Search results for: fuzzy data

Authors: Behnam Tavakkol

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Uncertain data mining algorithms use different ways to consider uncertainty in data such as by representing a data object as a sample of points or a probability distribution. Fuzzy methods have long been used for clustering traditional (certain) data objects. They are used to produce non-crisp cluster labels. For uncertain data, however, besides some uncertain fuzzy k-medoids algorithms, not many other fuzzy clustering methods have been developed. In this work, we develop a fuzzy kernel k-medoids algorithm for clustering uncertain data objects. The developed fuzzy kernel k-medoids algorithm is superior to existing fuzzy k-medoids algorithms in clustering data sets with non-linearly separable clusters.

Keywords: clustering algorithm, fuzzy methods, kernel k-medoids, uncertain data

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Authors: Jolly Puri, Shiv Prasad Yadav

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Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.

Keywords: multi-component DEA, fuzzy multi-component DEA, fuzzy resources, decision making units (DMUs)

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Authors: Ali Koam, Ismail Ibedou, S. E. Abbas

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In this paper, it is introduced the notion of r-fuzzy ideal separation axioms Tᵢi = 0; 1; 2 based on a fuzzy ideal I on a fuzzy topological space (X; τ). An r-fuzzy ideal connectedness related to the fuzzy ideal I is introduced which has relations with a previous r-fuzzy fuzzy connectedness. An r-fuzzy ideal compactness related to Ι is introduced which has also relations with many other types of fuzzy compactness.

Keywords: fuzzy ideal, fuzzy separation axioms, fuzzy compactness, fuzzy connectedness

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Authors: Michael Gidey Gebru

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Most of Data Envelopment Analysis models operate in a static environment with input and output parameters that are chosen by deterministic data. However, due to ambiguity brought on shifting market conditions, input and output data are not always precisely gathered in real-world scenarios. Fuzzy numbers can be used to address this kind of ambiguity in input and output data. Therefore, this work aims to expand crisp Data Envelopment Analysis into Data Envelopment Analysis with fuzzy environment. In this study, the input and output data are regarded as fuzzy triangular numbers. Then, the Data Envelopment Analysis model with fuzzy environment is solved using a multi-objective method to gauge the Decision Making Units' efficiency. Finally, the developed Data Envelopment Analysis model is illustrated with an application on real data 50 educational institutions.

Keywords: efficiency, Data Envelopment Analysis, fuzzy, higher education, input, output

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Authors: Michael Gidey Gebru

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Most DEA models operate in a static environment with input and output parameters that are chosen by deterministic data. However, due to ambiguity brought on shifting market conditions, input and output data are not always precisely gathered in real-world scenarios. Fuzzy numbers can be used to address this kind of ambiguity in input and output data. Therefore, this work aims to expand crisp DEA into DEA with fuzzy environment. In this study, the input and output data are regarded as fuzzy triangular numbers. Then, the DEA model with fuzzy environment is solved using a multi-objective method to gauge the Decision Making Units’ efficiency. Finally, the developed DEA model is illustrated with an application on real data 50 educational institutions.

Keywords: efficiency, DEA, fuzzy, decision making units, higher education institutions

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Authors: S. H. Nasseri, A. Ebrahimnejad

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Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.

Keywords: fuzzy linear programming, fuzzy numbers, duality, sensitivity analysis

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Authors: G. S. Thakur

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In this paper, four new operators (O1, O2, O3, O4) are proposed, defined and considered to study the new properties and identities on hesitant fuzzy sets. These operators are useful for different operation on hesitant fuzzy sets. The various theorems are proved using the new operators. The study of the proposed new operators has opened a new area of research and applications.

Keywords: vague sets, hesitant fuzzy sets, intuitionistic fuzzy set, fuzzy sets, fuzzy multisets

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Authors: E. Koyuncu

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The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Keywords: fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling

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Authors: T. Pathinathan, M. Peter

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Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

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Authors: Rishabh Srivastav, Divyam Sharma

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We propose an algorithm to cluster categorical data named as ‘Genetic algorithm initialized rough set based fuzzy K-Modes for categorical data’. We propose an amalgamation of the simple K-modes algorithm, the Rough and Fuzzy set based K-modes and the Genetic Algorithm to form a new algorithm,which we hypothesise, will provide better Centroid Model clustering results, than existing standard algorithms. In the proposed algorithm, the initialization and updation of modes is done by the use of genetic algorithms while the membership values are calculated using the rough set and fuzzy logic.

