Fuzzy Predicates Research Articles

Information Resources Usage in Project Management Digital Learning System

The article combines a theoretical approach to structuring knowledge that is based on the integrated use of fuzzy semantic network theory predicates, Boolean functions, theory of complexity of network structures and some practical aspects to be considered in the distance learning at the university. The paper proposes a methodological approach that takes into account these features. The paper deals with the structuring of project management programs of academic mobility. The features of these projects show their impact on the progress and results of the implementation.It is shown that traditional approaches to solving the problems of academic mobility management applications to integrate the process of setting objectives and planning projects. But due to the complexity of academic mobility programs to solve these problems effectively without decomposing it into components can be managed quite difficult. Therefore, the main idea of this paper is that an increasing the efficiency of the university on the basis of a possible application of rational structuring of academic mobility programs. The features of these projects shows their impact on the progress and results of their implementation and the ways of construction of project management Digital learning systems.The experience of universities of many countries shows that an effective tool to overcome these obstacles is Digital learning, which allows to get all necessary knowledge at any time and in any place. The identity of urgency takes in terms of academic mobility when students and teachers work in another country. The paper presents the analyse of the structure of scientific and methodological basis of project management systems. The model determines the effect of academic mobility project management tools through knowledge of business administration at the progress of the educational projects. In this structure are identified two parts: creation tool to identify knowledge users and how they change, and the creation of information tools effect on these people.

Discovering knowledge from data clustering using automatically-defined interval type-2 fuzzy predicates

In data clustering fuzzy predicates act as cluster descriptors providing linguistically expressed knowledge which indicates how features are related to each cluster. Fuzzy predicates directly and automatically obtained from data enable discovering knowledge inside clusters, even when there is no prior-information about the clustering problem. In this work a new method for automatic discovering of interval type-2 fuzzy predicates in data clustering is proposed, called Type-2 Data-based Fuzzy Predicate Clustering (T2-DFPC). In a first stage, a data analysis is performed by making a random partition of the original data and running a clustering scheme that automatically determines the suitable number of clusters. From this stage, interval type-2 fuzzy predicates are discovered. Results obtained on very different clustering datasets show that the T2-DFPC method was consistently one of the best in terms of accuracy. The method preserves all known advantages of the interval type-2 FL to deal with problems with vagueness, quantifying the degree of truth of the fuzzy predicates and modelling the variability of the data inside the clusters. The proposed method is a fast, useful, general, and unsupervised approach for interpretable data clustering, being the knowledge-extracting capabilities one of the main contributions. Linguistic expressions can be easily adapted to match the terminology used in the field the data are related to. The predicates are able to generalize the knowledge for new cases (new data), as an intelligent system. This new approach might be surprisingly useful in contexts where, besides the clustering partition, summary information from data is of interest.

Fuzzy Logic in Narrow Sense with Hedges

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 not have any dual one. In the other case, each hedge can have its own dual one. The resulting logics are shown to also have the Pavelka-style completeness

Fuzzy Semantics of Contract Language

In this paper, we focus on investigation of the predicate transformer semantics of the contract language introduced by Back and von Wright in their book titled as “Refinement Calculus: A Systematic Introduction” (Springer-Verlag, New York, 1998) in the framework of fuzziness. In order to define fuzzy operations, i.e., fuzzy logic connectives, we take into account implicator → and its associated based on residuated lattice theory. Based on these basic fuzzy operations, we introduce the angelic and demonic updates of fuzzy relations. They are the basis of fuzzy predicate transformers in the sense of that any strongly monotone fuzzy predicate transformer can be represented as the sequential composition of the angelic and demonic updates. Together with the standard strong negation , we set up the duality between the angel and demon. The fuzzy predicate transformers semantics of contract statements is established and a simple example of contract statements is given.

