Search results for: standard fuzzy sets (SFS)

Authors: J. Kavikumar, N. S. Manian, M.B.K. Moorthy

Abstract:

The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.

Keywords: Fuzzy best co-approximation, fuzzy quotient spaces, proximinality, Chebyshevity, best simultaneous co-approximation.

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Authors: M. G. C. A. Cimino, G. Frosini, B. Lazzerini, F. Marcelloni

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In the last decades, a number of robust fuzzy clustering algorithms have been proposed to partition data sets affected by noise and outliers. Robust fuzzy C-means (robust-FCM) is certainly one of the most known among these algorithms. In robust-FCM, noise is modeled as a separate cluster and is characterized by a prototype that has a constant distance δ from all data points. Distance δ determines the boundary of the noise cluster and therefore is a critical parameter of the algorithm. Though some approaches have been proposed to automatically determine the most suitable δ for the specific application, up to today an efficient and fully satisfactory solution does not exist. The aim of this paper is to propose a novel method to compute the optimal δ based on the analysis of the distribution of the percentage of objects assigned to the noise cluster in repeated executions of the robust-FCM with decreasing values of δ . The extremely encouraging results obtained on some data sets found in the literature are shown and discussed.

Keywords: noise prototype, robust fuzzy clustering, robustfuzzy C-means

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Authors: Tamanna Siddiqui, M. Afshar Alam

Abstract:

Censored Production Rule is an extension of standard production rule, which is concerned with problems of reasoning with incomplete information, subject to resource constraints and problem of reasoning efficiently with exceptions. A CPR has a form: IF A (Condition) THEN B (Action) UNLESS C (Censor), Where C is the exception condition. Fuzzy CPR are obtained by augmenting ordinary fuzzy production rule “If X is A then Y is B with an exception condition and are written in the form “If X is A then Y is B Unless Z is C. Such rules are employed in situation in which the fuzzy conditional statement “If X is A then Y is B" holds frequently and the exception condition “Z is C" holds rarely. Thus “If X is A then Y is B" part of the fuzzy CPR express important information while the unless part acts only as a switch that changes the polarity of “Y is B" to “Y is not B" when the assertion “Z is C" holds. The proposed approach is an attempt to discover fuzzy censored production rules from set of discovered fuzzy if then rules in the form: A(X) ÔçÆ B(Y) || C(Z).

Keywords: Uncertainty Quantification, Fuzzy if then rules, Fuzzy Censored Production Rules, Learning algorithm.

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Authors: E. A. Tkachenko, E. M. Rogova, V. V. Klimov

Abstract:

One of the basic issues of development management is connected with performance measurement as a prerequisite for identifying the achievement of development objectives. The aim of our research is to develop an improved model of assessing a company’s development results. The model should take into account the cyclical nature of development and the high degree of uncertainty in dealing with numerous management tasks. Our hypotheses may be formulated as follows: Hypothesis 1. The cycle of a company’s development may be studied from the standpoint of a project cycle. To do that, methods and tools of project analysis are to be used. Hypothesis 2. The problem of the uncertainty when justifying managerial decisions within the framework of a company’s development cycle can be solved through the use of the mathematical apparatus of fuzzy logic. The reasoned justification of the validity of the hypotheses made is given in the suggested article. The fuzzy logic toolkit applies to the case of technology shift within an enterprise. It is proven that some restrictions in performance measurement that are incurred to conventional methods could be eliminated by implementation of the fuzzy logic apparatus in performance measurement models.

Keywords: Fuzzy logic, fuzzy sets, performance measurement, project analysis.

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Authors: Amit Kumar, Pushpinder Singh, Parampreet Kaur, Amarpreet Kaur

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Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (2009) 6833-6842) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The main advantage of the proposed approach is that the proposed approach provide the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (2001) 375-385).

Keywords: Ranking function, Generalized trapezoidal fuzzy numbers

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Authors: Nisha Singhal, Usha Chouhan

Abstract:

At present, application of the extension of soft set theory in decision making problems in day to day life is progressing rapidly. The concepts of fuzzy soft set and its properties have been evolved as an area of interest for the researchers. The generalization of the concepts recently got importance and a rapid growth in the research in this area witnessed its vital-ness. In this paper, an application of the concept of generalized fuzzy soft set to make decision in a social problem is presented. Further, this paper also highlights some of the key issues of the related areas.

