Showing papers on "Fuzzy associative matrix published in 2018"

Sustainable supply chain management using approximate fuzzy DEMATEL method

Abstract: This study develops the approximate fuzzy Decision Making Trial and Evaluation Laboratory (AFDEMATEL) to analyze uncertain influential factors. The approximate fuzzy arithmetic operations under the weakest t-norm (Tω) arithmetic operations to evaluate sustainable supply chain management based on AFDEMATEL. The fuzzy DEMATEL is one of important decision-making method under uncertain environment. The fuzzy DEMATEL had to be developed for clearly display expert’s options with linguistic variables. The fuzzy operations usually adopt α-cut arithmetic in fuzzy DEMATEL. In this research, the fuzzy DEMATEL technology is substituted with the AFDEMATEL technology. In the sustainable supply chain management example, the AFDEMATEL is employed to find fuzzy cause and effect relationships among criteria. Particular note should be made of the following: [1] the fuzzy DEMATEL with α-cut arithmetic model cannot exactly handle fuzzy cause and effect relationships under uncertain environment, and the fuzziness accumulation phenomenon of the α-cut arithmetic may influence final fuzzy cause and effect relationships; and [2] the approximate fuzzy arithmetic operations gives a justifiable fuzziness spread to analyze fuzzy cause and effect relationships. In the case of selection of cans suppliers, the AFDEMATEL examines the influential factors. Proposed method provides justifiable fuzzy cause and effect relationships with approximate fuzzy arithmetic and can analyze across quadrants phenomenon under uncertain environment, since decision-makers usually want to accurately estimate uncertain influential factors.

Deep Takagi–Sugeno–Kang Fuzzy Classifier With Shared Linguistic Fuzzy Rules

Abstract: In many practical applications of classifiers, not only high accuracy but also high interpretability is required. Among a wide variety of existing classifiers, Takagi–Sugeno–Kang (TSK) fuzzy classifiers may be one of the best choices for achieving a good balance between interpretability and accuracy. In order to further improve their accuracy without losing their interpretability, we propose a highly interpretable deep TSK fuzzy classifier HID-TSK-FC (deep shared-linguistic-rule-based TSK fuzzy classifier) based on the concept of shared linguistic fuzzy rules. The proposed classifier has two characteristics: One is a stacked hierarchical structure of component TSK fuzzy classifiers for high accuracy, and the other is the use of interpretable linguistic rules with the same set of linguistic labels for all inputs. High interpretability is achieved at each layer by using the same set of linguistic values for all inputs, including the outputs from the previous layers in the stacked hierarchical structure. We show that a linguistic rule with the outputs from the previous layers as its inputs is equivalent to a fuzzy rule with a nonlinear consequent or a linear consequent with a certainty factor. We also show that HID-TSK-FC is mathematically equivalent to a novel TSK fuzzy classifier with shared interpretable linguistic fuzzy rules. Promising performance of HID-TSK-FC is demonstrated through extensive computational experiments on benchmark datasets and a real-world application case.

On Nie-Tan Operator and Type-Reduction of Interval Type-2 Fuzzy Sets

Abstract: Type-reduction of type-2 fuzzy sets is considered to be a defuzzification bottleneck because of the computational complexity involved in the process of type-reduction. In this paper, we prove that the closed-form Nie-Tan operator, which outputs the average of the upper and lower bounds of the footprint of uncertainty, is actually an accurate method for defuzzifying interval type-2 fuzzy sets.

IC-FNN: A Novel Fuzzy Neural Network With Interpretable, Intuitive, and Correlated-Contours Fuzzy Rules for Function Approximation

Abstract: In this paper, a novel fuzzy neural network with intuitive, interpretable, and correlated-contours fuzzy rules (IC-FNN), for function approximation, is presented. The surfaces of these fuzzy rules are similar to the surfaces of the hills in the function landscape. Contours of the hills could be correlated and nonseparable with different shapes and directions. Thus, to obtain nonseparable and correlated fuzzy rules, a proper optimization problem is introduced and solved. To form contours with different shapes, a novel shapeable membership function with an adaptive shape is introduced to define the fuzzy sets. Next, based on a hierarchical Levenberg–Marquardt learning method, the parameters of the extracted fuzzy rules are fine tuned. The performance of the proposed method is evaluated in real-world regression and time-series prediction problems, and compared with other existing methods. According to these experiments, the proposed method could construct more parsimonious structures with higher accuracy, in comparison to the existing methods. Although the performance of the proposed method for complex and correlated functions is premier, for simple and uncorrelated cases, it is appropriate but with a more complex structure.

