Defuzzification Operation Research Articles

Increasing the Quality Indicators of the Functioning of Fuzzy Solvers at the Defuzzification Stage

An approach to the implementation of the defuzzification procedure in microprocessor systems of fuzzy information processing is proposed. A computationally efficient model of the defuzzification operation is considered, based on the use of the concept of the measure of validity of a logical conclusion as a composition of the current values of the reliability of all elements of the conditional part of the rule that proposes this conclusion. The application of the approach provides a significant improvement in the quality of fuzzy approximation with little complexity of algorithmic and hardware-software tools. Examples of the use of this approach in practical problems are given.

The advanced defuzzification methods of the convex α – cut fuzzy sets

The main features of the fuzzy sets and their corresponding membership functions were presented in terms of the fuzzification process and further by the de-fuzzification operation. The convexity of the α -(alfa) cuts of the fuzzy sets is used in the decomposition of the fuzzy sets. The alfa cuts of the fuzzy sets were defined precisely in terms of the pair of functions and their lowest upper and greatest lower bounds. The convex combination of the intervals of the sub-regions of the fuzzy sets and their membership function were considered as the points of the defuzzified values of the fuzzy sets. The methods of the de-fuzzification to the crisp sets were presented by the formulas to find the defuzzification regions and de-fuzzified values. The compositional concepts of the inference as the expansion of the extension principle were introduced to formalize further the fuzzy reasoning by the set of fuzzy rules based on the approximate reasoning.

Comparison of Defuzzification Operators on Geographic Data of Ratio Scale

Comparison of Defuzzification Operators on Geographic Data of Ratio Scale

A Fuzzy Strategy to Eliminate Uncertainty in Grading Positive Tuberculosis

Sputum smear microscopic examination is an effective, fast, and low-cost technique that is highly specific in areas with a high prevalence of pulmonary tuberculosis. Since manual screening needs trained pathologist in high prevalence zones, the possibility of deploying adequate technicians during the epidemic sessions would be impractical. This condition can cause overburdening and fatigue of working technicians which may tend to reduce the potential efficiency of Tuberculosis (TB) diagnosis. Hence, automation of sputum inspection is the most appropriate aspect in TB outbreak zones to maximize the detection ability. Sputum collection, smear preparing, staining, interpreting smears, and reporting of TB severity are all part of the diagnosis of tuberculosis. This study has analyzed the risk of automating TB severity grading. According to the findings of the analysis, numerous TB-positive cases do not fit into the standard TB severity grade while applying direct rule-driven strategy. The manual investigation, on the other hand, arbitrarily labels the TB grade on those cases. To counter the risk of automation, a fuzzy-based Tuberculosis Severity Level Categorizing Algorithm (TSLCA) is introduced to eliminate uncertainty in classifying the level of TB infection. TSLCA introduces the weight factors, which are dependent on the existence of maximum number of Acid-Fast Bacilli (AFB) per microscopic Field of View (FOV). The fuzzification and defuzzification operations are carried out using the triangular membership function. In addition, the [Formula: see text]-cut approach is used to eliminate the ambiguity in TB severity grading. Several uncertain TB microscopy screening reports are tested using the proposed TSLCA. Based on the experimental results, it is observed that the TB grading by TSLCA is consistent, error-free, significant and fits exactly into the standard criterion. As a result of the proposed TSLCA, the uncertainty of grading is eliminated and the reliability of tuberculosis diagnosis is ensured when adapting automatic diagnosis.

