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In this paper we introduce a fuzzy version of symport/antiport membrane systems. Our fuzzy membrane systems handle possibly inexact copies of reactives and their rules are endowed with threshold functions that determine whether a rule can be applied or not to a given set of objects, depending of the degree of accuracy of these objects to the reactives specified in the rule. We prove that these fuzzy membrane systems generate exactly the recursively enumerable finite-valued fuzzy subsets of ℕ.

A kriging method is presented as a spatial filter for smoothing gray-scale images degraded by Gaussian white noise. The concepts are based on the analysis of semivariances, the linear combination scheme of kriging, and fuzzy sets. Application of fuzzy sets allows a gradual transition between two boundaries of semivariance levels as a criterion for smoothing the pixel values. This fuzzy thresholding also allows some degree of flexibility to suit various desired results for particular problems. Experimental results obtained by the fuzzy kriging filter are smoother and still preserve edges compared with those by the adaptive Wiener filter.

Diabetes mellitus is a common chronic disease in recent years. According to the World Health Organization, the estimated number of diabetic patients will increase 56% in Asia from the year 2010 to 2025, where the number of anti-diabetic drugs that doctors are able to utilize also increase as the development of pharmaceutical drugs. In this paper, we present a recommendation system for anti-diabetic drugs selection based on fuzzy reasoning and ontology techniques, where fuzzy rules are used to represent knowledge to infer the usability of the classes of anti-diabetic drugs based on fuzzy reasoning techniques. We adopt the "Medical Guidelines for Clinical Practice for the Management of Diabetes Mellitus" provided by the American Association of Clinical Endocrinologists to build the ontology knowledge base. The experimental results show that the proposed anti-diabetic drugs recommendation system gets the same accuracy rate as the one of Chen et al.'s method (R. C. Chen, Y. H. Huang, C. T. Bau and S. M. Chen, Expert Syst. Appl.39(4) (2012) 3995–4006.) and it is better than Chen et al.'s method (R. C. Chen, Y. H. Huang, C. T. Bau and S. M. Chen, Expert Syst. Appl.39(4) (2012) 3995–4006.) due to the fact that it can deal with the semantic degrees of patients' tests and can provide different recommend levels of anti-diabetic drugs. It provides us with a useful way for anti-diabetic drugs selection based on fuzzy reasoning and ontology techniques.

Software measures (metrics) provide software engineers with an important means of quantifying essential features of software products and software processes such as software reliability, maintenance, reusability and alike. Software measures interact between themselves. Some of them may be deemed redundant. Software measures are used to construct detailed prediction models. The objective of this study is to pursue an association analysis of software measures by revealing dependencies (associations) between them. More specifically, the introduced association analysis is carried out at the local level by studying dependencies between information granules of the software measures. This approach is contrasted with a global level such as e.g., regression analysis. We discuss the role of information granules as meaningful conceptual entities that facilitate analysis and give rise to a user-friendly, highly transparent environment.

In this study, we highlight some fundamental issues of knowledge management and cast them in the setting of Granular Computing (GrC). We show how its formal constructs — information granules are instrumental in knowledge representation and specification of its level of abstraction.

This paper proposes a case-based classifier using a new approach that integrates rule-based and case-based reasoning approaches for enhanced accuracy. The rule-based reasoning component uses rules generated from a concept lattice of training data, binarized using fuzzy sets. These binarized data are stored as cases in the case-based classification component. The case-based component complements the rule-based component to enhance classification accuracy. Moreover, we designed the case-based component with an embedded similarity measure that uses a vector model for concept approximations. Thus, this design makes it possible to generate high quality rules and classify unseen new cases. In addition, the ability to build a knowledge base in lattice form is important for discovering hierarchical patterns, incrementing or updating the existing knowledge base, and inducing rules with our rule learning algorithm. The novel methodology was implemented and evaluated with benchmark datasets from the UCI repository and historic rubber prices in Thailand, demonstrating improvements in accuracy of classification calls. The results from the fact their several hierarchical datasets are very promising, with improved classification performance over prior reported methods.

In this paper we describe an approach to define flexible Knowledge Extraction Systems able to deal with the inherent vagueness and uncertainty of the Extraction process. We also present a short survey of fuzzy and semantic approaches to knowledge extraction. The goal of such approaches is to address if and how some approaches met their goal.