Keywords: categorical data, fuzzy logic, genetic algorithm, K modes clustering, rough sets

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Authors: P. Bharathiraja

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Computer Aided decision making system is used to enhance diagnosis and prognosis of diseases and also to assist clinicians and junior doctors in clinical decision making. Medical Data used for decision making should be definite and consistent. Data Mining and soft computing techniques are used for cleaning the data and for incorporating human reasoning in decision making systems. Fuzzy rule based inference technique can be used for classification in order to incorporate human reasoning in the decision making process. In this work, missing values are imputed using the mean or mode of the attribute. The data are normalized using min-ma normalization to improve the design and efficiency of the fuzzy inference system. The fuzzy inference system is used to handle the uncertainties that exist in the medical data. Equal-width-partitioning is used to partition the attribute values into appropriate fuzzy intervals. Fuzzy rules are generated using Class Based Associative rule mining algorithm. The system is trained and tested using heart disease data set from the University of California at Irvine (UCI) Machine Learning Repository. The data was split using a hold out approach into training and testing data. From the experimental results it can be inferred that classification using fuzzy inference system performs better than trivial IF-THEN rule based classification approaches. Furthermore it is observed that the use of fuzzy logic and fuzzy inference mechanism handles uncertainty and also resembles human decision making. The system can be used in the absence of a clinical expert to assist junior doctors and clinicians in clinical decision making.

Keywords: decision making, data mining, normalization, fuzzy rule, classification

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Authors: B. Güney, Ç. Teke

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In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit.

Keywords: food industry, fuzzy linear programming, fuzzy logic, linear programming

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Authors: Lavinia B. Dulla

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The exploration study of the fuzzy regression approach attempts to present that fuzzy regression can be used as a possible alternative to classical regression. It likewise seeks to assess the differences and characteristics of simple linear regression and fuzzy regression using the width of prediction interval, mean absolute deviation, and variance of residuals. Based on the simple linear regression model, the fuzzy regression approach is worth considering as an alternative to simple linear regression when the sample size is between 10 and 20. As the sample size increases, the fuzzy regression approach is not applicable to use since the assumption regarding large sample size is already operating within the framework of simple linear regression. Nonetheless, it can be suggested for a practical alternative when decisions often have to be made on the basis of small data.

Keywords: fuzzy regression approach, minimum fuzziness criterion, interval regression, prediction interval

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Authors: Seyed Habib A. Rahmati, Mohsen Sadegh Amalnick

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Different terms of the statistical process control (SPC) has sketch in the fuzzy environment. However, measurement system analysis (MSA), as a main branch of the SPC, is rarely investigated in fuzzy area. This procedure assesses the suitability of the data to be used in later stages or decisions of the SPC. Therefore, this research focuses on some important measures of MSA and through a new method introduces the measures in fuzzy environment. In this method, which works based on Buckley approach, imprecision and vagueness nature of the real world measurement are considered simultaneously. To do so, fuzzy version of the gauge capability (Cg and Cgk) are introduced. The method is also explained through example clearly.

Keywords: measurement, SPC, MSA, gauge capability (Cg and Cgk)

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Authors: Shih-Pin Chen, Shih-Syuan You

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Fuzzy regression models are useful for investigating the relationship between explanatory variables and responses in fuzzy environments. To overcome the deficiencies of previous models and increase the explanatory power of fuzzy data, the graded mean integration (GMI) representation is applied to determine representative crisp regression coefficients. A fuzzy regression model is constructed based on the modified dissemblance index (MDI), which can precisely measure the actual total error. Compared with previous studies based on the proposed MDI and distance criterion, the results from commonly used test examples show that the proposed fuzzy linear regression model has higher explanatory power and forecasting accuracy.