New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic

Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of effect algebra/module that emerged in theoretical physics form the cornerstone. It is shown that under mild conditions on a category, its maps of the form X -> 1+1 carry such effect module structure, and can be used as predicates. Predicates are identified in many different situations, and capture for instance ordinary subsets, fuzzy predicates in a probabilistic setting, idempotents in a ring, and effects (positive elements below the unit) in a C*-algebra or Hilbert space. In quantum foundations the duality between states and effects plays an important role. It appears here in the form of an adjunction, where we use maps 1 -> X as states. For such a state s and a predicate p, the validity probability s |= p is defined, as an abstract Born rule. It captures many forms of (Boolean or probabilistic) validity known from the literature. Measurement from quantum mechanics is formalised categorically in terms of `instruments', using L\"uders rule in the quantum case. These instruments are special maps associated with predicates (more generally, with tests), which perform the act of measurement and may have a side-effect that disturbs the system under observation. This abstract description of side-effects is one of the main achievements of the current approach. It is shown that in the special case of C*-algebras, side-effect appear exclusively in the non-commutative case. Also, these instruments are used for test operators in a dynamic logic that can be used for reasoning about quantum programs/protocols. The paper describes four successive assumptions, towards a categorical axiomatisation of quantitative logic for probabilistic and quantum systems.

Automatic Composition of Semantic Web Services Based on Fuzzy Predicate Petri Nets

Web service composition is a challenging research issue. This paper presents an automatic Web service composition method that deals with both input/output compatibility and behavioral constraint compatibility of fuzzy semantic services. First, user input and output requirements are modeled as a set of facts and a goal statement in the Horn clauses, respectively. A service composition problem is transformed into a Horn clause logic reasoning problem. Next, a Fuzzy Predicate Petri Net (FPPN) is applied to model the Horn clause set, and T-invariant technique is used to determine the existence of composite services fulfilling the user input/output requirements. Then, two algorithms are presented to obtain the composite service satisfying behavioral constraints, as well as to construct an FPPN model that shows the calling order of the selected services.

Answering conjunctive fuzzy query using views: efficient algorithm to return the best k-tuples pervasive healthcare application

In this work, we consider the problem of efficiently finding the top-K answers for a conjunctive fuzzy query used to express users' preferences in a non-crisped way, from the top-N conjunctive query rewritings. We propose an 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 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.

Fuzzy split and merge for shadow detection

Presence of shadow in an image often causes problems in computer vision applications such as object recognition and image segmentation. This paper proposes a method to detect the shadow from a single image using fuzzy split and merge approach. Split and merge is a classical algorithm used in image segmentation. Predicate function in the classical approach is replaced by a Fuzzy predicate in the proposed approach. The method follows a top down approach of recursively splitting an image into homogeneous quadtree blocks, followed by a bottom up approach by merging adjacent unique regions. The method has been compared with previous approaches and found to be better in performance in terms of accuracy.

Formalization and Use of Fuzzy Predicates for Hybrid Processes Implementation

The technique of formalization of fuzzy predicates together with crisp logical variables for the specification of fuzzy logic-dynamic situations and crisp logical commands is considered. The technique is based on the submission of crisp and fuzzy logic variables by means of membership functions and on the use of fuzzy inference rules. Here we only used the forms of presentation of fuzzy logic functions which are also suitable for presentation of crisp logic functions. By the examples the possibility of using the considered technique for the computer implementation of hybrid processes is shown.

Quality measures for fuzzy predicates in conjunctive and disjunctive normal forms

Association rule mining is a very popular data mining technique. Rules in this technique are often used to identify and represent dependencies between attributes in databases. Specifically, fuzzy association rules are rules that use the concepts of fuzzy sets and can be considered as a special case of fuzzy predicates. Many quality measures have been defined for fuzzy association rules, but all consider a specific structure: antecedent and consequence. In the case of fuzzy predicates in the normal form (i.e., conjunctive or disjunctive), it is necessary to define different quality measures that do not consider the structure as an antecedent or a consequence. The only available measure for this scenario is the fuzzy predicate truth value (FPTV), which has serious limitations. The evaluation of fuzzy predicates in the normal form through appropriate quality measures has not yet been clearly defined in the literature. Thus, we propose several quality measures specifically for fuzzy predicates in the conjunctive (CNF) and disjunctive (DNF) normal forms. Experimental studies illustrate the use of the proposed measures and allow some general conclusions about each measure.

