Fuzzy Predicates Research Articles

AN ALGEBRAIC PROOF OF COMPLETENESS FOR MONADIC FUZZY PREDICATE LOGIC

Abstract Monoidal t-norm based logic $\mathbf {MTL}$ is the weakest t-norm based residuated fuzzy logic, which is a $[0,1]$ -valued propositional logical system having a t-norm and its residuum as truth function for conjunction and implication. Monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ that consists of the formulas with unary predicates and just one object variable, is the monadic fragment of fuzzy predicate logic $\mathbf {MTL\forall }$ , which is indeed the predicate version of monoidal t-norm based logic $\mathbf {MTL}$ . The main aim of this paper is to give an algebraic proof of the completeness theorem for monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and some of its axiomatic extensions. Firstly, we survey the axiomatic system of monadic algebras for t-norm based residuated fuzzy logic and amend some of them, thus showing that the relationships for these monadic algebras completely inherit those for corresponding algebras. Subsequently, using the equivalence between monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and S5-like fuzzy modal logic $\mathbf {S5(MTL)}$ , we prove that the variety of monadic MTL-algebras is actually the equivalent algebraic semantics of the logic $\mathbf {mMTL\forall }$ , giving an algebraic proof of the completeness theorem for this logic via functional monadic MTL-algebras. Finally, we further obtain the completeness theorem of some axiomatic extensions for the logic $\mathbf {mMTL\forall }$ , and thus give a major application, namely, proving the strong completeness theorem for monadic fuzzy predicate logic based on involutive monoidal t-norm logic $\mathbf {mIMTL\forall }$ via functional representation of finitely subdirectly irreducible monadic IMTL-algebras.

A Semantically Enhanced Knowledge Discovery Method for Knowledge Graph Based on Adjacency Fuzzy Predicates Reasoning

Discover the deep semantics from the massively structured data in knowledge graph and provide reasonable explanations are a series of important foundational research issues of artificial intelligence. However, the deep semantics hidden between entities in knowledge graph cannot be well expressed. Moreover, considering many predicates express fuzzy relationships, the existing reasoning methods cannot effectively deal with these fuzzy semantics and interpret the corresponding reasoning process. To counter the above problems, in this article, a new interpretable reasoning schema is proposed by introducing fuzzy theory. The presented method focuses on analyzing the fuzzy semantic between related entities in a knowledge graph. By annotating the fuzzy semantic features of adjacency predicates, a novel semantic reasoning model is designed to realize the fuzzy semantic extension over knowledge graph. The evaluation, based on both visualization and query experiments, shows that this proposal has advantages over the initial knowledge graph and can discover more valid semantic information.

Improvement of activity level detection in dynamic speckle patterns with fuzzy logic operators

In this work, the design of a multi-descriptor model is proposed to improve the identification of activity levels in dynamic laser speckle (DLS) image sequences. Fuzzy predicates evaluated with operators of different logic systems were used. The model considers both temporal and spatial effects of the DLS phenomenon. Experiments were carried out to characterize the drying times of a sample painted with water-based paint, illuminated with a coherent light, whose image sequences were captured with a CCD camera. To assess the improvement of the proposed model with respect to single descriptors, the Kruskal–Wallis test and the silhouette index were used. The compensatory logic operators achieved the best results to improve the discrimination of the activity levels, according to the different drying times in the dynamic laser speckle sequences.

A new approach to dominant motion pattern recognition at the macroscopic crowd level

Automatic analysis and the recognition and prediction of the behaviour of large-scale crowds in video-surveillance data is a research field of paramount importance for the security of modern societies. It serves to predict and help prevent disasters in public places where crowds of people gather. The paper proposes a novel method for generating meta-tracklets and recognition of dominant motion patterns as a basis for automatic crowd behaviour analysis at the macroscopic level, where a crowd is treated as an entity. The basic characteristic of macroscopic crowd scenes is that it is impossible to detect and track individuals in the scene. The idea of the method proposed in this paper is to recognize dominant crowd motion patterns, by avoiding time-consuming and error-sensitive crowd segmentation, crowd tracking and detection of regions of interest. Thus, the process of determining dominant motion patterns and recognizing crowd behaviour is accelerated. The method is inspired by a quantum mechanical approach. It combines a set of particles, which are considered as particles in quantum mechanics, tracklets of particles’ advection in a video clip, and the interaction of wave functions spread out from particle positions. A wave function is expressed in the form of an asymmetric potential function. Peaks of the wave field define the most probable particle flow, which defines a meta-tracklet. Dominant motion patterns are recognized by applying the functions of fuzzy predicates, which represent a combination of common-sense and human expert knowledge about crowd motions, to the meta-tracklets. The experimental results of the proposed method are presented for a subset of UCF dataset and AGORASET crowd simulation videos and have shown promising results in dominant motion pattern recognition.

