Fuzzy Items Research Articles

Solving NP-Hard Challenges in Logistics and Transportation under General Uncertainty Scenarios Using Fuzzy Simheuristics

In the field of logistics and transportation (L&T), this paper reviews the utilization of simheuristic algorithms to address NP-hard optimization problems under stochastic uncertainty. Then, the paper explores an extension of the simheuristics concept by introducing a fuzzy layer to tackle complex optimization problems involving both stochastic and fuzzy uncertainties. The hybrid approach combines simulation, metaheuristics, and fuzzy logic, offering a feasible methodology to solve large-scale NP-hard problems under general uncertainty scenarios. These scenarios are commonly encountered in L&T optimization challenges, such as the vehicle routing problem or the team orienteering problem, among many others. The proposed methodology allows for modeling various problem components—including travel times, service times, customers’ demands, or the duration of electric batteries—as deterministic, stochastic, or fuzzy items. A cross-problem analysis of several computational experiments is conducted to validate the effectiveness of the fuzzy simheuristic methodology. Being a flexible methodology that allows us to tackle NP-hard challenges under general uncertainty scenarios, fuzzy simheuristics can also be applied in fields other than L&T.

Information granulation-based fuzzy partition in decision tree induction

In this study, an interval information granulation-based fuzzy partition (InterIG-FP) method is established to define fuzzy items in the framework of fuzzy decision tree induction. The proposed method first employs the principle of justifiable granularity to build information granules in terms of different classes on different condition attributes, where the number of information granules is equal to the number of classes. Then, the average values of the representative samples determined by each information granule are utilized to define the membership functions of fuzzy items for each condition attribute. Finally, an interval information granulation-based fuzzy decision tree (InterIG-FDT) is constructed based on the predefined fuzzy items in a top-down recursive way. The experiments illustrate the effectiveness, comparability and immunity capability of the proposed method. The effectiveness is verified by some comparative analysis with several traditional no-fuzzy decision trees. Furthermore, under the same constructing framework, some fuzzy decision trees with different fuzzy partition methods are studied to show the comparability on classification accuracies and the immunity capability on noise data, respectively.

Finite-time sliding mode control for UVMS via T-S fuzzy approach

<p style='text-indent:20px;'>In order to solve the control problem of Underwater Vehicle with Manipulator System (UVMS), this paper proposes a finite-time sliding mode control strategy via T-S fuzzy approach. From the general dynamic model of UVMS and considering the influence between the manipulator and the underwater vehicle, hydrodynamic damping, buoyancy and gravity as the fuzzy items, we establish global fuzzy dynamic model and design a closed-loop fuzzy sliding mode controller. We prove the model in theory from two aspects: the reachability of sliding domain and the finite-time boundedness. We also give the solution of the controller gain. A simulation on the actual four joint dynamic model of UVMS with two fuzzy subsystems is carried out to verify the effectiveness of this method.</p>

Further results on fuzzy sampled-data stabilization of chaotic nonlinear systems

This work focuses on addressing the sampled-data stabilization problem for chaotic nonlinear systems, where the Takagi-Sugeno (T-S) fuzzy model is employed to dispose of the nonlinearity in the system as well as the controller. Contrasted to the traditional control strategy, a more practical piecewise sampled-data controller is developed, where the input delay during the signal transmission is considered. By introducing an approved method for processing fuzzy items and a novel Lyapunov-Krasovskii functional which is inspired by the Wirtinger inequality, as well as an advanced inequality derivation technique, some sufficient conditions with less conservatism are put forward. Appropriate controller gains can be acquired via the solution of the convex optimization problem. At last, the advantages and feasibility of the method proposed are explained by two numerical examples.