Keywords: Soft set, Fuzzy Soft set, Generalized Fuzzy Soft set, Membership and Non-Membership Score.

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Authors: J. Kavikumar, N. S. Manian, M. B. K. Moorthy

Abstract:

The main purpose of this paper is to consider the new kind of approximation which is called as t-best coapproximation in fuzzy n-normed spaces. The set of all t-best coapproximation define the t-coproximinal, t-co-Chebyshev and F-best coapproximation and then prove several theorems pertaining to this sets. 

Keywords: Fuzzy-n-normed space, best coapproximation, co-proximinal, co-Chebyshev, F-best coapproximation, orthogonality

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Authors: S. Yaman, S. Rostami

Abstract:

In this study, a black box modeling of the coupled-tank system is obtained by using fuzzy sets. The derived model is tested via adaptive neuro fuzzy inference system (ANFIS). In order to achieve a better control performance, the parameters of three different controller types, classical proportional integral controller (PID), fuzzy PID and function tuner method, are tuned by one of the evolutionary computation method, genetic algorithm. All tuned controllers are applied to the fuzzy model of the coupled-tank experimental setup and analyzed under the different reference input values. According to the results, it is seen that function tuner method demonstrates better robust control performance and guarantees the closed loop stability.

Keywords: Function tuner method, fuzzy modeling, fuzzy PID controller, genetic algorithm.

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Authors: Hossein Pazhoumand-Dar, Amir Mohsen Toliyat Abolhassani, Ehsan Saeedi

Abstract:

Speed estimation is one of the important and practical tasks in machine vision, Robotic and Mechatronic. the availability of high quality and inexpensive video cameras, and the increasing need for automated video analysis has generated a great deal of interest in machine vision algorithms. Numerous approaches for speed estimation have been proposed. So classification and survey of the proposed methods can be very useful. The goal of this paper is first to review and verify these methods. Then we will propose a novel algorithm to estimate the speed of moving object by using fuzzy concept. There is a direct relation between motion blur parameters and object speed. In our new approach we will use Radon transform to find direction of blurred image, and Fuzzy sets to estimate motion blur length. The most benefit of this algorithm is its robustness and precision in noisy images. Our method was tested on many images with different range of SNR and is satisfiable.

Keywords: Blur Analysis, Fuzzy sets, Speed estimation.

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Authors: C. Ardil

Abstract:

Aircraft supplier selection process, which is considered as a fundamental supply chain problem, is a multi-criteria group decision problem that has a significant impact on the performance of the entire supply chain. In practical situations are frequently incomplete and uncertain information, making it difficult for decision-makers to communicate their opinions on candidates with precise and definite values. To solve the aircraft supplier selection problem in an environment of incomplete and uncertain information, proximity measure method is proposed. It uses determinate fuzzy numbers. The weights of each decision maker are equally predetermined and the entropic criteria weights are calculated using each decision maker's decision matrix. Additionally, determinate fuzzy numbers, it is proposed to use the weighted normalized Minkowski distance function and Hausdorff distance function to determine the ranking order patterns of alternatives. A numerical example for aircraft supplier selection is provided to further demonstrate the applicability, effectiveness, validity and rationality of the proposed method.

Keywords: Aircraft supplier selection, multiple criteria decision making, fuzzy sets, determinate fuzzy sets, intuitionistic fuzzy sets, proximity measure method, Minkowski distance function, Hausdorff distance function, PMM, MCDM

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Authors: C. Ardil

Abstract:

Fuzzy set theory and its extensions (intuitionistic fuzzy sets, picture fuzzy sets, and neutrosophic sets) have been widely used to address imprecision and uncertainty in complex decision-making. However, they may struggle with inherent indeterminacy and inconsistency in real-world situations. This study introduces uncertainty sets as a promising alternative, offering a structured framework for incorporating both types of uncertainty into decision-making processes.This work explores the theoretical foundations and applications of uncertainty sets. A novel decision-making algorithm based on uncertainty set-based proximity measures is developed and demonstrated through a practical application: selecting the most suitable stealth combat aircraft.

The results highlight the effectiveness of uncertainty sets in ranking alternatives under uncertainty. Uncertainty sets offer several advantages, including structured uncertainty representation, robust ranking mechanisms, and enhanced decision-making capabilities due to their ability to account for ambiguity.Future research directions are also outlined, including comparative analysis with existing MCDM methods under uncertainty, sensitivity analysis to assess the robustness of rankings,and broader application to various MCDM problems with diverse complexities. By exploring these avenues, uncertainty sets can be further established as a valuable tool for navigating uncertainty in complex decision-making scenarios.