Smart Competence Management Using Business Analytics with Fuzzy Predicates

Organizations consider human capital as one of their most important assets. Experts in the field have focused on the research and development of human talent management skills. At present, companies are giving high importance to the management of this intangible resource. Management by competencies and skills is basic in the selection and development of the most valuable asset the organization has: its human capital. A conceptual framework of the intelligent management of human capital and some more advanced knowledge discovery techniques are presented in this paper. A methodology for smart detection of core competencies based on fuzzy logic predicates and business analytics is proposed. The proposed methodology allows: (1) the evaluation of the importance of competencies, (2) the identification of competencies achievement level of each employee, (3) the identification of competencies with difficulties, (4) the identification of competencies that have influence on others, and (5) a hierarchization of the competencies to select the most appropriated for the employee recruitment plan. Furthermore, an analysis is proposed using knowledge discovery, which allows one to identify which competences have influence on a specific one. All of the above is useful to build an ideal profile for a position. A case study was carried out in order to show the implementation and interpretation of our proposal.

Explaining Deep Learning Models Through Rule-Based Approximation and Visualization

This article describes a novel approach to the problem of developing explainable machine learning models. We consider a deep reinforcement learning (DRL) model representing a highway path planning policy for autonomous highway driving [1]. The model constitutes a mapping from the continuous multidimensional state space characterizing vehicle positions and velocities to a discrete set of actions in longitudinal and lateral direction. It is obtained by applying a customized version of the double deep Q-network learning algorithm [2]. The main idea is to approximate the DRL model with a set of IF-THEN rules that provide an alternative interpretable model, which is further enhanced by visualizing the rules. This concept is rationalized by the universal approximation properties of the rule-based models with fuzzy predicates. The proposed approach includes a learning engine composed of zero-order fuzzy rules, which generalize locally around the prototypes by using multivariate function models. The adjacent (in the data space) prototypes, which correspond to the same action, are further grouped and merged into the so-called MegaClouds reducing significantly the number of fuzzy rules. The input selection method is based on ranking the density of the individual inputs. Experimental results show that the specific DRL agent can be interpreted by approximating with families of rules of different granularity. The method is computationally efficient and can be potentially extended to addressing the explainability of the broader set of fully connected deep neural network models.

A weighted fuzzy process neural network model and its application in mixed-process signal classification

A weighted fuzzy process neural network (WFPNN) model, and its corresponding classification algorithm, are proposed for quantitative and qualitative mixed-process signal classification problems. Based on predicate logic, fuzzy process neurons (FPN) are expressed as weighted fuzzy process inference rules on the semantic. Among them, the premise and conclusion are fuzzy predicates defined on a fuzzy set containing process information. Considering the applicability of rules to practical problems, confidence factor and applicable threshold are introduced to make the rules based on FPN have adaptive application ability. Based on FPN, the WFPNN was constructed with a process signal input layer, an FPN hidden layer, and a Takagi-Sugeno fuzzy classifier. It can integrate the learning properties and classification mechanisms of process neural networks (P-NNs) for time-vary signals with the logical inference abilities of fuzzy systems. So then to realize the quantitative and qualitative mixed process signal processing and direct classification. This study proposes a fusion analysis model that combining fuzzy decision theory with the process information processing method of P-NNs. It can automatically deduce the membership function and the fuzzy predicate logic rules from a set of given training examples, quickly build a fuzzy expert system prototype. And it can provide a new method for the construction and application of an expert system based on models or rules. Meanwhile, due to the adaptive learning property of WFPNN and the representation mechanism of inference rules based on the FPN, it is easy to realize the extension of the rule bases, model bases and application fields of the expert systems. This paper analyzes the properties of WFPNN, and establishes a corresponding learning algorithm. The discrimination of reservoir water-flooded states based on well-logging curves was used as an example for experimental analysis. The continuous measurement values of five physical quantities, such as resistivity, acoustic and radioactivity levels in the oil layer, were taken as input. The output was the discriminating result for four types of water-flooded states. The accuracy of the proposed method was 82.5%. Our accuracy was more than 7% higher than other existing automatic identification methods. These results demonstrate the viability and effectiveness of the proposed model and algorithms.