Triangular dense fuzzy lock sets

Abstract: This article deals with a triangular dense fuzzy set having special property on Cauchy sequence. In this set, the normality will never be attained unless we unlock by a special key on triangular dense fuzzy set at its final defuzzified state. We give several definitions on triangular dense fuzzy lock sets first and then discuss its locking unlocking property for single-key, double-key, and multiple keys environments with special reference to the convergence of Cauchy sequence. The non-membership function of the proposed lock set has also been studied. The graphical representations of the (non-)membership functions are developed, and the defuzzifications are done by existing methods of dense fuzzy sets as well as cloudy fuzzy sets implicitly. However, we have extended this fuzzy lock set into fuzzy lock matrix to generalize the concept. Finally, we discuss the fields of its practical application and draw a conclusion for better motivation.

Defuzzification and application of trapezoidal type-2 fuzzy variables to green solid transportation problem

Abstract: The main objective of this investigation is to propose a defuzzification process of a trapezoidal type-2 fuzzy variable centred on critical value-based reduction method and nearest interval approximation, i.e. $$\alpha $$ź-cut of fuzzy number. In this context, this paper proposes some theorems with proof. Also as an application of the proposed defuzzification process, a new multi-objective green solid transportation model has been formulated with all of its parameters as trapezoidal type-2 fuzzy variables, where the objectives are profit maximization and minimization of carbon emission produced by the modes of transport depending upon their loads, fuel type used, type of engine, driving characteristics, etc. After defuzzification, to solve the equivalent crisp multi-objective solid transportation problem the intuitionistic fuzzy programming technique is used. Also we have proposed the MOGA and LINGO 13.0 iterative platform for the soft computation related to the problem. At the end, proposed methodologies are finally illustrated by providing numerical examples which incorporate some real-life data and demonstrate how a decision maker makes a balance between the maximum profit and minimum carbon emission. Also a comparative study with N---T method has been provided, and some managerial decisions are drawn.

A Time/Space Separation Based 3D Fuzzy Modeling Approach for Nonlinear Spatially Distributed Systems

Abstract: Spatially distributed systems (SDSs) are usually infinite-dimensional spatio-temporal systems with unknown nonlinearities. Therefore, to model such systems is difficult. In real applications, a low-dimensional model is required. In this paper, a time/space separation based 3D fuzzy modeling approach is proposed for unknown nonlinear SDSs using input-output data measurement. The main characteristics of this approach is that time/space separation and time/space reconstruction are fused into a novel 3D fuzzy system. The modeling methodology includes two stages. The first stage is 3D fuzzy structure modeling which is based on Mamdani fuzzy rules. The consequent sets of 3D fuzzy rules consist of spatial basis functions estimated by Karhunen-Love decomposition. The antecedent sets of 3D fuzzy rules are used to construct temporal coefficients. Going through 3D fuzzy rule inference, each rule realizes time/space synthesis. The second stage is parameter identification of 3D fuzzy system using particle swarm optimization algorithm. After an operation of defuzzification, the output of the 3D fuzzy system can reconstruct the spatio-temporal dynamics of the system. The model is suitable for the prediction and control design of the SDS since it is of low-dimension and simple nonlinear structure. The simulation and experiment are presented to show the effectiveness of the proposed modeling approach.

New Mechanisms for Reasoning and Impacts Accumulation for Rule-Based Fuzzy Cognitive Maps

Abstract: Rule-based fuzzy cognitive maps (RBFCMs) have been developed for modeling nonmonotonic, uncertain, cause-effect systems. However, the standard reasoning and impact accumulation mechanisms developed for RBFCMs assume that the level of variation that a fuzzy set represents is directly linked with the shape of the fuzzy set. It poses a big restriction on how the corresponding fuzzy sets have to be constructed. In this paper, we propose a new reasoning and impact accumulation mechanisms which take into consideration standard semantics of fuzzy sets, where their uncertainty is measured by fuzziness. New type of complex fuzzy relationships and reasoning on them is introduced to model a joint impact of several causal nodes on one effect node. With these new mechanisms, RBFCMs become much more flexible, provide more means to capture complexity of real-world systems, and are less computational demanding than standard mechanisms. The advantages of the new RBFCMs are demonstrated using different examples and compared with standard mechanisms.