Keywords: dissemblance index, fuzzy linear regression, graded mean integration, mathematical programming

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Authors: Murat Yazici

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Anomalies are irregularities found in data that do not adhere to a well-defined standard of normal behavior. The identification of outliers or anomalies in data has been a subject of study within the statistics field since the 1800s. Over time, a variety of anomaly detection techniques have been developed in several research communities. The cluster analysis can be used to detect anomalies. It is the process of associating data with clusters that are as similar as possible while dissimilar clusters are associated with each other. Many of the traditional cluster algorithms have limitations in dealing with data sets containing categorical properties. To detect anomalies in categorical data, fuzzy clustering approach can be used with its advantages. The fuzzy k-Mode (FKM) clustering algorithm, which is one of the fuzzy clustering approaches, by extension to the k-means algorithm, is reported for clustering datasets with categorical values. It is a form of clustering: each point can be associated with more than one cluster. In this paper, anomaly detection is performed on two simulated data by using the FKM cluster algorithm. As a significance of the study, the FKM cluster algorithm allows to determine anomalies with their abnormality degree in contrast to numerous anomaly detection algorithms. According to the results, the FKM cluster algorithm illustrated good performance in the anomaly detection of data, including both one anomaly and more than one anomaly.

Keywords: fuzzy k-mode clustering, anomaly detection, noise, categorical data

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Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

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In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: N. Samarinas, C. Evangelides, C. Vrekos

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The aim of this paper is the comparison of three different methods, in order to produce fuzzy tolerance relations for rainfall data classification. More specifically, the three methods are correlation coefficient, cosine amplitude and max-min method. The data were obtained from seven rainfall stations in the region of central Greece and refers to 20-year time series of monthly rainfall height average. Three methods were used to express these data as a fuzzy relation. This specific fuzzy tolerance relation is reformed into an equivalence relation with max-min composition for all three methods. From the equivalence relation, the rainfall stations were categorized and classified according to the degree of confidence. The classification shows the similarities among the rainfall stations. Stations with high similarity can be utilized in water resource management scenarios interchangeably or to augment data from one to another. Due to the complexity of calculations, it is important to find out which of the methods is computationally simpler and needs fewer compositions in order to give reliable results.

Keywords: classification, fuzzy logic, tolerance relations, rainfall data

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Authors: Bader Alkandari, Jamal Y. Madouh, Ahmad M. Alkandari, Anwar A. Alnaqi

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A new formulation of fuzzy linear estimation problem is presented. It is formulated as a linear programming problem. The objective is to minimize the spread of the data points, taking into consideration the type of the membership function of the fuzzy parameters to satisfy the constraints on each measurement point and to insure that the original membership is included in the estimated membership. Different models are developed for a fuzzy triangular membership. The proposed models are applied to different examples from the area of fuzzy linear regression and finally to different examples for estimating the electrical load on a busbar. It had been found that the proposed technique is more suited for electrical load estimation, since the nature of the load is characterized by the uncertainty and vagueness.

Keywords: fuzzy regression, load estimation, fuzzy linear parameters, electrical load estimation

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Authors: O. Poleshchuk, E. Komarov

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This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: interval type-2 fuzzy sets, fuzzy regression, weighted interval

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Authors: Tri Wijayanti Septiarini, Agus Maman Abadi, Muhammad Rifki Taufik

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The exchange rate of IDR/USD can be the indicator to analysis Indonesian economy. The exchange rate as a important factor because it has big effect in Indonesian economy overall. So, it needs the analysis data of exchange rate. There is decomposition data of exchange rate of IDR/USD to be frequency and time. It can help the government to monitor the Indonesian economy. This method is very effective to identify the case, have high accurate result and have simple structure. In this paper, data of exchange rate that used is weekly data from December 17, 2010 until November 11, 2014.

Keywords: the exchange rate, fuzzy mamdani, discrete wavelet transforms, fuzzy wavelet

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Authors: Feng Tao, Ma Jing, Guo Xian, Wang Jing

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Named Data Networking (NDN) replaces IP address of traditional network with data name, and adopts dynamic cache mechanism. In the existing mechanism, however, only one-to-one search can be achieved because every data has a unique name corresponding to it. There is a certain mapping relationship between data content and data name, so if the data name is intercepted by an adversary, the privacy of the data content and user’s interest can hardly be guaranteed. In order to solve this problem, this paper proposes a one-to-many fuzzy search scheme based on order-preserving encryption to reduce the query overhead by optimizing the caching strategy. In this scheme, we use hash value to ensure the user’s query safe from each node in the process of search, so does the privacy of the requiring data content.

Keywords: NDN, order-preserving encryption, fuzzy search, privacy

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Authors: Sachin Kumar

Abstract:

Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: K. M. Alsager, N. O. Alshehri

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In this paper, we proposed the notion of single valued neutrosophic hesitant fuzzy rough set, by combining single valued neutrosophic hesitant fuzzy set and rough set. The combination of single valued neutrosophic hesitant fuzzy set and rough set is a powerful tool for dealing with uncertainty, granularity and incompleteness of knowledge in information systems. We presented both definition and some basic properties of the proposed model. Finally, we gave a general approach which is applied to a decision making problem in disease diagnoses, and demonstrated the effectiveness of the approach by a numerical example.

