Concept Of Fuzzy Number Research Articles

Novel decision making approach for sustainable renewable energy resources with cloud fuzzy numbers

Decision making approaches depending on the assessments of individual decision makers produce inaccurate results due to the existence of multiple uncertainties. To model intrapersonal uncertainty, interpersonal uncertainty and randomness in decision making assessments, this research study proposes a novel approach by integrating linear and non-linear type of fuzzy numbers with cloud model theory using novel technique of computing entropy of these fuzzy numbers. A novel mathematical model known as cloud fuzzy numbers is introduced using the concepts of fuzzy numbers and cloud theory. The self-evaluated relative weights of experts are computed using a non-linear optimization method which is based on maximum deviation method and Lagrange multipliers of cloud fuzzy numbers. The new cloud fuzzy numbers are then combined with CODAS (combinative distance based assessment) approach that is based on the largest Euclidean and Taxicab distances for the selection of suitable criteria. Firstly, the linguistics evaluations are converted into the fuzzy numbers and then cloud fuzzy numbers using formulae of expectation and entropy ensuring that the obtained interval cloud values follows a normal distribution. Secondly, the cloud fuzzy weighted arithmetic averaging operator is used to aggregate cloud fuzzy numbers using the self-evaluated fuzzy weights Thirdly, the assessment score is determined to rank the alternatives by computing the distance between normalized weighted matrix and the negative ideal solution. Finally, a case study is discussed for the selection of best renewable energy resource in Turkey to elaborate the significance of the proposed research. The convergence and accuracy of the proposed model is proved with certain mathematical and theoretical results.

Network intrusion detection using data dimensions reduction techniques

Due to the increasing growth of the Internet and its widespread application, the number of attacks on the network has also increased. Therefore, maintaining network security and using intrusion detection systems is of critical importance. The connection between devices leads to a large number of data being generated and saved. The era of “big data” emerges over time. This paper presents a new method for selecting effective features on network intrusion detection based on the concept of fuzzy numbers and scoring methods based on correlation feature selection for intrusion detection systems. The goal of this paper is to present a new approach for reducing data size using the concept of fuzzy numbers and scoring methods based on correlation feature selection for intrusion detection systems. In this method, to eliminate inefficient features and reduce data dimensions, number of features are defined as a fuzzy number, and the heuristic function of the correlation-based feature selection algorithm is expressed as a triangular fuzzy number membership function. To evaluate the proposed method, it is then compared to previous intrusion detection methods. The results show that the proposed method selects several features less than the conventional methods with a higher detection rate. The proposed method is compared with the correlation-based feature selection method on two datasets. The proposed method is evaluated and validated on KDD Cup, NSL-KDD and CICIDS datasets. The achieved accuracy is 99.9% which is 96.01% with CFS method.

Fourth-Order Numerical Solutions for a Fuzzy Time-Fractional Convection–Diffusion Equation under Caputo Generalized Hukuhara Derivative

The fuzzy fractional differential equation explains more complex real-world phenomena than the fractional differential equation does. Therefore, numerous techniques have been timely derived to solve various fractional time-dependent models. In this paper, we develop two compact finite difference schemes and employ the resulting schemes to obtain a certain solution for the fuzzy time-fractional convection–diffusion equation. Then, by making use of the Caputo fractional derivative, we provide new fuzzy analysis relying on the concept of fuzzy numbers. Further, we approximate the time-fractional derivative by using a fuzzy Caputo generalized Hukuhara derivative under the double-parametric form of fuzzy numbers. Furthermore, we introduce new computational techniques, based on fuzzy double-parametric form, to shift the given problem from one fuzzy domain to another crisp domain. Moreover, we discuss some stability and error analysis for the proposed techniques by using the Fourier method. Over and above, we derive several numerical experiments to illustrate reliability and feasibility of our proposed approach. It was found that the fuzzy fourth-order compact implicit scheme produces slightly better results than the fourth-order compact FTCS scheme. Furthermore, the proposed methods were found to be feasible, appropriate, and accurate, as demonstrated by a comparison of analytical and numerical solutions at various fuzzy values.