Fuzzy querying with SQL: Fuzzy view-based approach

Nowadays several works have been proposed that allow users to perform fuzzy queries on relational databases. But most of these systems based on an additional software layer to translate a fuzzy query and a supplementary layer of a classic database management system (DBMS) to evaluate fuzzy predicates, which induces an important overhead. They are not also easy to implement by a non-expert user. Here we have proposed a simple and intelligent approach to extend the SQL language to allow us to write flexible conditions in our queries without the need for translation. The main idea is to use a view to manipulate the satisfaction degrees related to user-defined fuzzy predicates, instead of calculating them at runtime employing user functions embedded in the query. Consequently, the response time of executing a fuzzy query statement will be reduced. This approach allows us to easily integrate most fuzzy request characters such as fuzzy modifiers, fuzzy quantifiers, fuzzy joins, etc. Moreover, we present a user-friendly interface to make it easy to use fuzzy linguistic values in all clauses of a select statement. The main contribution of this paper is to accelerate the execution of fuzzy query statements.

Perspectives of Fuzzy Logic and Their Applications

Fuzzy logic is a highly suitable and applicable basis for developing knowledge-based systems in engineering and applied sciences. The concepts of a fuzzy number plays a fundamental role in formulating quantitative fuzzy variable. These are variable whose states are fuzzy numbers. When in addition, the fuzzy numbers represent linguistic concepts, such as very small, small, medium, and so on, as interpreted in a particular contest, the resulting constructs are usually called linguistic variables. Each linguistic variable the states of which are expressed by linguistic terms interpreted as specific fuzzy numbers is defined in terms of a base variable, the value of which are real numbers within a specific range. A base variable is variable in the classical sense, exemplified by the physical variable (e.g., temperature, pressure, speed, voltage, humidity, etc.) as well as any other numerical variable (e.g., age, interest rate, performance, salary, blood count, probability, reliability, etc.). Logic is the science of reasoning. Symbolic or mathematical logic is a powerful computational paradigm. Just as crisp sets survive on a 2-state membership (0/1) and fuzzy sets on a multistage membership [0 - 1], crisp logic is built on a 2-state truth-value (true or false) and fuzzy logic on a multistage truth-value (true, false, very true, partly false and so on). The author now briefly discusses the crisp logic and fuzzy logic. The aim of this paper is to explain the concept of classical logic, fuzzy logic, fuzzy connectives, fuzzy inference, fuzzy predicate, modifier inference from conditional fuzzy propositions, generalized modus ponens, generalization of hypothetical syllogism, conditional, and qualified propositions. Suitable examples are given to understand the topics in brief.

APPLICATION OF MATRIX APPROACH OF FUZZY LOGIC FOR DECISION SUPPORT IN OIL MINING EQUIPMENT SERVICE

The work solves the problem of building an intelligent decision support system for servicing oil production equipment. At the first stage – the choice of an intelligent model – it is shown that in the existing conditions it is difficult to obtain a training sample in digital form. On the other hand, there is an opportunity to gain knowledge of subject matter experts – masters and technologists – in the form of a set of linguistic rules. Based on this, a conclusion about the effectiveness of the use of fuzzy logic to solve this problem is made. At the stage of constructing an intelligent model, the use of the matrix approach of fuzzy logic is proposed. To elaborate this approach an algorithm of fuzzy inference based on vector fuzzy predicates is developed. Capabilities and advantages of new algorithm are demonstrated. In particular, it is shown that the matrix representation makes possible reducing computations to solving a system of linear equations. Matrix inference also allows to explicitly determine the range of values of the analyzed parameters at which the knowledge base does not allow making a clear conclusion. A model of a fuzzy logic machine in the form of a fuzzy combinational circuit that analyzes an external memory block is proposed for the analysis of retrospective information on the change in the values of the parameters of technological equipment over time. Specific cases allowing the transition from a state machine to a combinational circuit are shown. Article also shows how this can be done. The main advantage of this approach is the absence of the need to use the difficult to formalize concept of a fuzzy state, which leads to a simplified construction of fuzzy logical devices with memory. At the end work contains brief conclusions about the application of the proposed methods and algorithms for building, testing, implementing a decision support system and about its effectiveness.

