It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN.
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in the presence of vagueness, imprecision, and uncertainty, fuzzy logic should have the ability to deal with linguistic hedges, which play a very important role in the modification of fuzzy predicates. In this paper, we extend fuzzy logic in narrow sense with graded syntax, introduced by Novak et al., with many hedge connectives. In one case, each hedge does n…
Institute of Informatics, University of Warsaw（华沙大学信息学研究所）；Faculty of Information Technology, Nguyen Tat Thanh University（阮必成大学信息技术学院）
The problem of minimizing finite fuzzy interpretations in fuzzy description logics (FDLs) is worth studying. For example, the structure of a fuzzy/weighted social network can be treated as a fuzzy interpretation in FDLs, where actors are individuals and actions are roles. Minimizing the structure of a fuzzy/weighted social network makes it more compact, thus making network analysis tasks more efficient. In this work, we study the problem of minimizing a finite fuzzy interpretation in a FDL by using the largest crisp auto-bisimulation. The considered FDLs use the Baaz projection operator and th…
ISTI - CNR（意大利国家研究委员会信息科学与技术研究所）；CAIR - University of Cape Town（开普敦大学CAIR）
Lehmann and Magidor's rational closure is acknowledged as a landmark in the field of non-monotonic logics and it has also been re-formulated in the context of Description Logics (DLs). We show here how to model a rational form of entailment for expressive DLs, such as SROIQ, providing a novel reasoning procedure that compiles a non-monotone DL knowledge base into a description logic program (dl-program).
Kim Il Sung University（金日成综合大学）；Kim Chaek University of Technology（金策工业综合大学）
In this article, we describe the fuzzy logic, fuzzy language and algorithms as the basis of fuzzy reasoning, one of the intelligent information processing method, and then describe the general fuzzy reasoning method.
This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical concepts; (2) the potentials and links between fuzzy logic and probability logic that have not been discussed in one document in literature; (3) representation of real-life random and fuzzy uncertainties and ambiguities that arise in data-driven real-life problems, due to uncertain mathematical and vague verbal terms in datasets.
Technical Engineering College / Northern Technical University（北方技术大学技术工程学院）
This paper describes the design and development of a prototype technique for artificial intelligence based on the fusion of genetic algorithm, neural network and fuzzy logic. It starts by establishing a relationship between the neural network and fuzzy logic. Then, it combines the genetic algorithm with them. Information fusions are at the confidence level, where matching scores can be reported and discussed. The technique is called the Genetic Neuro-Fuzzy (GNF). It can be used for high accuracy real-time environments.
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence bases are not currently available. These two different heuristic assumptions lead to two different sets of formulas for propagating quantitative truth values through lattice operations. It is shown that these two sets of formulas provide a natural grounding for the multiplicative and additive operator-sets in linear logic. The standard rules of linear logic th…
CentraleSupélec（中央理工-高等电力学院）；Laboratoire des Signaux et Systèmes（信号与系统实验室）；Université Paris-Saclay（巴黎-萨克雷大学）；AFSCET（法国系统科学协会）；Conservatoire National des Arts et Métiers（法国国立工艺学院）
This work proposes a formulation of propositional logic, named Eigenlogic, using quantum observables as propositions. The eigenvalues of these operators are the truth-values and the associated eigenvectors the interpretations of the propositional system. Fuzzy logic arises naturally when considering vectors outside the eigensystem, the fuzzy membership function is obtained by the Born rule of the logical observable.This approach is then applied in the context of quantum robots using simple behavioral agents represented by Braitenberg vehicles. Processing with non-classical logic such as multiv…
In this book we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), plithogenic logic (as generalization of classical, fuzzy, intuitionistic fuzzy, and neutrosophic logics), plithogenic probability (as generalization of classical, imprecise, and neutrosophic probabilities), and plithogenic statistics (as generalization of classical, and neutrosophic statistics). Plithogenic Set is a set whose elements are characterized by one or more attributes, and each attribute may have many values. An attribute value v has a corresponding (fuzzy, …
The paper aims to develop a framework for coalgebraic fuzzy geometric logic by adding modalities to the language of fuzzy geometric logic. Using the methods of coalgebra, the modal operators are introduced in the language of fuzzy geometric logic. To define the modal operators, we introduce a notion of fuzzy-open predicate lifting. Based on coalgebras for an endofunctor $T$ on the category $\textbf{Fuzzy-Top}$ of fuzzy topological spaces and fuzzy continuous maps, we build models for the coalgebraic fuzzy geometric logic. Bisimulations for the defined models are discussed in this work.