Dynamic programming based fuzzy partition in fuzzy decision tree induction

Fuzzy decision trees are one of the most popular extensions of decision trees for symbolic knowledge acquisition by fuzzy representation. Among the majority of fuzzy decision trees learning methods, the number of fuzzy partitions is given in advance, that is, there are the same amount of fuzzy items utilized in each condition attribute. In this study, a dynamic programming-based partition criterion for fuzzy items is designed in the framework of fuzzy decision tree induction. The proposed criterion applies an improved dynamic programming algorithm used in scheduling problems to establish an optimal number of fuzzy items for each condition attribute. Then, based on these fuzzy partitions, a fuzzy decision tree is constructed in a top-down recursive way. A comparative analysis using several traditional decision trees verify the feasibility of the proposed dynamic programming based fuzzy partition criterion. Furthermore, under the same framework of fuzzy decision trees, the proposed fuzzy partition solution can obtain a higher classification accuracy than some cases with the same amount of fuzzy items.

Developing a novel methodology based on the adaptive neuro-fuzzy interference system for the exergoeconomic optimization of energy systems

Optimal control and design of energy systems in some instances require the fast exergoeconomic optimization. Fuzzy inference systems (FIS) were previously employed for either the computerized iterative exergoeconomic optimization or fast optimization of the energy system. The shortcoming of the FIS system was that the requirement to have numerous fuzzy rules and fuzzy membership function that must be collected based on experts' knowledge and usually with try and error steps. On the other hand, conventional optimization methods such as genetic algorithm consume significant calculation time that makes them unsuitable for the fast optimization. In this paper, the adaptive neuro-fuzzy interference system known as the ANFIS was introduced for fast exergoeconomic optimization of energy systems. The ANFIS system automatically developed the required fuzzy items and used them for fast optimization of energy systems. It was employed on two case studies, one for exergoeconomic design and optimization of a benchmark energy system known as the CGAM problem. It was shown that the ANFIS could achieve the optimal solutions of systems with reasonable accuracy, very low computation time, and without dependency on experts' knowledge to develop fuzzy data. The ANFIS was found as an optimistic alternative for the fast optimization of energy systems.

Meta-association rules for mining interesting associations in multiple datasets

Association rules have been widely used in many application areas to extract new and useful information expressed in a comprehensive way for decision makers from raw data. However, raw data may not always be available, it can be distributed in multiple datasets and therefore there resulting number of association rules to be inspected is overwhelming. In the light of these observations, we propose meta-association rules, a new framework for mining association rules over previously discovered rules in multiple databases. Meta-association rules are a new tool that convey new information from the patterns extracted from multiple datasets and give a “summarized” representation about most frequent patterns. We propose and compare two different algorithms based respectively on crisp rules and fuzzy rules, concluding that fuzzy meta-association rules are suitable to incorporate to the meta-mining procedure the obtained quality assessment provided by the rules in the first step of the process, although it consumes more time than the crisp approach. In addition, fuzzy meta-rules give a more manageable set of rules for its posterior analysis and they allow the use of fuzzy items to express additional knowledge about the original databases. The proposed framework is illustrated with real-life data about crime incidents in the city of Chicago. Issues such as the difference with traditional approaches are discussed using synthetic data.

Fuzzy Models and Resolution Methods for Covering Location Problems: an Annotated Bibliography

In this paper, the literature associated with the covering location problems addressing uncertainty under a fuzzy approach is reviewed. Specifically, the papers related to the most commonly applied models such as set covering location problem, maximal covering location problem, and hub covering location problem are examined. An annotated bibliography is presented in which such papers have been classified according to the following criteria: the fuzzy items considered in the proposed model, the type of problem addressed, the fuzzy approach applied, the method of resolution, and field of application considered. This research provides useful information that helps to identify some opportunities for the application of fuzzy approaches to the covering location problems.