Keywords: single valued neutrosophic fuzzy set, single valued neutrosophic fuzzy hesitant set, rough set, single valued neutrosophic hesitant fuzzy rough set

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Authors: Raziyeh Shamsi

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In this paper, we present a multiple objective linear programming (MOLP) problem in full fuzzy case and find Data Envelopment Analysis(DEA) targets. In the presented model, we are seeking the least inputs and the most outputs in the production possibility set (PPS) with the variable return to scale (VRS) assumption, so that the efficiency projection is obtained for all decision making units (DMUs). Then, we provide an algorithm for finding DEA targets interactively in the full fuzzy case, which solves the full fuzzy problem without defuzzification. Owing to the use of interactive methods, the targets obtained by our algorithm are more applicable, more realistic, and they are according to the wish of the decision maker. Finally, an application of the algorithm in 21 educational institutions is provided.

Keywords: DEA, MOLP, full fuzzy, target

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Authors: Ismail Karaca, Ridvan Saracoglu, Omer Soner

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Fuzzy Logic, an advanced method to support decision-making, is used by various scientists in many disciplines. Fuzzy programming is a product of fuzzy logic, fuzzy rules, and implication. In marine science, fuzzy programming for ships is dramatically increasing together with autonomous ship studies. In this paper, a program to support the decision-making process for ship navigation has been designed. The program is produced in fuzzy logic and rules, by taking the marine accidents and expert opinions into account. After the program was designed, the program was tested by 46 ship accidents reported by the Transportation Safety Investigation Center of Turkey. Wind speed, sea condition, visibility, day/night ratio have been used as input data. They have been converted into a risk factor within the Fuzzy Logic Designer application and fuzzy rules set by marine experts. Finally, the expert's meteorological risk factor for each accident is compared with the program's risk factor, and the error rate was calculated. The main objective of this study is to improve the navigational safety of ships, by using the advance decision support model. According to the study result, fuzzy programming is a robust model that supports safe navigation.

Keywords: calculation of risk factor, fuzzy logic, fuzzy programming for ship, safety navigation of ships

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Authors: Luiz F. J. Maia

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This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

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Authors: Yas Barzegaar, Atrin Barzegar

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The aim of this research is to develop an intelligent system to analyze the risk level of wheat flour product manufacturing system. The model consists of five Fuzzy Inference Systems in two different layers to analyse the risk of a wheat flour product manufacturing system. The first layer of the model consists of four Fuzzy Inference Systems with three criteria. The output of each one of the Physical, Chemical, Biological and Environmental Failures will be the input of the final manufacturing systems. The proposed model based on Mamdani Fuzzy Inference Systems gives a performance ranking of wheat flour products manufacturing systems. The first step is obtaining data to identify the failure modes from expert’s opinions. The second step is the fuzzification process to convert crisp input to a fuzzy set., then the IF-then fuzzy rule applied through inference engine, and in the final step, the defuzzification process is applied to convert the fuzzy output into real numbers.

Keywords: failure modes, fuzzy rules, fuzzy inference system, risk assessment

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Authors: Chuanbo Xu, Xinying Li, Gejirifu De, Yunna Wu

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Energy Internet (EI) is a new form that deeply integrates the Internet and the entire energy process from production to consumption. The assessment of energy efficient performance is of vital importance for the long-term sustainable development of EI project. Although the newly proposed fuzzy integrated cloud evaluation algorithm considers the randomness of uncertainty, it relies too much on the experience and knowledge of experts. Fortunately, the enrichment of EI data has enabled the utilization of data-driven methods. Therefore, the main purpose of this work is to assess the energy efficient of park-level EI by using a combination of a data-driven method with the fuzzy integrated cloud evaluation algorithm. Firstly, the indicators for the energy efficient are identified through literature review. Secondly, the artificial neural network (ANN)-based data-driven method is employed to cluster the values of indicators. Thirdly, the energy efficient of EI project is calculated through the fuzzy integrated cloud evaluation algorithm. Finally, the applicability of the proposed method is demonstrated by a case study.

Keywords: energy efficient, energy internet, data-driven, fuzzy integrated evaluation, cloud model

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