An advanced TOPSIS method with new fuzzy metric based on interval type-2 fuzzy sets

Decision-making techniques are among important topics applied in operations research. Multi-Criteria Decision-Making (MCDM) is one of the very commonly used subjects of this issue. Technique for Order Preference by Similarity to Ideal Solutions (TOPSIS) is among the most utilized MCDM approaches in terms of both convenience and efficiency. To provide the reality and ease of application of these methods as much as possible Interval Type-2 Fuzzy Numbers (IT2FN)s, a special kind of type-2 fuzzy sets (T2FS)s, are frequently used together with MCDM methods. However, before the final stage of the solution to the problem, defuzzification techniques are applied for obtaining the optimum solution. Switching to crisp numbers before the last step of the procedure reduces the effectiveness of using the IT2FNs. The aim of this paper is to contribute to the literature with a new idea of fuzzy metric function whose result is again a fuzzy number. The result of this study will be a serious contribution to the literature with its metric function structure that is a fuzzy number. A metric function whose result will be a fuzzy set can also be made for different fuzzy structures. Also, a new partial order relation will be given for IT2FNs to define this fuzzy metric function. Moreover, this new fuzzy metric will be adapted to the TOPSIS method. Hence, it will be assured that the defuzzification operations are used only in the final sorting stage and the advantage of using fuzzy numbers will be able to continue in further steps. The advanced TOPSIS with a new fuzzy metric will be applied to a video chat program selection problem as an example.

Spherical fuzzy extension of DEMATEL (SF‐DEMATEL)

In recent years, many versions of fuzzy sets are introduced in the literature. Spherical fuzzy sets (SFSs) concept is one of these latest developments. An SFS is a synthesis of Pythagorean fuzzy set (PFS) and neutrosophic set for providing a larger preference domain for experts and allowing them to express their hesitancy more comprehensively. The distinctive feature of SFSs is that the squared sum of membership, nonmembership, and hesitancy degrees is between 0 and 1 while each degree should be independently defined in [0,1]. The application of SFS on decision-making field may be about describing expert evaluations more informatively and explicitly. In this study, spherical fuzzy version of DEMATEL, one of the most cited multiple criteria decision-making approach, is introduced for considering the hesitancy degrees of experts when they evaluate the potential influences among the criteria. Another contribution made is the fuzzification of all the steps in DEMATEL until the last ones since the existing propositions in literature perform early defuzzification operations. The defuzzification is here applied as close to the end as possible for keeping the whole process fuzzy. The applicability of the proposition is shown in an illustrative example of a building contractor evaluation problem, and its robustness is shown by comparing the results with PFS-based and neutrosophic DEMATEL versions.

Improvement of Rainfall Prediction Model by Using Fuzzy Logic

This paper presents the improvement of the fuzzy inference model for predicting rainfall. Fuzzy rule based system is used in this study to predict rainfall. Fuzzy inference is the actual procedure of mapping with a given set of input and output through a set of fuzzy systems. Two operations were performed on the fuzzy logic model; the fuzzification operation and defuzzification operation. This study is obtaining two input variables and one output variable. The input variables are temperature and wind speed at a particular time and output variable is the amount of predictable rainfall. Temperature, wind speed and rainfall have to construct eight equations for different categories and which are shows the diagram of the graph. Fuzzy levels and membership functions obtained after minimum composition of inference part of the fuzzifications done for temperature and wind speed are considered as they represent the environmental condition enhance a rainfall occurrence which is effect on agricultural production.

A novel spherical fuzzy analytic hierarchy process and its renewable energy application

The extensions of ordinary fuzzy sets such as intuitionistic fuzzy sets, Pythagorean fuzzy sets, and neutrosophic sets, whose membership functions are based on three dimensions, aim at collecting experts’ judgments more informatively and explicitly. In the literature, generalized three-dimensional spherical fuzzy sets have been introduced by Kutlu Gundogdu and Kahraman (J Intell Fuzzy Syst 36(1):337–352, 2019a), including their arithmetic operations, aggregation operators, and defuzzification operations. In this paper, our aim is to extend classical analytic hierarchy process (AHP) to spherical fuzzy AHP (SF-AHP) method and to show its applicability and validity through a renewable energy location selection example and a comparative analysis between neutrosophic AHP and SF-AHP.

A Protocol for Deciding on the Location of Production Unit Using Fuzzy Economic Variables

ABSTRACT In this paper, a fuzzy protocol for a decision-making problem on the choice of location for establishing a production unit from a set of possible locations is presented. Trapezoidal fuzzy numbers are used in the protocol. The ordering between fuzzy numbers is central to the protocol. A remarkable feature is that there is no case of failure, that is, there exists no case leading to indecision in this protocol. No defuzzification operation is used. A numerical illustration is given. The methodology used is a part of Fuzzy Analytical Hierarchical Methods (FAHM).