Keywords: Uncertainty set, stealth combat aircraft selection multiple criteria decision-making analysis, MCDM, uncertainty proximity analysis

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Authors: Huei-Fu Lu

Abstract:

This paper is to develop a fuzzy net present value (FNPV) method by taking vague cash flow and imprecise required rate of return into account for evaluating the value of the Build-Operate-Transfer (BOT) sport facilities. In order to clearly manifest a more realistic capital budgeting model based on the classical net present value (NPV) method, some uncertain financial elements in NPV formula will be fuzzified as triangular fuzzy numbers. Through the conscientious manipulation of fuzzy set theory, we will find that the proposed FNPV model is a more explicit extension of classical (crisp) model and could be more practicable for the financial managers to capture the essence of capital budgeting of sport facilities than non-fuzzy model.

Keywords: Fuzzy sets; Capital budgeting, Sport facility, Net present value (NPV), Build-Operate-Transfer (BOT) scheme

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Authors: Pankaj Dutta, Debjani Chakraborty

Abstract:

This paper investigates the effect of product substitution in the single-period 'newsboy-type' problem in a fuzzy environment. It is supposed that the single-period problem operates under uncertainty in customer demand, which is described by imprecise terms and modelled by fuzzy sets. To perform this analysis, we consider the fuzzy model for two-item with upward substitution. This upward substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. We show that the explicit consideration of this substitution opportunity increase the average expected profit. Computational study is performed to observe the benefits of product's substitution.

Keywords: Fuzzy demand, Newsboy, Single-period problem, Substitution.

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Authors: Bogdan Walek, Jiri Bartos, Cyril Klimes, Jaroslav Prochazka, Pavel Smolka, Juraj Masar, Martin Pesl

Abstract:

This paper focuses on creating a component model of information system under uncertainty. The paper identifies problem in current approach of component modeling and proposes fuzzy tool, which will work with vague customer requirements and propose components of the resulting component model. The proposed tool is verified on specific information system and results are shown in paper. After finding suitable sub-components of the resulting component model, the component model is visualised by tool.

Keywords: Component, component model, fuzzy, fuzzy rules, fuzzy sets, information system, modelling, tool.

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Authors: Ayman A. Aly, Abdallah A. Alshnnaway

Abstract:

The general idea behind the filter is to average a pixel using other pixel values from its neighborhood, but simultaneously to take care of important image structures such as edges. The main concern of the proposed filter is to distinguish between any variations of the captured digital image due to noise and due to image structure. The edges give the image the appearance depth and sharpness. A loss of edges makes the image appear blurred or unfocused. However, noise smoothing and edge enhancement are traditionally conflicting tasks. Since most noise filtering behaves like a low pass filter, the blurring of edges and loss of detail seems a natural consequence. Techniques to remedy this inherent conflict often encompass generation of new noise due to enhancement. In this work a new fuzzy filter is presented for the noise reduction of images corrupted with additive noise. The filter consists of three stages. (1) Define fuzzy sets in the input space to computes a fuzzy derivative for eight different directions (2) construct a set of IFTHEN rules by to perform fuzzy smoothing according to contributions of neighboring pixel values and (3) define fuzzy sets in the output space to get the filtered and edged image. Experimental results are obtained to show the feasibility of the proposed approach with two dimensional objects.

Keywords: Additive noise, edge preserving filtering, fuzzy image filtering, noise reduction, two dimensional mechanical images.

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Authors: Tahseen A. Jilani, S. M. Aqil Burney, C. Ardil

Abstract:

In this paper, we have presented a new multivariate fuzzy time series forecasting method. This method assumes mfactors with one main factor of interest. History of past three years is used for making new forecasts. This new method is applied in forecasting total number of car accidents in Belgium using four secondary factors. We also make comparison of our proposed method with existing methods of fuzzy time series forecasting. Experimentally, it is shown that our proposed method perform better than existing fuzzy time series forecasting methods. Practically, actuaries are interested in analysis of the patterns of causalities in road accidents. Thus using fuzzy time series, actuaries can define fuzzy premium and fuzzy underwriting of car insurance and life insurance for car insurance. National Institute of Statistics, Belgium provides region of risk classification for each road. Thus using this risk classification, we can predict premium rate and underwriting of insurance policy holders.