Ai movement, Center of Artificial Intelligence, Mohammed VI Polytechnic University（穆罕默德六世理工大学人工智能中心 Ai movement）；Lip6, Sorbonne University（索邦大学 Lip6）
Fuzzy logic has been proposed in previous studies for machine diagnosis, to overcome different drawbacks of the traditional diagnostic approaches used. Among these approaches Failure Mode and Effect Critical Analysis method(FMECA) attempts to identify potential modes and treat failures before they occur based on subjective expert judgments. Although several versions of fuzzy logic are used to improve FMECA or to replace it, since it is an extremely cost-intensive approach in terms of failure modes because it evaluates each one of them separately, these propositions have not explicitly focused …
Mutah University（穆塔大学）；Eotvos Lorand University（厄特沃什·罗兰大学）；University of California Riverside（加州大学河滨分校）；King Abdulaziz City for Science and Technology（阿卜杜勒阿齐兹国王科技城）
The classic win-win has a key flaw in that it cannot offer the parties the right amounts of winning because each party believes they are winners. In reality, one party may win more than the other. This strategy is not limited to a single product or negotiation; it may be applied to a variety of situations in life. We present a novel way to measure the win-win situation in this paper. The proposed method employs Fuzzy logic to create a mathematical model that aids negotiators in quantifying their winning percentages. The model is put to the test on real-life negotiations scenarios such as the I…
Mazandaran Regional Electric Company（马赞达兰地区电力公司）；State University of New York at Binghamton（纽约州立大学宾汉姆顿分校）；University of Hawaii at Manoa（夏威夷大学马诺阿分校）；University of Nebraska（内布拉斯加大学）；Mapna Turbine Engineering and Manufacturing Company（Mapna涡轮工程与制造公司）
Reliability assessment of distribution system, based on historical data and probabilistic methods, leads to an unreliable estimation of reliability indices since the data for the distribution components are usually inaccurate or unavailable. Fuzzy logic is an efficient method to deal with the uncertainty in reliability inputs. In this paper, the ENS index along with other commonly used indices in reliability assessment are evaluated for the distribution system using fuzzy logic. Accordingly, the influential variables on the failure rate and outage duration time of the distribution components, …
Rift Valley Technical Training Institute（裂谷技术培训学院）
This paper discusses obstacle avoidance using fuzzy logic and shortest path algorithm. This paper also introduces the sliding blades problem and illustrates how a drone can navigate itself through the swinging blade obstacles while tracing a semi-optimal path and also maintaining constant velocity
A fuzzy inference system was developed for predicting the heat index from temperature and relative humidity data. The effectiveness of fuzzy logic in using imprecise mapping of input to output to encode interconnectedness of system variables was exploited to uncover a linguistic model of how the temperature and humidity conditions impact the heat index in a growth room. The developed model achieved an R2 of 0.974 and a RMSE of 0.084 when evaluated on a test set, and the results were statistically significant (F1,5915 = 222900.858, p < 0.001). By providing the advantage of linguistic summarizat…
Ithaca is a Fuzzy Logic (FL) plugin for developing artificial intelligence systems within the Unity game engine. Its goal is to provide an intuitive and natural way to build advanced artificial intelligence systems, making the implementation of such a system faster and more affordable. The software is made up by a C\# framework and an Application Programming Interface (API) for writing inference systems, as well as a set of tools for graphic development and debugging. Additionally, a Fuzzy Control Language (FCL) parser is provided in order to import systems previously defined using this standa…
Risk specialists are trying to understand risk better and use complex models for risk assessment, while many risks are not yet well understood. The lack of empirical data and complex causal and outcome relationships make it difficult to estimate the degree to which certain risk types are exposed. Traditional risk models are based on classical set theory. In comparison, fuzzy logic models are built on fuzzy set theory and are useful for analyzing risks with insufficient knowledge or inaccurate data. Fuzzy logic systems help to make large-scale risk management frameworks more simple. For risks t…
We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic entailment and provability in graded setting which allows to draw partially true conclusions from partially true assumptions. We follow the Pavelka approach and define general degrees of semantic entailment and provability using complete residuated lattices as structures of truth degrees. We prove the logic is Pavelka-style complete. Furthermo…
Indian Institute of Technology Kharagpur（印度理工学院克勒格布尔分校）
A college student's life can be primarily categorized into domains such as education, health, social and other activities which may include daily chores and travelling time. Time management is crucial for every student. A self realisation of one's daily time expenditure in various domains is therefore essential to maximize one's effective output. This paper presents how a mobile application using Fuzzy Logic and Global Positioning System (GPS) analyzes a student's lifestyle and provides recommendations and suggestions based on the results.