Fuzzy Interpolation Curve Modelling of Earthquake Magnitude Data

This research discussed on developing the fuzzy interpolation curve model which only used spline and B-spline functions in designing curve interpolation. The development of this model is used fuzzy set theory and more specifically fuzzy number concepts since the modeling problem is focused on modeling data. These data are known as uncertainty data and defined through fuzzy numbers which the properties of these data set belong to fuzzy numbers. There are also several steps to be implemented to obtain the crisp fuzzy model of crisp fuzzy data. These steps include fuzzification and defuzzification. For the fuzzification process which used alpha-cut triangular fuzzy numbers, an enhancement is also applied in process of determining the value of alpha based on the fuzzy data in triangular form. A numerical example is implemented to show the fuzzy interpolation curve modeling in which earthquake magnitude data are selected.

On Nash-Coalitive Fuzzy Continuous Differential Games

This paper concentrates on providing a simple and effective technique to solve the Nash-coalitive fuzzy continuous differential games. These games are featured by having fuzzy coefficients, fuzzy controls, and fuzzy state functions. The proposed technique utilizes the α-cut set concept of fuzzy numbers to transform the problem under study into a corresponding interval problem. The latter one is sliced into two problems, lower problem and upper problem, to obtain the optimal solution for the Nash-coalitive fuzzy continuous differential games problem in a range form. The sufficient and necessary conditions for this problem are derived. A numerical example is provided to clarify the presented concepts. Keywords— fuzzy control, fuzzy differential games, fuzzy numbers, Nash-coalitive differential games

Hardware Reliability Analysis of a Coal Mine Gas Monitoring System Based on Fuzzy-FTA

The hardware reliability of a gas monitoring system was investigated using the fuzzy fault tree analysis method. A fault tree was developed considering the hardware failure of the gas monitoring system as a top event. Two minimum path sets were achieved through qualitative analysis using the ascending method. The concept of fuzzy number of the fuzzy set theory was applied to describe the probability of basic event occurrence in the fault tree, and the fuzzy failure probabilities of the middle and top events were calculated using fuzzy AND and OR operators. The results show that the proposed fuzzy fault tree is an effective method of reliability analysis for gas monitoring systems. Results of calculations using this method are more reasonable than those obtained with the conventional fault tree method.

Model of Regional Tourism Competitiveness: Fuzzy Multiple-Criteria Approach (FDM-FAHP-PROMETHE II Framework)

Purpose: The aim of the article is to build a research, comprehensive and objective model that takes into account various factors determining the regional tourism competitiveness on the example of 21 counties in the West Pomeranian Voivodeship. Degign/Methodology/Approach: The model uses the concept of fuzzy numbers, the Delphi method and two multi-criteria methods: AHP and PROMETHE II. An important scientific contribution to the issue of regional competitiveness of tourism is an in-depth look at several dozen different criteria, that have an impact on it. Collected data and the used research methods made it possible to reliably select those that should be noticed and developed by various stakeholders in the region. Findings: The main conclusion resulting from the research is the fact that the most important criteria for the level of tourist competitiveness of a destination include natural tourist attraction, anthropological tourist attractions, accommodation base, recreational infrastructure and catering base; whereas the criterion of safety and facilities for disabled tourists and para-tourist infrastructure is of little importance. The county with the highest level of tourism competitiveness is Kolobrzeg county, and the lowest - Pyrzycki county. Practical implications: An important scientific and practical contribution to the issue of regional competitiveness of tourism is an in-depth look at several dozen different criteria, that have an impact on it. Collected data and the used research methods made it possible to reliably select those that should be noticed and developed by various stakeholders in the region. Originallity value: Comprehensive approach to tourism competitiveness of regions with the use of multi-criteria method, which in an objective way indicates the aspects, features, attributes, factors evaluated as key in building the entity's position on the market.

Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

Fuzzy Type RK4 Solutions to Fuzzy Hybrid Retarded Delay Differential Equations

This paper constructs the numerical solution of particular type of differential equations called fuzzy hybrid retarded delay-differential equations using the method of Runge-Kutta for fourth order.The concept of fuzzy number, hybrid-differential equations and delay-differential equations binds together to form our equations.An example following the algorithm is presented to understand the Concept of fuzzy hybrid retarded delay-differential equations and its accuracy is discussed in terms of decimal places for easy understanding of laymen.