Producing fuzzy inclusion and entropy measures and their application on global image thresholding

Abstract: In this presentation, we continue and expand our previous work on fuzzy subsethood and entropy measures. After a minor alteration to the axioms of fuzzy inclusion, we are able to produce new possible fuzzy inclusion and entropy indicators. We believe that these measures could be used in applications which require or properly exploit fuzzy inclusion and entropy measurements (e.g., image processing, feature selection, fuzzy controllers, similarity measures). Possibly they could offer us more information or lead to alternative ways of solving specific problems of these areas of research. We back up this by introducing a general method of global image thresholding which effectively uses some of these measures. Unlike other common techniques of global image thresholding, this method does not depend on histogram concativity analysis nor does it rely on optimizing some statistical measure (e.g. variance minimization) of the gray-level information. It only needs specific attributes of the image which are measured by some of our fuzzy inclusion and entropy indicators. It’s more of an adaptable process rather than a “strict” procedure and we believe that it can be easily adjusted to meet the needs of different domains or fields of research.

Optimization-based inverse analysis for membership function identification in fuzzy steady-state heat transfer problem

Abstract: Based on the optimization design technology and fuzzy uncertainty theory, this paper proposes a novel inverse analysis method for membership function identification in steady-state heat transfer problem with fuzzy modeling parameters. The system subjective uncertainties associated with expert opinions are quantified as fuzzy parameters, which can be converted into interval variables by level-cut strategy. By means of the errors between measured and calculated temperature data, the parameter identification process is executed as a nested-loop optimization model. To avoid the considerable computational cost caused by nested-loop, an interval vertex method is presented to replace the inner-loop for predicting the temperature response bounds. The eventual membership functions of input fuzzy parameters are constructed by using the fuzzy decomposition theorem. Comparing results with traditional Monte Carlo method, a numerical example about 3D air cooling system is provided to verify the feasibility of proposed method for fuzzy parameter identification in engineering.

Storing fuzzy description logic ontology knowledge bases in fuzzy relational databases

Abstract: In the context of the Semantic Web, fuzzy extensions to OWL (the W3C standard ontology language) and Description Logics (DLs, the logical foundation of OWL) have been extensively investigated, and there are many real fuzzy DL ontology knowledge bases. Therefore, how to store fuzzy DL ontology knowledge bases has become an important issue. In this paper, we propose an approach and implement a tool for storing fuzzy DL ontology knowledge bases in fuzzy relational databases. Our chosen formalism is a fuzzy extension of the very expressive DL SHOIN(D), which is the main logical foundation of the standard ontology language OWL, so that our storage approach can store not only fuzzy DL-knowledge bases but also fuzzy ontology knowledge bases. Firstly, we give a formal definition of fuzzy DL-knowledge bases. In the definition, we consider the constructors of both fuzzy SHOIN(D) DL and fuzzy OWL ontology and add some common fuzzy datatypes (e.g., trapezoidal values, interval values, approximate values, and labels) into the knowledge bases. On this basis, we propose an approach which can store fuzzy DL-knowledge bases in fuzzy relational databases, and provide an example to well explain the approach. The correctness and quality of the storage approach are proved and analyzed. Furthermore, following the proposed approach, we implemented a prototype tool, which can automatically store fuzzy DL-knowledge bases. Finally, we make a discussion about the query problem and make a comparison with the existing works.

A Fuzzy Logic Based Approach for Data Classification

Abstract: In this paper, we have developed a new algorithm to handle the classification of data by using fuzzy rules on real world data set Our proposed algorithm helps banks to decide whether to grant loan to customers by classifying them into three clusters—accepted, rejected and those who have probability to get loan To handle third cluster, fuzzy logic based approach is appropriate We have implemented our proposed algorithm on standard bank of England data set Our algorithm makes prediction for getting loan on basis of various attributes like job status, applicant is the chief loan applicant or not, source of income, weight factor etc Fuzzy rules generated from the numerical data give output in linguistic terms We have compared our algorithm with the state of the art algorithms—K-Means, Fuzzy C-means etc Our algorithm has proved to be more efficient than others in terms of performance

Automatic estimation of parameters for the hierarchical reduction of rules of complex fuzzy controllers

Abstract: The application of fuzzy control to large-scale complex systems is not a trivial task. For such systems the number of the fuzzy IF-THEN rules exponentially explodes. If we have m linguistic properties for each of n variables, we will have m rules combinations of input values. Large-scale systems require special approaches for modelling and control. In our work the system’s hierarchical structure is studied in an attempt to reduce the size of the inference engine for large-scale systems. This method reduces the number of rules considerably. But, in order to do so, the adequate parameters should be estimated, which, in the traditional way, depends on the experience and knowledge of a skilled operator. In this work, we are proposing a method to automatically estimate the corresponding parameters for the hierarchical rule base reduction method to be applied to fuzzy control complex systems. In our approach, the parameters of the hierarchical structure are found through the use of genetic algorithms. The implementation process, the simulation experiments and some results are presented.