Keywords: Average forecasting error rate (AFER), Fuzziness offuzzy sets Fuzzy, If-Then rules, Multivariate fuzzy time series.

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Authors: K.C. Deshmukh, P.G. Khot, Nikhil

Abstract:

In the literature of information theory, there is necessity for comparing the different measures of fuzzy entropy and this consequently, gives rise to the need for normalizing measures of fuzzy entropy. In this paper, we have discussed this need and hence developed some normalized measures of fuzzy entropy. It is also desirable to maximize entropy and to minimize directed divergence or distance. Keeping in mind this idea, we have explained the method of optimizing different measures of fuzzy entropy.

Keywords: Fuzzy set, Uncertainty, Fuzzy entropy, Normalization, Membership function

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Authors: Pilar Rey-del-Castillo, Jesús Cardeñosa

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There are many situations where input feature vectors are incomplete and methods to tackle the problem have been studied for a long time. A commonly used procedure is to replace each missing value with an imputation. This paper presents a method to perform categorical missing data imputation from numerical and categorical variables. The imputations are based on Simpson-s fuzzy min-max neural networks where the input variables for learning and classification are just numerical. The proposed method extends the input to categorical variables by introducing new fuzzy sets, a new operation and a new architecture. The procedure is tested and compared with others using opinion poll data.

Keywords: Classifier, imputation techniques, fuzzy systems, fuzzy min-max neural networks.

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Authors: Faisal Alshuwaier, Ali Areshey

Abstract:

Text mining techniques are generally applied for classifying the text, finding fuzzy relations and structures in data sets. This research provides plenty text mining capabilities. One common application is text classification and event extraction, which encompass deducing specific knowledge concerning incidents referred to in texts. The main contribution of this paper is the clarification of a concept graph generation mechanism, which is based on a text classification and optimal fuzzy relationship extraction. Furthermore, the work presented in this paper explains the application of fuzzy relationship extraction and branch and bound (BB) method to simplify the texts.

Keywords: Extraction, Max-Prod, Fuzzy Relations, Text Mining, Memberships, Classification.

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Authors: C.Natarajan, S.K.Ayyaswamy

Abstract:

Let G be a fuzzy graph. Then D Ôèå V is said to be a strong (weak) fuzzy dominating set of G if every vertex v ∈ V -D is strongly (weakly) dominated by some vertex u in D. We denote a strong (weak) fuzzy dominating set by sfd-set (wfd-set). The minimum scalar cardinality of a sfd-set (wfd-set) is called the strong (weak) fuzzy domination number of G and it is denoted by γsf (G)γwf (G). In this paper we introduce the concept of strong (weak) domination in fuzzy graphs and obtain some interesting results for this new parameter in fuzzy graphs.

Keywords: Fuzzy graphs, fuzzy domination, strong (weak) fuzzy domination number.

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Authors: K. A. Sumithradevi, Vijayalakshmi. M. N., Annamma Abraham., Dr. Vasanta

Abstract:

The various applications of VLSI circuits in highperformance computing, telecommunications, and consumer electronics has been expanding progressively, and at a very hasty pace. This paper describes a new model for partitioning a circuit using DBSCAN and fuzzy ARTMAP neural network. The first step is concerned with feature extraction, where we had make use DBSCAN algorithm. The second step is the classification and is composed of a fuzzy ARTMAP neural network. The performance of both approaches is compared using benchmark data provided by MCNC standard cell placement benchmark netlists. Analysis of the investigational results proved that the fuzzy ARTMAP with DBSCAN model achieves greater performance then only fuzzy ARTMAP in recognizing sub-circuits with lowest amount of interconnections between them The recognition rate using fuzzy ARTMAP with DBSCAN is 97.7% compared to only fuzzy ARTMAP.

Keywords: VLSI, Circuit partitioning, DBSCAN, fuzzyARTMAP.

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Authors: Melike Şah, Konstantin Y.Degtiarev

Abstract:

This paper proposes a novel improvement of forecasting approach based on using time-invariant fuzzy time series. In contrast to traditional forecasting methods, fuzzy time series can be also applied to problems, in which historical data are linguistic values. It is shown that proposed time-invariant method improves the performance of forecasting process. Further, the effect of using different number of fuzzy sets is tested as well. As with the most of cited papers, historical enrollment of the University of Alabama is used in this study to illustrate the forecasting process. Subsequently, the performance of the proposed method is compared with existing fuzzy time series time-invariant models based on forecasting accuracy. It reveals a certain performance superiority of the proposed method over methods described in the literature.