Statistical Hypothesis Testing (SHT) is a class of inference methods whereby one makes use of empirical data to test a hypothesis and often emit a judgment about whether to reject it or not. In this paper we focus on the logical aspect of this strategy, which is largely independent of the adopted school of thought, at least within the various frequentist approaches. We identify SHT as taking the form of an unsound argument from Modus Tollens in classical logic, and, in order to rescue SHT from this difficulty, we propose that it can instead be grounded in t-norm based fuzzy logics. We reformul…
Over past several years, deep learning has achieved huge successes in various applications. However, such a data-driven approach is often criticized for lack of interpretability. Recently, we proposed artificial quadratic neural networks consisting of second-order neurons in potentially many layers. In each second-order neuron, a quadratic function is used in the place of the inner product in a traditional neuron, and then undergoes a nonlinear activation. With a single second-order neuron, any fuzzy logic operation, such as XOR, can be implemented. In this sense, any deep network constructed …
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Civic AI Lab, Amsterdam（阿姆斯特丹公民人工智能实验室）
The AI community is increasingly putting its attention towards combining symbolic and neural approaches, as it is often argued that the strengths and weaknesses of these approaches are complementary. One recent trend in the literature are weakly supervised learning techniques that employ operators from fuzzy logics. In particular, these use prior background knowledge described in such logics to help the training of a neural network from unlabeled and noisy data. By interpreting logical symbols using neural networks, this background knowledge can be added to regular loss functions, hence making…
University of Alberta（阿尔伯塔大学）；Carnegie Mellon University（卡内基梅隆大学）
Natural language inference (NLI) aims to determine the logical relationship between two sentences, such as Entailment, Contradiction, and Neutral. In recent years, deep learning models have become a prevailing approach to NLI, but they lack interpretability and explainability. In this work, we address the explainability of NLI by weakly supervised logical reasoning, and propose an Explainable Phrasal Reasoning (EPR) approach. Our model first detects phrases as the semantic unit and aligns corresponding phrases in the two sentences. Then, the model predicts the NLI label for the aligned phrases…
SAPIENZA University of Rome（罗马大学）；Ryerson University（瑞尔森大学）
Bio-inspired algorithms like Genetic Algorithms and Fuzzy Inference Systems (FIS) are nowadays widely adopted as hybrid techniques in commercial and industrial environment. In this paper we present an interesting application of the fuzzy-GA paradigm to Smart Grids. The main aim consists in performing decision making for power flow management tasks in the proposed microgrid model equipped by renewable sources and an energy storage system, taking into account the economical profit in energy trading with the main-grid. In particular, this study focuses on the application of a Hierarchical Genetic…
Institute for Research in Fundamental Sciences (IPM)（基础科学研究所（IPM））；The University of Quebec at Trois-Rivieres（魁北克大学三河分校）
In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy attribute. To do so, we associate some specific crisp random variables to the random experiment. Then, several formulas are presented, which make it easier to compute different conditional probabilities and expected values of these random variables. Also, we provide measure theoretical basis for our probabilistic fuzzy logic framework. Note that in our theory,…
College of Computer, University of Anbar（安巴尔大学计算机学院）
In this paper we designed an efficient expert system to diagnose diseases for human beings. The system depended on several clinical features for different diseases which will be used as knowledge base for this system. We used fuzzy logic system which is one of the most expert systems techniques that used in building knowledge base of expert systems. Fuzzy logic will be used to inference the results of disease diagnosing. We also provided the system with multimedia such as videos, pictures and information for most of disease that have been achieved in our system. The system implemented using Ma…
In recent years, adaptive learning systems rely increasingly on learning hierarchy to customize the educational logic developed in their courses. Most approaches do not consider that the relationships of prerequisites between the skills are fuzzy relationships. In this article, we describe a new approach of a practical application of fuzzy logic techniques to the construction of learning hierarchies. For this, we use a learning hierarchy predefined by one or more experts of a specific field. However, the relationships of prerequisites between the skills in the learning hierarchy are not defini…
Two Online Map Matching Algorithms Based on Analytic Hierarchy Process and Fuzzy Logic
University of California Irvine（加州大学欧文分校）；Tohoku University（东北大学）；University of Minnesota, Twin Cities（明尼苏达大学双城分校）；Nagoya University（名古屋大学）；Advanced Technology R&D Center, Mitsubishi Electric Corporation（三菱电机公司先进技术研发中心）