ANALYTICAL FORMULATIONS FOR THE LEVEL BASED WEIGHTED AVERAGE VALUE OF DISCRETE TRAPEZOIDAL FUZZY NUMBERS

In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers are commonly performed. Aggregation and defuzzification operations are some of these often used operations. Many aggregation and defuzzification operators produce results independent to the decisionmaker’s strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take into account the level weights and the decision maker's optimism strategy. This gives flexibility to the WABL operator and, through machine learning, can be trained in the direction of the decision maker's strategy, producing more satisfactory results for the decision maker. However, in order to determine the WABL value, it is necessary to calculate some integrals. In this study, the concept of WABL for discrete trapezoidal fuzzy numbers is investigated, and analytical formulas have been proven to facilitate the calculation of WABL value for these fuzzy numbers. Trapezoidal and their special form, triangular fuzzy numbers, are the most commonly used fuzzy number types in fuzzy modeling, so in this study, such numbers have been studied. Computational examples explaining the theoretical results have been performed.

Analytical Formulations for the Level Based Weighted Average Value of Discrete Trapezoidal Fuzzy Numbers

In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers are commonly performed. Aggregation and defuzzification operations are some of these often used operations. Many aggregation and defuzzification operators produce results independent to the decision makers strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take into account the level weights and the decision makers optimism strategy. This gives flexibility to the WABL operator and, through machine learning, can be trained in the direction of the decision makers strategy, producing more satisfactory results for the decision maker. However, in order to determine the WABL value, it is necessary to calculate some integrals. In this study, the concept of WABL for discrete trapezoidal fuzzy numbers is investigated, and analytical formulas have been proven to facilitate the calculation of WABL value for these fuzzy numbers. Trapezoidal and their special form, triangular fuzzy numbers, are the most commonly used fuzzy number types in fuzzy modeling, so in this study, such numbers have been studied. Computational examples explaining the theoretical results have been performed.

Designing cylindrical springs of minimum weight with restriction on the own frequency of longitudinal oscillations under condition of full and fuzzy information

Formulation of the problem. Elastic elements such as springs are common іn many products of the machine-building, railway, construction industry. They are designed to accumulate or absorb mechanical energy. These elements of various designs and devices have been and are being given enough attention. There is a large number of publications in this field, where questions of calculation and manufacturing are considered. At the same time, a small number of scientific papers are devoted to optimal design, in which the optimization of the characteristics of springs by various criteria is carried out using nonlinear programming methods.This paper is devoted to the problems of optimal design of a cylindrical tension spring by the weight criterion, while its own frequency of longitudinal oscillations is limited. Direct and dual optimization problems are formulated. Realization is provided with the method of Lagrange multipliers and necessary conditions for the existence of an extremum. Purpose of the article. To consider optimization dynamic problems of design of helical cylindrical springs in conditions of complete and incomplete information about the output data. To analyze the influence of the number of active spring turns on the optimal design parameters, as well as the influence of the fuzzy information about weight setting and the value of the natural frequency of the longitudinal oscillations. Conclusion. As a result of solving the direct and dual optimizing dynamic problem for a helical spring it is found that the dependence of the optimal weight from the natural frequency of the intrinsic longitudinal oscillations and the number of active turns is a nonlinear function. The dependence of the optimum frequency of natural oscillations and the diameter of the wire from the given weight is also nonlinear. The estimation of the influence of the fuzzy initial data on the result of the project (the diameter of the wire of the spring) is obtained. The transformation of fuzzy numbers into deterministic ones is performed by the center method (defuzzification operation). Accounting of fuzzy information leads to increasing in the weight parameter and in the wire diameter parameter.