Modelo basado en predicados difusos para la evaluación de la vulnerabilidad a la contaminación del agua subterránea

Groundwater plays a substantial role in resource supply, in ecosystem functioning and human well-being. The aim of this study is develop a tool to assess the groundwater vulnerability through of fuzzy predicates in an area in the Pampas Plain in Argentina. Knowledge is represented as a main fuzzy predicate whose degree of truth is computed by means of numerical variables to determine a degree of groundwater vulnerability. Thematic Fuzzy System (TFS) software has been developed using MATLAB® to design and optimize a fuzzy predicates based model. The results in the final fuzzy map identified the middle and lower basin as areas with high and very high truth values for the main predicate “Groundwater is vulnerable”, thus, these sectors were defined as the main areas of greatest vulnerability. This study showed that fuzzy models are more efficient computer-base tools for decision-makers in the water resources management due to high discrimination of the territory, producing successful results using fewer variables than other ordinary approaches.

FuzzyFeatureRank. Bringing order into fuzzy classifiers through fuzzy expressions

This work presents FuzzyFeatureRank, a new feature reduction method inspired on PageRank to reduce the dimensionality of the feature space in supervised classification problems. More precisely, as it relies on a weighted directed graph, it is ultimately inspired on TextRank, a PageRank based method that adds weights to the edges to express the strength of the connections between nodes. The method is based on dividing each original feature used to describe the data into a set of fuzzy predicates and then ranking all of them by their ability to differentiate among classes in the light of the training set. In order to do that, both the information gained by each predicate and their redundancy with other already selected predicates are taken into account. The fuzzy predicates with the best scores can then be used as a reduced input to construct fuzzy classifiers that consider only the preselected predicates to build the antecedents of the fuzzy rules. The novelty of the proposal relies on being an approach halfway between feature selection and feature extraction approaches, being able to improve the discrimination ability of the original features but preserving the interpretability of the new features in the sense that they are fuzzy expressions. The experimental results support the suitability of the proposal.

Formalization of the optimality criteria based on fuzzy predicates

The paper considers logical approach to solution of multi-objective optimization problems, which consists in representing a certain optimality principle in the form of a predicate with subsequent generalization in the form of a membership function of a fuzzy set of optimal solutions. The results of the study of the dependence of the optimal solution of the fuzzy multi-objective problem on the principle of optimality, functional representation and parameters of fuzzy logical connectives are presented.

Application of fuzzy logic for an enterprise production activity management

For knowledge representation and solving problems of qualitative nature, an applied calculus of fuzzy predicates of the first order has been developed. This theory and methods were used to create an expert system for scientific research in the field of molecular spectroscopy, as well as for a number of other subject areas. One of these areas is the planning and management of the enterprise production activities. A system of fuzzy predicates was developed to formalize basic knowledge of production and commercial activities related to solving the problems of managing production orders. The applied theoretical methods and practical approaches to solving problems of a qualitative nature are considered in the paper.

Applied calculus of fuzzy predicates for the formalization of knowledge

The formalization of knowledge remains one of the main problems of informatization. Special, applied knowledge can be streamlined, brought to a logical level and used to solve specific problems of a qualitative nature. The problems of applied fuzzy knowledge formalization from the point of view of mathematical logic and the theory of fuzzy sets are considered. Use of the applied calculus of fuzzy predicates of the first order was developed and proposed for the representation of knowledge and problem solving. The developed methods were used in the expert system for scientific research in the field of molecular spectroscopy, as well as other subject areas.

The Persistence of 'Dumb' Contracts

“Smart contracts” are a hot topic. Presently, smart contracts are mostly evidence of property, like crypto-currencies or mortgages, created and/or transferred on blockchain technology. This is an exploration of the theoretical possibilities of artificial intelligence in a far broader range of complex and heretofore negotiated transactions that occur over time. My goal is to understand what it means to make a contract smarter, i.e. to delegate more and more of the creation, performance, and disposition of legally binding transactions to machine thinking. Moreover, I want to do so from the perspective of one who is neither a true believer in the purported technological singularity to come nor a digital Luddite. There are two primary themes. First, the extent to which complex transactions occurring over time can be embodied in computer programs – the ability of the contracts to be smarter rather than dumber – depends on the extent to which the subject of the transaction becomes not just a social fact, but an institutional reality. The dumb contract is merely a map of an antecedent reality, but the smart one is a real thing in itself. Second, smart rather than dumb contracts will require the translation of often fuzzy legal predicates, otherwise capable of expression in truth-functional logic, into digital proxies expressible in the non-ambiguous discrete units of code. The upshot of these two themes is that, at least until there is some better evidence that a technological singularity will occur, deciding will remain something that is fundamentally different than reasoning by way of logic or code. Hence, for the time being, dumb contracts, ones that leave open the possibility of what Karl Llewellyn called situation sense, will persist.