Fuzzy Correlated Association Mining: Selecting altered associations among the genes, and some possible marker genes mediating certain cancers

Association mining is a well explored topic applied to various fields. In this article, the associations among the genes have been identified from microarray gene expression data. Here a methodology, called Fuzzy Correlated Association Mining (FCAM), is developed for identifying the associations among the genes that have altered quite significantly from normal state to diseased state with respect to their expression patterns. This idea leads to predict the disease mediating genes along with their altered associations. The proposed methodology involves generation of fuzzy gene sets, construction of fuzzy items, computation of fuzzy support for fuzzy items and fuzzy correlation coefficient of a pair of fuzzy items, generation of associations, and identification of altered associations from normal to diseased state. The concept of finding fuzzy correlation between two groups of items, generation of altered associations among the items (groups of items) and then rank these items (groups of items) according to their importance are the novel contribution of the present article. The effectiveness of the methodology has been demonstrated on five gene expression data sets dealing with human lung cancer, colon cancer, sarcoma, breast cancer and leukemia. As a result, some possible genes, like IGFBP3, ERBB2, TP53, HBB, KRAS, PTEN, CALCA, CDKN2A, has been found as important genes that may mediate the development of various cancers considered here. For comparison, we have considered 11 existing association rule mining algorithms. The results are appropriately validated in terms of gene–gene interactions, functional enrichment, biochemical pathways, and using NCBI database.

A novel associative classification model based on a fuzzy frequent pattern mining algorithm

Associative classification models are based on two different data mining paradigms, namely pattern classification and association rule mining. These models are very popular for building highly accurate classifiers and have been employed in a number of real world applications.During the last years, several studies and different algorithms have been proposed to integrate associative classification models with the fuzzy set theory, leading to the so-called fuzzy associative classifiers.In this paper, we propose a novel efficient fuzzy associative classification approach based on a fuzzy frequent pattern mining algorithm. Fuzzy items are generated by discretizing the input variables and defining strong fuzzy partitions on the intervals resulting from these discretizations. Then, fuzzy associative classification rules are mined by employing a fuzzy extension of the FP-Growth algorithm, one of the most efficient frequent pattern mining algorithms. Finally, a set of highly accurate classification rules is generated after a pruning stage.We tested our approach on seventeen real-world datasets and compared the achieved results with the ones obtained by using both a non-fuzzy associative classifier, namely CMAR, and two recent state-of-the-art classifiers, namely FARC-HD and D-MOFARC, based on fuzzy association rules. Using non-parametric statistical tests, we show that our approach outperforms CMAR and achieves accuracies similar to FARC-HD and D-MOFARC.

Mining Fuzzy Association Rules on Has-A and Is-A Hierarchical Structures

Preliminary studies on data mining focus on finding association rules from transaction databases containing items without relationships among them. However, relationships among items often exist in real applications. Most of the previous works only concern about Is-A hierarchy. In this paper, hierarchical relationships include a Has-A hierarchy and multiple Is-A hierarchies are discussed. The proposed method first reduces a Has-A & Is-A hierarchy into an extended Has-A hierarchy using the IsA-Reduce algorithm. The quantitative data is transformed into fuzzy items. The RPFApriori algorithm is then applied to find fuzzy association rules from the fuzzy item data and the extended Has-A hierarchy.

Mining Fuzzy Association Patterns in Gene Expression Databases

In this paper, we propose two fuzzy data mining approaches for microarray analysis, namely Fuzzy Associative Gene Expression (FAGE) and Ripple Effective Gene Expression Rule (REGER) algorithms. Both of them first transform microarray data into fuzzy items, and then use fuzzy operators and specially-designed data structures to discover the relationships among genes. Through the proposed algorithms, a novel pattern named Ripple Pattern is discovered that indicates the genes active at the same time with their linguistic terms being monotone increasing or decreasing. The experimental results show that the proposed algorithms are effective in discovering novel and useful rules from microarray data.