Crop yield forecasting using fuzzy logic and regression model

Time-Series data has been of great importance to the research field of prediction models. Over the past two decades, multitudinous fuzzy time series blueprints have been put forth for agricultural yield production. However, most of these predictions were based on 7th interval partitioning. A surprising insight was that nobody gave a sound reason to justify the choice of that particular interval. So, this paper focuses on predicting data values on a large spectrum of fuzzy logic computations based on second and third-degree relationships. This paper showcases work on 4 different types of the fuzzy interval, where each interval is tested with 4 degrees of regression equations. Each of these 16 cases is performed for the fuzzy logic relationship (FLR) 2 and 3 separately. Apart from this, the robustness of algorithm is a testament to an incredible solution for the time series model. In addition to this, A Regression analysis model has been enforced to accomplish the efficient defuzzification operation. To elucidate the process of forecasting, the historical data of wheat yield of University of Agriculture and Technology has been used.

Improvements to Earthquake Location with a Fuzzy Logic Approach

In this study, improvements to the earthquake location method were investigated using a fuzzy logic approach proposed by Lin and Sanford (Bull Seismol Soc Am 91:82–93, 2001). The method has certain advantages compared to the inverse methods in terms of eliminating the uncertainties of arrival times and reading errors. In this study, adopting this approach, epicentral locations were determined based on the results of a fuzzy logic space concerning the uncertainties in the velocity models. To map the uncertainties in arrival times into the fuzzy logic space, a trapezoidal membership function was constructed by directly using the travel time difference between the two stations for the P- and S-arrival times instead of the P- and S-wave models to eliminate the need for obtaining information concerning the velocity structure of the study area. The results showed that this method worked most effectively when earthquakes occurred away from a network or when the arrival time data contained phase reading errors. In this study, to resolve the problems related to determining the epicentral locations of the events, a forward modeling method like the grid search technique was used by applying different logical operations (i.e., intersection, union, and their combination) with a fuzzy logic approach. The locations of the events were depended on results of fuzzy logic outputs in fuzzy logic space by searching in a gridded region. The process of location determination with the defuzzification of only the grid points with the membership value of 1 obtained by normalizing all the maximum fuzzy output values of the highest values resulted in more reliable epicentral locations for the earthquakes than the other approaches. In addition, throughout the process, the center-of-gravity method was used as a defuzzification operation.

Assessing and simulation of membrane technology for modifying starchy wastewater treatment

In this study, a hydrophilic polyethersulfone membrane was used to modify the expensive and low efficient conventional treatment method of wheat starch production that would result in a cleaner starch production process. To achieve a cleaner production, the efficiency of starch production was enhanced and the organic loading rate of wastewater that was discharged into treatment system was decreased, simultaneously. To investigate the membrane performance, the dependency of rejection factor and permeate flux on operative parameters such as temperature, flow rate, concentration, and pH of feed were studied. Response surface methodology (RSM) has been applied to arrange the experimental layout which reduced the number of experiments and also the interactions between the parameters were considered. The maximum achieved rejection factor and permeate flux were 97.5% and 2.42 L min−1 m−2, respectively. Furthermore, a fuzzy inference system was selected to model the non-linear relations between input and output variable which cannot easily explained by physical models. The best agreement between the experimental and predicted data for permeate flux was denoted by correlation coefficient index (R2) of 0.9752 and mean square error (MSE) of 0.0072 where defuzzification operator was center of rotation (centroid). Similarly, the maximum R2 for rejection factor was 0.9711 where the defuzzification operator was mean of maxima (mom).

Statistics Model for Meteorological Forecasting Using Fuzzy Logic Model

The key atmospheric variables that impact crops are weather and rainfall. Extreme rainfall or drought at critical periods of a crop's development can have dramatic influences on productivity and yields. The analysis of effect of rainfall is needed to evaluate crop production in Northeastern Thailand. Two operations were performed on the Fuzzy Logic model; the fuzzification operation and defuzzification operation. The model predicted outputs were compared with the actual rainfall data. Simulation results reveal that predicted results are in good agreement with measured data. Prediction Error and Root Mean Square Error (RMSE) were calculated, and on the basis of the results obtained, it can be suggested that fuzzy methodology is efficiently capable of handling scattered data.