The Quintuple Implication Principle of fuzzy reasoning

Fuzzy Modus Ponens (FMP) and Fuzzy Modus Tollens (FMT) are two fundamental patterns of approximate reasoning. Suppose A and B are fuzzy predicates and “IF A THEN B” is a fuzzy rule. Approximate reasoning often requires to derive an approximation B∗ of B from a given approximation A∗ of A, or vice versa. To solve these problems, Zadeh introduces the well-known Compositional Rule of Inference (CRI), which models fuzzy rule by implication and computes B∗ (A∗, resp.) by composing A∗ (B∗, resp.) with A→B. Wang argues that the use of the compositional operation is logically not sufficiently justified and proposes the Triple Implication Principle (TIP) instead. Both CRI and TIP do not explicitly use the closeness of A and A∗ (or that of B and B∗) in the process of calculating the consequence, which makes the thus computed approximation sometimes useless or misleading.In this paper, we propose the Quintuple Implication Principle (QIP) for fuzzy reasoning, which characterizes the approximation B∗ of B (A∗ of A, resp.) as the formula which is best supported by A→B,A∗→A and A∗ (A→B,B→B∗ and B∗, resp.). Based upon Monoidal t-norm Logic (MTL), this paper applies QIP to solve FMP and FMT for four important implications. Most importantly, we show that QIP, when using Gödel implication, computes exactly the same approximation as Mamdani-type fuzzy inference does. This is surprising as Mamdani interprets fuzzy rules in terms of the minimum operation, while CRI, TIP and QIP all interpret fuzzy rules in terms of implication.

Performance Analysis and Evaluation of Fuzzy Pattern Tree Induction

Machine learning, data mining, and several related research areas are concerned with methods for the automated induction of models and the extraction of patterns from realistic data. Fuzzy classification is one of the important applications in fuzzy set where values ranges between 0 and 1 .Main objective of the fuzzy logic and fuzzy set to find a set of fuzzy rules that form a classification model. The set is major advantage of using fuzzy rules for classification applications to maintain transparency as well as high accuracy rate. Fuzzy pattern tree induction introduced as a novel for machine learning method for classification. Pattern tree is a hierarchical tree-like structure, whose inner nodes are marked with generalized (fuzzy) logical operators and whose leaf nodes are associated with fuzzy predicates on input attributes. Pattern tree make use of different aggregation including t-norms and t-conorms. There are two types of Fuzzy Pattern trees: (i) Bottom up induction: Information propagates from bottom to top. (ii) Top down induction: Information propagates from top to down. In this paper performance analysis and comparative study of above both approaches using number of parameters like accuracy rate, model size is mentioned. The paper is divided into five sections: section 1 is introduction of Fuzzy pattern tree, section 2 describes types of fuzzy pattern tree schemes and section 3 presents their comparative performance, section 4 does the conclusion. Section 5 includes future scope.

Qualified Syllogisms with Fuzzy Predicates

A previous publication introduced the logic Q for qualified syllogisms, which formalizes arguments such as Most birds can fly; Tweety is a bird; therefore it is likely that Tweety can fly. This provided a probabilistic semantics for fuzzy quantifiers most, many, few, etc., fuzzy usuality modifiers usually, often, seldom, etc., and fuzzy likelihood modifiers likely, uncertain, unlikely, etc.. That work dealt only with crisp nonfuzzy predicates like Bird and CanFly, however. The present work proposes a simple and intuitively natural way to expand the semantics of Q so as to accommodate syllogisms such as Most Swedes are tall; Helge is a Swede; therefore it is likely that Helge is tall, where tall is a fuzzy predicate. To accomplish this, a formulation of the notion of the probability of a fuzzy event is proposed. It is shown that the new semantics validates the intended syllogisms as well as numerous other propositions and rules, including a rendition of the axioms and inference rules of classical first-order predicate calculus. These results may be viewed as steps toward future applications. A future work will follow the lines of the previous work and show how Q thus extended may be employed for nonmonotonic reasoning with fuzzy predicates.[a]