Interpretable interval type-2 fuzzy predicates for data clustering: A new automatic generation method based on self-organizing maps

In previous works, we proposed two methods for data clustering based on automatically discovered fuzzy predicates which were referred to as SOM-based Fuzzy Predicate Clustering (SFPC) [Meschino et al., Neurocomputing, 147, 47–59 (2015)] and Type-2 Data-based Fuzzy Predicate Clustering (T2-DFPC) [Comas et al., Expert Syst. Appl., 68, 136–150 (2017)]. In such methods, fuzzy predicates allow both data clustering and knowledge discovering about the obtained clusters. This last feature constitutes novelty comparing to other existing approaches and it is a major contribution in the data clustering field. Based on these previous methods, in the present paper a new automatic clustering method based on fuzzy predicates is proposed which uses Self-Organizing Maps (SOMs) and is called Type-2 SOM-based Fuzzy Predicate Clustering (T2-SFPC). The new method does not require any prior knowledge about the clustering addressed. First, a random partition is defined on the dataset to be clustered and SOMs are configured and trained using the resulting data subsets. Second, an automatic clustering approach is applied on the SOM codebooks, discovering representative data of the different clusters, which are called cluster prototypes. Third, interval type-2 membership function formed by Gaussian-shape sub-functions and fuzzy predicates are defined, allowing data clustering and its interpretation. The proposed method preserves all the advantages of the previous methods SFPC and T2-DFPC in relation to the knowledge extraction capabilities and their potential application on distributed clustering and parallel computing, but results obtained on several public datasets tested showed more compactness and separation of the clusters defined by the T2-SFPC, outperforming both the previous methods and the several classical clustering approaches tested, considering internal and external validation indices. Additionally, both clustering interpretation and optimization capabilities are improved by the proposed method when compared to the methods SFPC and T2-DFPC.

Efficient Algorithm for Answering Fuzzy Medical Requests in Pervasive Healthcare Information Systems

The progress in mobile devices and wireless networks technologies has considerably contributed to integrate pervasive computing expertise in many domains with the aim of improving the quality of services and users' mobility. However, in many situations, users may face difficult situations, needing faster decisions, where classical systems impose the submission of classic queries in which crisp conditions must be carefully fixed. This inconvenience limits the potential of pervasive applications accessed by users having few times to make the right decisions. To introduce the contributions of this paper, we choose the medical domain as example. We considered a pervasive healthcare application under which physicians haven't enough time to fix carefully their queries in some emergency cases. Therefore, they are allowed to flexibly express their preferences using conjunctive fuzzy queries and to quickly receive best answers anywhere and anytime while treating patients in the shortest time and consequently free resources for eventually other urgent requests. In this work, we consider, in general, the problem of efficiently finding the top-K answers for a conjunctive fuzzy query from the top-N conjunctive query rewritings of the query. In particular, we propose an efficient algorithm called the Top-N rewritings algorithm for finding the top-N query rewritings of a medical conjunctive fuzzy query using a set of conjunctive crisp views. At the best of our knowledge, this algorithm is the first to generate, without computing all possible rewritings, the N best ones ordered according to their satisfaction degrees and that are likely to return the best K-answers for the user fuzzy query. The relevance of a query rewriting is estimated using a second algorithm called the Query-satisfaction computing algorithm proposed to estimate, through the histograms maintained to approximate the distribution of set of values returned by the rewriting and to which fuzzy predicates are related, the pertinence of a conjunctive fuzzy query rewriting rather than accessing the database relations.

Implementation of scalable fuzzy relational operations in MapReduce

One of the main restrictions of relational database models is their lack of support for flexible, imprecise and vague information in data representation and querying. The imprecision is pervasive in human language; hence, modeling imprecision is crucial for any system that stores and processes linguistic data. Fuzzy set theory provides an effective solution to model the imprecision inherent in the meaning of words and propositions drawn from natural language (Zadeh, Inf Control 8(3):338–353, doi:10.1016/S0019-9958(65)90241-X, 1965; IGI Global, https://books.google.com/books?id=nt-WBQAAQBAJ, 2013). Several works in the last 20 years have used fuzzy set theory to extend relational database models to permit representation and retrieval of imprecise data. However, to our knowledge, such approaches have not been designed to scale-up to very large datasets. In this paper, the MapReduce framework is used to implement flexible fuzzy queries on a large-scale dataset. We develop MapReduce algorithms to enhance the standard relational operations with fuzzy conditional predicates expressed in natural language.

Local β compactness as fuzzy predicates defined in Łukasiewicz logic

Local β compactness as fuzzy predicates defined in Łukasiewicz logic