Does a post with specific emotional content that is posted on Twitter by an influential user have the capability to affect and even alter the opinions of those who read it? Accordingly, “influential” users affected by this post can then affect their followers so that eventually a large number of users may change their opinions about the subject the aforementioned post was made on? Social Influence can be described as the power or even the ability of a person to yet influence the thoughts and actions of other users. So, User Influence stands as a value that depends on the interest of the followers (via replies, mentions, retweets, favorites). Our study focuses on identifying such phenomena on the Twitter graph of posts and on determining which users’ posts can trigger them. Furthermore, we analyze the Influence Metrics of all users taking part in specific discussions and verify the differences among them. Finally the percentage of Graph cover when the diffusion starts from the “influential” users, is measured and corresponding results are extracted. Hence, results show that the proposed implementations and methodology can assist in identifying “influential” users, that play a dominant role in information diffusion.

This paper proposes a recurrent neural network of fuzzy units, which may be used for approximating a hetero-associative mapping and also for pattern classification. Since classification is concerned with set membership, and objects generally belong to sets to various degrees, a fuzzy network seems a natural for doing classification. In the network proposed here each fuzzy unit defines a fuzzy set. The fuzzy unit in the network determines the degree to which the input vector to the unit lies in that fuzzy set. The fuzzy unit may be compared to a perceptron in which case the input vector is compared to the weighting vector associated with the unit by taking the dot product. The resulting membership value in case of the fuzzy unit is compared to a threshold. Training of a fuzzy unit is based on an algorithm for solving linear inequalities similar to the method used for Ho-Kashyap recording. Training of the whole network is done by training each unit separately. The training algorithm is tested by trying the algorithm out on representations of letters of the alphabet with their noisy versions. The results obtained by the simulation are very promising.

Conceptual graphs and fuzzy logic are two logical formalisms that emphasize the target of natural language, where conceptual graphs provide a structure of formulas close to that of natural language sentences while fuzzy logic provides a methodology for computing with words. This paper proposes fuzzy conceptual graphs as a knowledge representation language that combines the advantages of both the two formalisms for artificial intelligence approaching human expression and reasoning. Firstly, the conceptual graph language is extended with functional relation types for representing functional dependency, and conjunctive types for joining concepts and relations. Then fuzzy conceptual graphs are formulated as a generalization of conceptual graphs where fuzzy types and fuzzy attribute-values are used in place of crisp types and crisp attribute-values. Projection and join as basic operations for reasoning on fuzzy conceptual graphs are defined, taking into account the semantics of fuzzy set-based values.

The purpose of the paper is to introduce a new type of fuzzy matrix games: fuzzy constrained matrix games. A computational method for its solution based on establishment of the auxiliary fuzzy linear programming for each player is proposed. The approach based on the multiobjective programming is establisched to solve these fuzzy linear programming. Effectiveness is illustrated with a numerical example.

The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexbility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.

Queries to a database can be made more powerful by allowing flexibility in the specification of what has to be retrieved, and by referring to cases either for expressing the request, or for computing the answer. In this paper, we present an implemented information system (applied to a database describing houses to let), based on an approach developed in the fuzzy set and possibility theory setting. This provides a unified framework for expressing users' preferences about what they are looking for, for weighting the importance of requirements, for referring to examples that they like and/or counter-examples that they dislike, and for making case-based predictions. Thus information querying goes beyond the retrieving of items from a database, and involves associated tools which help the user to figure out the actual contents of the database.

Since fuzzy knowledge representation can facilitate interaction between an expert system and its users, the effective construction of a fuzzy knowledge base is important. Fuzzy sequential patterns described by natural language are one type of fuzzy knowledge representation, and can thus be helpful in building a prototype fuzzy knowledge base. We define that a fuzzy sequence is an ordered list of frequent fuzzy grids, and the length of a fuzzy sequence is the number of frequent fuzzy grids in the frequent fuzzy sequence. Frequent fuzzy grids and frequent fuzzy sequences can be determined by comparing individual fuzzy supports with the user-specified minimum fuzzy support. A fuzzy sequential pattern is just a frequent fuzzy sequence, but it is not contained in any other frequent fuzzy sequence. In this paper, an effective algorithm called the Fuzzy Grids Based Sequential Patterns Mining Algorithm (FGBSPMA) is proposed to generate fuzzy sequential patterns. A numerical example is used to show an analysis of the user visit to websites, demonstrating the usefulness of the proposed algorithm.