A Fuzzy Temporal Object-Relational Database: Model and Implementation

In real world, some data have a specific temporal validity that must be appropiately managed. To deal with this kind of data, several proposals of temporal databases have been introduced. Moreover, time can also be affected by imprecision, vagueness, and/or uncertainty, since human beings manage time using temporal indications and temporal notions, which may also be imprecise. For this reason, information systems require appropriate support to accomplish this task. In this work, we present a novel possibilistic valid time model for fuzzy databases including the data structures, the integrity constraints, and the DML. Together with this model, we also present its implementation by means of a fuzzy valid time support module on top of a fuzzy object-relational database system. The integration of these modules allows to perform queries that combines fuzzy valid time constraints together with fuzzy predicates. Besides, the model and implementation proposed support the crisp valid time model as a particular case of the fuzzy valid time support provided.

Automatic design of interpretable fuzzy predicate systems for clustering using self-organizing maps

In the area of pattern recognition, clustering algorithms are a family of unsupervised classifiers designed with the aim to discover unrevealed structures in the data. While this is a never ending research topic, many methods have been developed with good theoretical and practical properties. One of such methods is based on self organizing maps (SOM), which have been successfully used for data clustering, using a two levels clustering approach. Newer on the field, clustering systems based on fuzzy logic improve the performance of traditional approaches. In this paper we combine both approaches. Most of the previous works on fuzzy clustering are based on fuzzy inference systems, but we propose the design of a new clustering system in which we use predicate fuzzy logic to perform the clustering task, being automatically designed based on data. Given a datum, degrees of truth of fuzzy predicates associated with each cluster are computed using continuous membership functions defined over data features. The predicate with the maximum degree of truth determines the cluster to be assigned. Knowledge is discovered from data, obtained using the SOM generalization aptitude and taking advantage of the well-known SOM abilities to discover natural data grouping when compared with direct clustering. In addition, the proposed approach adds linguistic interpretability when membership functions are analyzed by a field expert. We also present how this approach can be used to deal with partitioned data. Results show that clustering accuracy obtained is high and it outperforms other methods in the majority of datasets tested.

Approximations on intuitionistic fuzzy predicate calculus through rough computing

In 1986, Attansov introduced the intuitionistic fuzzy set which is the generalized approach of fuzzy set model introduced by Zadeh. Considering the importance of these two theories, various hybridizations with the available mathematical tools have been derived and they are in practice. Related to the concept of rough sets, the hybridized work of Nakamura, Dubois and Prade are noteworthy. In 2005, G. Ganesan et al., have introduced the concept of thresholds in Rough Fuzzy Hybridizations. Later, in 2008, G. Ganesan et al, derived a naive approach on approximating the connectives in fuzzy predicate calculus through rough sets. This concept was developed by introducing a threshold on the membership of the arguments in the fuzzy predicates. This work yielded the Two way approximations for the fuzzy connectives. In this work, it is noticed that the complement and the negation of the predicates are found in a unique way, whereas in case of intuitionistic fuzziness, the complement and the negation are to be found in two different ways namely membership based and non membership based. Using this concept, in this paper, we introduce Two way approach on Intuitionistic Fuzzy Logic. Also, in this paper, we derive Two way approximations on each intuitionistic fuzzy connectives using rough sets.