Optimal parameters of an ELM-based interval type 2 fuzzy logic system: a hybrid learning algorithm

Abstract: An optimized design of a fuzzy logic system can be regarded as setting of different parameters of the system automatically. For a single parameter, there may exist multiple feasible values. Consequently, with the increase in number of parameters, the complexity of a system increases. Type 2 fuzzy logic system has more parameters than the type 1 fuzzy logic system and is therefore much more complex than its counterpart. This paper proposes optimal parameters for an extreme learning machine-based interval type 2 fuzzy logic system to learn its best configuration. Extreme learning machine (ELM) is utilized to tune the consequent parameters of the interval type 2 fuzzy logic system (IT2FLS). A disadvantage of ELM is the random generation of its hidden neuron that causes additional uncertainty, in both approximation and learning. In order to overcome this limitation in an ELM-based IT2FLS, artificial bee colony optimization algorithm is utilized to obtain its antecedent parts parameters. The simulation results verified better performance of the proposed IT2FLS over other models with the benchmark data sets.

Fuzzy topologies generated by fuzzy relations

Abstract: In this paper, we have introduced and studied fuzzy topologies generated by fuzzy relations. Several related results have been proved. In particular, we have obtained characterizations of a fuzzy topology generated by a fuzzy relation, a fuzzy topology generated by a fuzzy interval order, a preorderable fuzzy topology and an orderable fuzzy topology. We have also introduced and studied fuzzy bitopological spaces generated by fuzzy relations.

Rule number and approximation of the hybrid fuzzy system based on binary tree hierarchy

Abstract: To effectively avoid internal rule explosion of a fuzzy system or computer memory overflow caused by increased input variables, a hybrid fuzzy system is established by unifying the Takagi–Sugeno and the Mamdani fuzzy systems based on a binary tree hierarchical method. This method can greatly reduce the total number of rules within the system. Firstly, a calculation formula of the total number of rules for the hybrid fuzzy system is given, by comparing with other layered systems, the total number of rules based on the binary tree hierarchy has the largest decline. Secondly, a new K-integral norm is redefined by introducing a K-quasi-subtraction operator. Using the piecewise linear function the approximation capability of the hybrid fuzzy system after hierarchy to a kind of integrable functions is studied. Finally, the binary tree hierarchical structure expressions of the hybrid fuzzy system are given through two simulation examples.

Fuzzy Generalization and Comparisons for the Rand Index

Abstract: To generalize the Rand index (RI) from crisp partitions to fuzzy partitions, we first propose a graph method in which color edges in the graph for crisp partitions are used to determine the relation matrix between objects such that the matrix trace can be employed to calculate the RI This approach is then introduced into fuzzy partitions to generalize the RI to the fuzzy RI (FRI) Compared with previous fuzzy generalizations, the most unique aspect of our method has the following important characteristics that for any two partition matrices M(1) and M(2), the result with M(1)=M(2) is the necessary and sufficient condition for the result that the FRI is equal to 1 This important characteristic renders our fuzzy generalization of the RI is not only able to determine the similarities between fuzzy partitions and crisp reference partitions, but also to identify the similarity between fuzzy partitions and fuzzy reference partitions The method can even be used to explore and compare the similarities between various data sets and the same fuzzy reference partition Finally, we use synthetic data and real data to give more demonstrations, and further perform comparisons of our method with those existing fuzzy extensions of the RI

Fuzzy Logic Control

Abstract: Classical control algorithms require an exact specification of reference values, however, it is difficult to give exact definitions of properties such as the warmth of a heater, the color of a piece of fabric or the speed of a car. Fuzzy logic uses rules on linguistic variables such as “fast” and “slow” to implement control algorithms. Values from the sensors are fuzzified into linguistic variables, then the rules are applied, and finally the consequents of the rules are defuzzified to obtain numerical values that can be applied to the actuators.

Generalized Fuzzy Soft Rough Matrices and Their Applications in Decision-Making Problems

Abstract: In this paper, generalized fuzzy soft rough matrices and their operations which are more essential to make theoretical studies in the fuzzy soft rough sets are defined. Further, based on the analysis of generalized fuzzy soft rough matrices, several algebraic properties are established. Using the notions of generalized fuzzy soft rough matrices, a novel method for choosing an optimum choice in a multi-criteria decision-making problem is developed. Moreover, the proposed method is compared with the well-known existing methods of fuzzy soft matrices, and the effectiveness of the proposed method has been demonstrated through numerical example.