We discuss the OWA and Choquet integral aggregation operators and point out the central role the ordering operation plays in these operators. We extend the capabilities of the Choquet integral aggregation by allowing the ordering to be induced by some values other then those being aggregated. This allows us to consider an induced Choquet Choquet integral aggregation operator. We look at the properties of this operator. We then look at its applications. Among the applications considered are aggregations guided by linguistic and other ordinal structures. We look at the use of induced aggregation in nearest neighbor methods. We also consider the Choquet aggregation of complex objects such as matrices and vectors.

Studying comparison methods for fuzzy sets is an essential task for the good understanding of the underlying theory in this field. Most of these tools deal with fuzzy sets from the view of similarity, order relationships and so forth. In this paper however, based on a former comparison measures introduced by the authors, the so called Coherence Measures, the extension and analysis of these tools to a measurable Lebesgue set X is carried out. Furthermore we present how coherence measures could be linked to the Fishburn-Yager's ambiguity measures. Besides, two methods for constructing coherence measures, one from ambiguity measures and another from metrics on Pf(X), the set of fuzzy sets on X, are shown and exemplified by a variety of measures and metrics. Finally some illustrative examples testing the coherence measures introduced are provided.

In this paper, a computational system is developed that estimates a survival curve and a point estimate when very few data are available and a high proportion of the data are censored. Standard statistical methods require a more complete data set. With any less data expert knowledge or heuristic methods are required. The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The "fuzzy" data is then used to estimate a survival curve and the mean survival time is calculated from the curve. The new estimator converges to the Product-Limit estimator when a complete data set is available. In addition, this method allows for the incorporation of expert knowledge. Finally, simulation results are provided to demonstrate the performance of the new method and its improvement over the Product-Limit estimator.

Technology and management are two broad categories of factors that have major influence on the productivity of manufacturing firms. The ratio of the actual productivity of a firm to its maximal productivity is a measure of efficiency. Since the automation technology level and production management achievement of a firm cannot be measured precisely, a fuzzy data envelopment analysis (FDEA) model is applied to calculate the efficiency scores of a sample of machinery firms in Taiwan. Different from the conventional crisp DEA, the efficiency scores calculated from the FDEA model are fuzzy numbers, in that ranges of values at different possibility levels rather than a single crisp value are provided. When the observations are fuzzy in nature, the FDEA methodology avoids the top management from being over-confident with the results as opposed to that of using the conventional DEA methodology by simplifying the fuzzy observations to crisp values.

Tandem queueing models play an important role in many real world systems such as computer systems, production lines, and service systems. This paper proposes a procedure to construct the membership functions of the performance measures in tandem queueing systems, in that the arrival rate and service rates are fuzzy numbers. The basic idea is to transform a fuzzy tandem queue to a family of crisp tandem queues by applying the α -cut approach. Then on the basis of α -cut representation and the extension principle, a pair of mathematical programs is formulated to describe this family of crisp tandem queues, via which the membership functions of the performance measures are derived. Two numerical examples are solved successfully to demonstrate the validity of the proposed approach. Since the performance measures are expressed by membership functions rather than by crisp values, the fuzziness of input information is completely conserved. Thus the proposed approach for fuzzy systems can represent the system more accurately, and more information is provided for designing queueing systems. The successful extension of tandem queues to fuzzy environments permits tandem queueing models to have wider applications.

Neural networks are good at representing functions or data transformations. However just as in the case of the biological brain the mathematical description of the data transformation is hidden. In the case of the human brain the transformation, in terms of rules, may be extracted by interviewing the person, In the case of the artificial neural network other approaches have to be utilized.

In the case described here a second neural network that represents the transformation in terms of fuzzy rules is trained using gradient descent. The parameters that are learned are the parameters of the fuzzy sets and also the connection weights in [0,1] between the outputs of the membership function units and the final output units. There is an output unit for each rule and consequent membership function. The fuzzy output set with the highest membership value is taken to be the output fuzzy set. The extracted rules are of the form if x₀ is Small or x₀ is Medium and x₁ is Large or x₁ is Medium then y is Large. x₀ and x₁ are inputs and y is the output.

The cost measure consists of several terms indicating how close the actual output is to a target output, how close the weights are to 0 and 1, and how close the output of membership values is to a 1 of n vector. The cost measure is a linear combination of these individual terms. By changing the constant multipliers the relative importance of the cost measures can be changed and studied.

The method has been tried on randomly generated feedforward neural networks and also on data produced by functions with specific properties. The fizzy network is trained using data produced by the feedforward neural network or the known function. This method can also be used in extracting rules such as control rules implicitly used by a human if input and output data is gathered from the human.