Keywords: Forecasting, fuzzy time series, linguistic values, student enrollment, time-invariant model.

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Authors: K. Chandrasekhara Rao, V. Swaminathan

Abstract:

The anti-homomorphic image of fuzzy ideals, fuzzy ideals of near-rings and anti ideals are discussed in this note. A necessary and sufficient condition has been established for near-ring anti ideal to be characteristic.

Keywords: Fuzzy Ideals, Anti fuzzy subgroup, Anti fuzzy ideals, Anti homomorphism, Lower α level cut.

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Authors: Arsham Borumand Saeid

Abstract:

In this note the notion of interval-valued fuzzy BG-algebras (briefly, i-v fuzzy BG-algebras), the level and strong level BG-subalgebra is introduced. Then we state and prove some theorems which determine the relationship between these notions and BG-subalgebras. The images and inverse images of i-v fuzzy BG-subalgebras are defined, and how the homomorphic images and inverse images of i-v fuzzy BG-subalgebra becomes i-v fuzzy BG-algebras are studied.

Keywords: BG-algebra, fuzzy BG-subalgebra, interval-valued fuzzy set, interval-valued fuzzy BG-subalgebra.

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Authors: Yuli Hu, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the concepts of fuzzy subalgebras, fuzzy ideals and fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras, BCI-algebras with operators, fuzzy subalgebras, fuzzy ideals, fuzzy quotient algebras.

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Authors: D.R Prince Williams

Abstract:

In this paper, we introduce the notion θ-Euclidean k-fuzzy ideal in semirings and to study the properties of the image and pre image of a θ -Euclidean k-fuzzy ideal in a semirings under epimorphism.

Keywords: semiring, fuzzy ideal, k–fuzzy ideal, θ -Euclidean Lfuzzyideal, θ -Euclidean fuzzy k–ideal, θ -Euclidean k-fuzzy ideal.

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Authors: Hassan M. Elragal

Abstract:

This paper discusses a method for improving accuracy of fuzzy-rule-based classifiers using particle swarm optimization (PSO). Two different fuzzy classifiers are considered and optimized. The first classifier is based on Mamdani fuzzy inference system (M_PSO fuzzy classifier). The second classifier is based on Takagi- Sugeno fuzzy inference system (TS_PSO fuzzy classifier). The parameters of the proposed fuzzy classifiers including premise (antecedent) parameters, consequent parameters and structure of fuzzy rules are optimized using PSO. Experimental results show that higher classification accuracy can be obtained with a lower number of fuzzy rules by using the proposed PSO fuzzy classifiers. The performances of M_PSO and TS_PSO fuzzy classifiers are compared to other fuzzy based classifiers

Keywords: Fuzzy classifier, Optimization of fuzzy systemparameters, Particle swarm optimization, Pattern classification.

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Authors: R. Uthayakumar, D. Easwaramoorthy

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The purpose of this paper is to present the fuzzy contraction properties of the Hutchinson-Barnsley operator on the fuzzy hyperspace with respect to the Hausdorff fuzzy metrics. Also we discuss about the relationships between the Hausdorff fuzzy metrics on the fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces.

Keywords: Fractals, Iterated Function System, Hutchinson- Barnsley Operator, Fuzzy Metric Space, Hausdorff Fuzzy Metric.

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Authors: Hamed Rafiei, Masoud Rabbani

Abstract:

This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.

Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.

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Authors: Praveen Boinee, Alessandro De Angelis, Gian Luca Foresti

Abstract:

Leo Breimans Random Forests (RF) is a recent development in tree based classifiers and quickly proven to be one of the most important algorithms in the machine learning literature. It has shown robust and improved results of classifications on standard data sets. Ensemble learning algorithms such as AdaBoost and Bagging have been in active research and shown improvements in classification results for several benchmarking data sets with mainly decision trees as their base classifiers. In this paper we experiment to apply these Meta learning techniques to the random forests. We experiment the working of the ensembles of random forests on the standard data sets available in UCI data sets. We compare the original random forest algorithm with their ensemble counterparts and discuss the results.

Keywords: Random Forests [RF], ensembles, UCI.

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