English

English

Similarity measure on incomplete imprecise interval information and its applications

The concept of fuzzy numbers has been generalized to intuitionistic fuzzy interval numbers (IFINs) to solve problems with imprecision in the information modeling. Similarity measure is an important tool to measure the degree of resemblance between any two objects in real-life situations and is applied in many areas such as decision making, image processing, pattern recognition, etc. In this paper, a new distance-based similarity measure between IFINs is proposed using which a similarity measure on incomplete imprecise interval information is attempted. Some properties of the proposed distance measure and similarity measure are studied using illustrative examples. The nominal decreasing and increasing properties based on the proposed distance measure and similarity measure are proved. Further, the superiority of the proposed similarity measure over familiar existing methods is shown by different numerical examples and the proposed measure is applied to technique for order preference by similarity to ideal solution method under interval-valued intuitionistic fuzzy environment. Finally, the applicability of the proposed method in pattern recognition problems is illustrated.

Multi-objective assembly line balancing problem under uncertainty using genetic algorithm

This paper addresses the single-model multi-objective assembly line balancing (ALB) problem with fuzzy processing time. A fuzzy optimisation model is formulated for the problem. In the classical mathematical formulation of SALBP, the relevant data are considered deterministic. But, the data of the real world problems are imprecise, vague or uncertain. The input data should be estimated within uncertainty represented by a fuzzy number. The concept of fuzzy numbers is introduced to treat imprecise data, such as the processing time of each task. Due to the NP-hard nature of the ALB problem, heuristics are used to solve real life cases. In this paper, an efficient heuristic is proposed to solve the fuzzy multi-objective ALB problem. The proposed heuristic is based on genetic algorithm (GA) that is efficient to handle fuzzy job time through the evolution process. As the proposed algorithm can find out the optimum solution as a trade-off among several objectives, it outperforms the existing heuristics on several test cases. The proposed algorithm can be effectively used in the design phase of an assembly line.

Multi-objective assembly line balancing problem under uncertainty using genetic algorithm

This paper addresses the single-model multi-objective assembly line balancing (ALB) problem with fuzzy processing time. A fuzzy optimisation model is formulated for the problem. In the classical mathematical formulation of SALBP, the relevant data are considered deterministic. But, the data of the real world problems are imprecise, vague or uncertain. The input data should be estimated within uncertainty represented by a fuzzy number. The concept of fuzzy numbers is introduced to treat imprecise data, such as the processing time of each task. Due to the NP-hard nature of the ALB problem, heuristics are used to solve real life cases. In this paper, an efficient heuristic is proposed to solve the fuzzy multi-objective ALB problem. The proposed heuristic is based on genetic algorithm (GA) that is efficient to handle fuzzy job time through the evolution process. As the proposed algorithm can find out the optimum solution as a trade-off among several objectives, it outperforms the existing heuristics on several test cases. The proposed algorithm can be effectively used in the design phase of an assembly line.

Monte Carlo Simulation for Modified Parametric Of Sample Selection Models Through Fuzzy Approach

The sample selection model is a combination of the regression and probit models. The models are usually estimated by Heckman’s two-step estimator. However, Heckman’s two-step estimator often performs poorly. In the context of the parametric method, Monte Carlo simulations are studied. The goal is to simulate and test as early as possible so that we can anticipate the problem of the accuracy of a model. The best approach is to take advantage of the tools provided by the theory of fuzzy sets. It appears very suitable for modeling vague concepts. It is difficult to determine some of the criteria and arrive at a quantitative value. Fuzzy sets theory and its properties through the concept of fuzzy number. The fuzzy function used for solving uncertain of a parametric sample selection model. Estimates from the fuzzy are used to calculate some of equation of the sample selection model. Finally, estimates of the Mean, Root Mean Square Error (RMSE) and the other estimators can be obtained by Heckman two-step estimator through iteration from some parameters and some of values.

Prediction interval methodology based on fuzzy numbers and its extension to fuzzy systems and neural networks

Prediction interval modelling has been proposed in the literature to characterize uncertain phenomena and provide useful information from a decision-making point of view. In most of the reported studies, assumptions about the data distribution are made and/or the models are trained at one step ahead, which can decrease the quality of the interval in terms of the information about the uncertainty modelled for a higher prediction horizon. In this paper, a new prediction interval modelling methodology based on fuzzy numbers is proposed to solve the abovementioned drawbacks. Fuzzy and neural network prediction interval models are developed based on this proposed methodology by minimizing a novel criterion that includes the coverage probability and normalized average width. The fuzzy number concept is considered because the affine combination of fuzzy numbers generates, by definition, prediction intervals that can handle uncertainty without requiring assumptions about the data distribution. The developed models are compared with a covariance-based prediction interval method, and high-quality intervals are obtained, as determined by the narrower interval width of the proposed method. Additionally, the proposed prediction intervals are tested by forecasting up to two days ahead of the load of the Huatacondo microgrid in the north of Chile and the consumption of the residential dwellings in the town of Loughborough, UK. The results show that the proposed models are suitable alternatives to electrical consumption forecasting because they obtain the minimum interval widths that characterize the uncertainty of this type of stochastic process. Furthermore, the information provided by the obtained prediction interval could be used to develop robust energy management systems that, for example, consider the worst-case scenario.