Modeling Fuzzy Data in Qualitative Marketing Research

In marketing, qualitative data are used in theory development to investigate marketing phenomena in more depth. After qualitative data are collected, the judgment-based classification of items into categories is routinely used to summarize and communicate the information contained in the data. In this article, the authors provide marketing researchers with a method that (1) provides useful substantive information about the proportion and degree to which items belong to several categories and (2) measures the classification accuracy of the judges. The model is called the fuzzy latent class model (FLCM), because it extends Dillon and Mulani's (1984) latent class model by freeing it from the restrictive assumption that all items are crisp for a given categorization. Instead, FLCM allows for items to be either crisp or fuzzy. Crisp items belong exclusively to one category, whereas fuzzy items belong—in varying degree—to multiple categories. This relaxation in the assumption about the nature of qualitative data makes FLCM more widely applicable: Qualitative data in marketing research are often fuzzy, because they involve open-ended descriptions of complex phenomena. The authors also propose a moment-based measure of overall data fuzziness that is bounded by 0 (completely crisp) and 1 (completely fuzzy).

A chaos based revitalization of large reliability knowledge bases

An interdependence among individual knowledge items makes any development of large reliability knowledge bases difficult. The key problem is to maintain a reasonable level of internal consistency in spite of heterogeneity of different knowledge items. A fairly general and efficient formal tools are presented in [1, 2]. They have been used for evaluation of an internal (in)consistency (represented e.g. by a level of chaos) of industrial knowledge bases. The only precondition for their application is an ability to distinguish between specific and general fuzzy items. A realistic case study (control valves) is presented in details.

Fuzzy controlled robot arm playing two-dimensional ping-pong game

A robot-arm system equipped with a CCD camera which is able to play two-dimensional ping-pong game has been built. The system is able to play in the form of both robot versus robot and robot versus human. In the robot control part, 25 fuzzy production rules are used. Ambiguous instructions in terms of membership functions are generated by the robot itself using imagery data from a CCD-camera. Each of these instructions consists of three fuzzy items. Two of them are input (ambiguous) information concerning the fuzzy point, that is where the ball was hit, and the fuzzy angle, that is from which direction the ball is coming, and the other is output information which shows the point that the ball will reach. This output information, which also indicates the point the robot should move to, is calculated based on a fuzzy inference method. The whole system is controlled by only one 16-bit personal computer, and works in real time. The advantage of the proposed method are the reduction of processing time and the availability of low level devices, which have not been realized by other methods.

Category width and differentiation in semantic categories

The hypothesis that the judgemental categorizing behaviour measured by Pettigrew's Category‐Width scale is linked to semantic categorization is investigated. Individual differences in broad vs. narrow categorizing behaviour measured by the C‐W scale are reconceptualized within the framework of Rosch's (1977) theory of human categorization. Two extreme groups on the C‐W scale, broad categorizers and narrow categorizers, were selected as subjects. One experiment employed a short‐term release‐from‐proactive‐inhibition paradigm. The amount of discrepancy in recall between the preshift and the shift trials was used as an index to perceived semantic distance. The result showed that narrow categorizers perceived the same fuzzy items in a semantic category as less similar to the good exemplars of that category than broad categorizers did. In a further experiment using a semantic‐categorization technique, narrow categorizers judged the same fuzzy items as category members less frequently than broad categorizers did, indicating that narrow categorizers possess more differentiated semantic categories than do broad categorizers. These findings are seen as an extension of the differential categorizing behaviour on artificial categories in the C‐W scale to semantic categorization for which there is a pre‐existing system.

About membership functions estimation

A logical approach to fuzzy sets method originated by Giles is developed. The infinitely many-valued logic t ω is taken as basic. We accept, it is correct to use the strong conjunction by the logical analysis of the summation of fuzzy items. Under some broad conditions it is proved. that the sum of many fuzzy variables is a variable whose membership function is approximately equal to ϱ(x) = max{1 − 1 2 c(x − α) 2, 0} , where a and c are some constant parameters. A method of estimation of the unknown parameters is developed in a general case. The proposed fuzzy method coincides with the method of maximum likelihood if used in problems of classical mathematical statistics.