Adaptive Intuitionistic Fuzzy Enhancement of Brain Tumor MR Images.

Image enhancement techniques are able to improve the contrast and visual quality of magnetic resonance (MR) images. However, conventional methods cannot make up some deficiencies encountered by respective brain tumor MR imaging modes. In this paper, we propose an adaptive intuitionistic fuzzy sets-based scheme, called as AIFE, which takes information provided from different MR acquisitions and tries to enhance the normal and abnormal structural regions of the brain while displaying the enhanced results as a single image. The AIFE scheme firstly separates an input image into several sub images, then divides each sub image into object and background areas. After that, different novel fuzzification, hyperbolization and defuzzification operations are implemented on each object/background area, and finally an enhanced result is achieved via nonlinear fusion operators. The fuzzy implementations can be processed in parallel. Real data experiments demonstrate that the AIFE scheme is not only effectively useful to have information from images acquired with different MR sequences fused in a single image, but also has better enhancement performance when compared to conventional baseline algorithms. This indicates that the proposed AIFE scheme has potential for improving the detection and diagnosis of brain tumors.

Image enhancement based on intuitionistic fuzzy sets theory

Enhancement of images with weak edges faces great challenges in imaging applications. In this study, the authors propose a novel image enhancement approach based on intuitionistic fuzzy sets. The proposed method first divides an image into sub-object and sub-background areas, and then successively implements new fuzzification, hyperbolisation, and defuzzification operations on each area. In this way, an enhanced image is obtained, where the visual quality of region of interest (ROI) is significantly improved. Several types of images are utilised to validate the proposed method with respect to the enhancement performance. Experimental results demonstrate that the proposed algorithm not only works more stably for different types of images, but also has better enhancement performance, in comparison to conventional methods. This is a great merit of such design for discerning specific ROIs.

Rainfall and financial forecasting using fuzzy time series and neural networks based model

In this study, the author presents a new model to deal with four major issues of fuzzy time series (FTS) forecasting, viz., determination of effective lengths of intervals (i.e., intervals which are used to fuzzify the numerical values), repeated fuzzy sets, trend associated with fuzzy sets, and defuzzification operation. To resolve the problem of determination of length of intervals, this study suggests the application of an artificial neural network (ANN) based algorithm. After generating the intervals, the historical time series data set is fuzzified based on FTS theory. In part of existing FTS models introduced in the literature, each fuzzy set is given equal importance, which is not effective to solve real time problems. Therefore, in this model, it is recommended to assign weights on the fuzzy sets based on their frequency of occurrences. In the FTS modeling approach, fuzzified time series values are further used to establish the fuzzy logical relations (FLRs). To determine the trends associated with the fuzzy sets in the corresponding FLR, this article also introduces three trend-based conditions. To deal repeated fuzzy sets and trend associated with them, this study proposes a new defuzzification technique. The proposed model is verified and validated with real-world time series data sets. Empirical analyzes signify that the proposed model has the robustness to deal one-factor time series data sets very efficiently than existing FTS models. Experimental results show that the proposed model also outperforms over the conventional statistical models.

High-order fuzzy-neuro-entropy integration-based expert system for time series forecasting

In this study, a new fuzzy time series (FTS) forecasting model is introduced. The proposed model tries to deal with four major issues associated with the FTS modeling approach, viz., determination of the lengths of intervals, determination of fuzzy logical relations (FLRs), inclusion of repeated FLRs, and defuzzification operation. For the determination of effective lengths of intervals, “frequency-based discretization” approach is proposed, which partitions the time series data set into various lengths. For establishment of the FLRs and their better representation, an artificial neural network-based architecture is developed. Another novel idea is contributed to the article by considering repeated FLRs during forecasting. Last but not the least, this study introduces a new “entropy-based defuzzification” technique for the defuzzification operation. The model is verified and validated with real-world data sets. Various comparison studies and performance evaluations over the data sets signify the effectiveness and efficiency of the model.