conditions. Moreover, analog input–output relationships, involving not only electrical but also other physical and chemical variables can be exploited to build fuzzy logic systems. The development of “fuzzy chemical systems” is tracing a new path in the field of artificial intelligence. This new path shows that artificially intelligent systems can be implemented not only through software and electronic circuits but also through solutions of properly chosen chemical compounds. The design of chemical artificial intelligent systems and chemical robots promises to have a significant impact on science, medicine, economy, security, and wellbeing. Therefore, it is my great pleasure to announce a Special Issue of Molecules entitled “The Fuzziness in Molecular, Supramolecular, and Systems Chemistry.” All researchers who experience the Fuzziness of the molecular world or use Fuzzy logic to understand Chemical Complex Systems will be interested in this book

Sensor Fusion Based Model for Collision Free Mobile Robot Navigation

Autonomous mobile robots have become a very popular and interesting topic in the last decade. Each of them are equipped with various types of sensors such as GPS, camera, infrared and ultrasonic sensors. These sensors are used to observe the surrounding environment. However, these sensors sometimes fail and have inaccurate readings. Therefore, the integration of sensor fusion will help to solve this dilemma and enhance the overall performance. This paper presents a collision free mobile robot navigation based on the fuzzy logic fusion model. Eight distance sensors and a range finder camera are used for the collision avoidance approach where three ground sensors are used for the line or path following approach. The fuzzy system is composed of nine inputs which are the eight distance sensors and the camera, two outputs which are the left and right velocities of the mobile robot’s wheels, and 24 fuzzy rules for the robot’s movement. Webots Pro simulator is used for modeling the environment and the robot. The proposed methodology, which includes the collision avoidance based on fuzzy logic fusion model and line following robot, has been implemented and tested through simulation and real time experiments. Various scenarios have been presented with static and dynamic obstacles using one robot and two robots while avoiding obstacles in different shapes and sizes.https://doi.org/10.3390/s1601002