A fuzzy description logic F-SHIQ(G)

It is widely recognized that management of data types is an indispensable component in intelligent knowledge-based applications. Recent research has shown that OWL (Web Ontology Language) has a serious limitation on data types and does not support customized data types and predicates. Some work has been carried out to address this issue in crisp situations. In order to deal with fuzzy information in the Semantic Web, this paper proposes a new kind of fuzzy description logic F-SHIQ(G), which can support not only the representation and reasoning of fuzzy concept knowledge, but also fuzzy data information with customized fuzzy data types and customized fuzzy data type predicates. The syntax, semantics and reasoning algorithm of the F-SHIQ(G) are investigated in the paper, and its decidability, soundness, completeness and complexity of the reasoning algorithm are discussed in the paper also. For the reasoning for F-SHIQ(G), the paper adopts a traditional reasoning architecture for fuzzy data type reasoning and as a result, new fuzzy data type reasoners can be added without changing the fuzzy concept reasoner.

Interpretability-based fuzzy decision tree classifier a hybrid of the subtractive clustering and the multi-objective evolutionary algorithm

The fuzzy decision tree (FDT) is a powerful, top---down, hierarchical search scheme to extract human interpretable classification rules. Furthermore, the FDT is considered an approach to model a system by making use of a descriptive language with fuzzy logic and fuzzy predicates. There exist two contradictory requirements with fuzzy modeling, namely, accuracy and interpretability. In this study, the subtractive clustering and a multi-objective evolutionary algorithm are used to develop a novel fuzzy modeling scheme based on the FDT classifier to construct an accurate and interpretable system that is defined as the interpretability-based fuzzy decision tree classifier. Two interpretability measures, namely, complexity interpretability and semantics interpretability are considered to reach acceptable accuracy. These measures are optimized as different objectives within the multi-objective framework. Results obtained in several benchmark classification problems are encouraging because they show the ability of the developed scheme while yielding accuracy comparable to that achieved by other methods like neural networks and the crisp decision tree (C4.5). The experimental results demonstrate the superiority of the developed scheme.

Uni-norm Fuzzy Pattern Trees For Evolving Classification By Imperialist Competitive Algorithm

Fuzzy pattern trees induction was recently introduced as a novel machine learning method for classification. Roughly speaking, a pattern tree is a hierarchical, tree-like structure, whose inner nodes are marked with generalized fuzzy logical or arithmetic operators and whose leaf nodes are associated with fuzzy predicates on input attributes. Operators perform an important role in fuzzy pattern trees. These operators include arithmetic and logical operators. Unlike arithmetic operators,logical operators that were used in these trees are not parameterized. As arithmetic operators, we can choose weighted arithmetic mean and ordered weighted arithmetic mean. There are several families which contain the standard triangular norms and conorms as special cases. This way, we would implicitly select from an infinite number of operators, just like in the case of arithmetic operators. We develop this algorithm by proposing a method to using parameterized logical operators and tuning their parameters by imperialist competitive algorithm. In experimental studies, we compare our method to previous version of algorithm, showing that our method is significantly outperformsthe previous method in terms of predictive accuracy andflexibilityin operator selection.

Semantics of non-deterministic possibility computation

Possibility computation, introduced by Chen and Wu in 2008, is a kind of computational model to deal with non-determinism, based on the axiomatic rule of possibility measures in the framework of domain theory. In this paper, we consider the case of non-determinism of possibility computation, i.e., non-deterministic and possibility computations co-exist. Both its denotational semantics, i.e., state transformer semantics, and logical semantics, i.e., predicate transformer semantics are established and their duality is verified in the framework of fuzziness. The denotational semantics is defined to be a Scott-continuous function from the input spaces to Hoare possibilistic powerdomain of output spaces. The logical semantics is given by strongly healthy fuzzy predicate transformers from fuzzy predicates on the domain of output spaces to the ones on the domain of input spaces. We prove a duality property between these two semantics by means of Sugeno integral with respect to possibility valuations. Finally, we establish the semantics of a fuzzy programming language in terms of our methods.