Certain Algorithms for Modeling Uncertain Data Using Fuzzy Tensor Product Bézier Surfaces

Real data and measures are usually uncertain and cannot be satisfactorily described by accurate real numbers. The imprecision and vagueness should be modeled and represented in data using the concept of fuzzy numbers. Fuzzy splines are proposed as an integrated approach to uncertainty in mathematical interpolation models. In the context of surface modeling, fuzzy tensor product Bézier surfaces are suitable for representing and simplifying both crisp and imprecise surface data with fuzzy numbers. The framework of this research paper is concerned with various properties of fuzzy tensor product surface patches by means of fuzzy numbers including fuzzy parametric curves, affine invariance, fuzzy tangents, convex hull and fuzzy iso-parametric curves. The fuzzification and defuzzification processes are applied to obtain the crisp Beziér curves and surfaces from fuzzy data points. The degree elevation and de Casteljau’s algorithms for fuzzy Bézier curves and fuzzy tensor product Bézier surfaces are studied in detail with numerical examples.

Fuzzy reliability estimation using the new operations of transmission average on Rational-linear patchy fuzzy numbers

This paper presents a new practical method for fuzzy system reliability analysis based on the fuzzy arithmetic operations of transmission average (TA) (Abbasi et al. in J Intell Fuzzy Syst 29:851–861, 2015) on Rational-linear patchy fuzzy numbers. The concept of fuzzy numbers is extended by idea of Rational-linear patchy fuzzy numbers. Then, we have introduced fuzzy arithmetic operations of TA between two Rational-linear patchy fuzzy numbers. Finally, a new method has been developed for analyzing the fuzzy system reliability of series and parallel systems based on the fuzzy arithmetic operations of TA, where the reliability of each component is represented by a Rational-linear patchy fuzzy number. A technical example is given to illustrate applying the method and comparing the results of the new method with the previous methods. The proposed method can model and analyze the fuzzy system reliability in a more flexible and intelligent manner in comparison with the other methods.

Enhanced fuzzy-analytic hierarchy process

Application of fuzzy-analytic hierarchical process (fuzzy-AHP) has been growing continuously to select the best alternative. In the fuzzy-AHP approach, first the complex problem is itemized into a hierarchical structure for pairwise comparisons. Once a comparison matrix is formed, a triangular fuzzy number concept is adopted to assign priority weights with a view to capture the inherent vagueness in linguistic terms of the decision-maker. In evaluation, if two triangular fuzzy numbers are not intersecting $$({ t}_{11}- { t}_{23}\ge ~0)$$ , then corresponding degree of possibility value is assumed to be zero (0). However, such situation simply represents the case of one criterion being immensely stronger than other and should not receive a zero value. In this regard, the article proposes an enhanced fuzzy-AHP approach where the triangles are extended about x-axis. This allows developing a mathematical formulation to estimate the true values of height of ordinate (degree of possibility). The empirical study of ranking the SECI modes in the order they influence the performance of the detailed design phase is considered to demonstrate the applicability and usefulness of the proposed framework. In order to measure the performance, five criteria are selected based on a rigorous literature review. After stringent experimentation, it is found that combination and externalization modes highly influence but other modes in order of internalization and socialization loosely have an effect on underlying phase.

THE SERIES OF FUZZIFIED FUZZY BEZIER CURVE

This paper discusses about the series of fuzzified Bezier curves. This series of fuzzified Bezier curves constructed based on the fuzzy set theory especially fuzzy number concepts. The series of fuzzified represented by the alpha-cut of fuzzy number with various values of alpha. Then, the results were blended with Bezier curve function to produce the series of fuzzified fuzzy Bezier curves.

Approximate controllability result for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions

This paper deals with the approximate controllability of impulsive neutral fuzzy stochastic differential equations with nonlocal conditions in a Banach space by using the concept of fuzzy numbers whose values are normal, convex, upper semicontinuous and compact. The hypotheses are obtained by Schauder’s and Banach fixed point theorems. The results are obtained by the evolution operator.