Search results for: fuzzy analytic hierarchy process

Authors: C. Ardil

Abstract:

The decision to select an unmanned combat aircraft is complicated since several options and conflicting criteria must be considered at simultaneously. When making multiple criteria decision, it is important to consider the selected evaluation criteria, including priceability, payloadability, stealthability, speedability , and survivability. The fundamental goal of the study is to select the best unmanned combat aircraft by taking these evaluation criteria into account. The optimal aircraft was chosen using the fuzzy proximity measure method, which enables decision-makers to designate preferences as standard fuzzy set numbers during the multiple criteria decision-making process. To assess the applicability of the proposed approach, a numerical example is provided. Finally, by comparing determined unmanned combat aircraft, the proposed method produced a successful application, and the best aircraft was selected.

Keywords: standard fuzzy sets (SFS), unmanned combat aircraft selection, multiple criteria decision making (MCDM), multiple criteria group decision making (MCGDM), proximity measure method (PMM)

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Authors: R. Karbalaei, A. Ghaffari, R. Kazemi, S. H. Tabatabaei

Abstract:

An integrated vehicle dynamics control system is developed in this paper by a combination of active front steering (AFS) and direct yaw-moment control (DYC) based on fuzzy logic control. The control system has a hierarchical structure consisting of two layers. A fuzzy logic controller is used in the upper layer (yaw rate controller) to keep the yaw rate in its desired value. The yaw rate error and its rate of change are applied to the upper controlling layer as inputs, where the direct yaw moment control signal and the steering angle correction of the front wheels are the outputs. In the lower layer (fuzzy integrator), a fuzzy logic controller is designed based on the working region of the lateral tire forces. Depending on the directions of the lateral forces at the front wheels, a switching function is activated to adjust the scaling factor of the fuzzy logic controller. Using a nonlinear seven degrees of freedom vehicle model, the simulation results illustrate considerable improvements which are achieved in vehicle handling through the integrated AFS/DYC control system in comparison with the individual AFS or DYC controllers.

Keywords: Intelligent strategy, integrated control, fuzzy logic, AFS/DYC.

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Authors: R. Tur, A. Yardımcı

Abstract:

Imperfect knowledge cannot be avoided all the time. Imperfections may have several forms; uncertainties, imprecision and incompleteness. When we look to classification of methods for the management of imperfect knowledge we see fuzzy set-based techniques. The choice of a method to process data is linked to the choice of knowledge representation, which can be numerical, symbolic, logical or semantic and it depends on the nature of the problem to be solved for example decision support, which will be mentioned in our study. Fuzzy Logic is used for its ability to manage imprecise knowledge, but it can take advantage of the ability of neural networks to learn coefficients or functions. Such an association of methods is typical of so-called soft computing. In this study a new method was used for the management of imprecision for collected knowledge which related to economic analysis of construction industry in Turkey. Because of sudden changes occurring in economic factors decrease competition strength of construction companies. The better evaluation of these changes in economical factors in view of construction industry will made positive influence on company-s decisions which are dealing construction.

Keywords: Fuzzy logic, decision support systems, construction industry.

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Authors: Zeynep Sener, Mehtap Dursun

Abstract:

Supplier evaluation and selection is one of the most important components of an effective supply chain management system. Due to the expanding competition in healthcare, selecting the right medical device suppliers offers great potential for increasing quality while decreasing costs. This paper proposes a fuzzy decision making approach for medical supplier selection. A real-world medical device supplier selection problem is presented to illustrate the application of the proposed decision methodology.

Keywords: Fuzzy decision making, fuzzy multiple objective programming, medical supply chain, supplier selection.

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Authors: Arati Siddharth Petkar, Joel E. M. Macwan

Abstract:

Preferences for residential location are of a diverse nature. Primarily they are based on the socio-economic, socio-cultural, socio-demographic characteristics of the household. It also depends on character, and the growth potential of different areas in a city. In the present study, various criteria affecting residential location preferences from the Urban Dwellers’ perspective have been analyzed. The household survey has been conducted in two parts: Existing Buyers’ survey and Future Buyers’ survey. The analysis reveals that workplace location is the most governing criterion in deciding residential location from the majority of the urban dwellers perspective. For analyzing the importance of varied criteria, Analytical Hierarchy Process approach has been explored. The suggested approach will be helpful for urban planners, decision makers and developers, while designating a new residential area or redeveloping an existing one.

Keywords: Analytical hierarchy process, household, preferences, residential location preferences, residential land use, urban dwellers.

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Authors: Y. Harold Robinson, E. Golden Julie

Abstract:

Dynamic Routing in Wireless Sensor Networks (WSNs) has played a significant task in research for the recent years. Energy consumption and data delivery in time are the major parameters with the usage of sensor nodes that are significant criteria for these networks. The location of sensor nodes must not be prearranged. Clustering in WSN is a key methodology which is used to enlarge the life-time of a sensor network. It consists of numerous real-time applications. The features of WSNs are minimized the consumption of energy. Soft computing techniques can be included to accomplish improved performance. This paper surveys the modern trends in routing enclose fuzzy logic and Neuro-fuzzy logic based on the clustering techniques and implements a comparative study of the numerous related methodologies.

Keywords: Wireless sensor networks, clustering, fuzzy logic, neuro-fuzzy logic, energy efficiency.

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Authors: Madhukar Nagare, Pankaj Dutta

Abstract:

Inventory decisional environment of short life-cycle products is full of uncertainties arising from randomness and fuzziness of input parameters like customer demand requiring modeling under hybrid uncertainty. Prior inventory models incorporating fuzzy demand have unfortunately ignored stochastic variation of demand. This paper determines an unambiguous optimal order quantity from a set of n fuzzy observations in a newsvendor inventory setting in presence of fuzzy random variable demand capturing both fuzzy perception and randomness of customer demand. The stress of this paper is in providing solution procedure that attains optimality in two steps with demand information availability in linguistic phrases leading to fuzziness along with stochastic variation. The first step of solution procedure identifies and prefers one best fuzzy opinion out of all expert opinions and the second step determines optimal order quantity from the selected event that maximizes profit. The model and solution procedure is illustrated with a numerical example.

Keywords: Fuzzy expected value, Fuzzy random demand, Hybrid uncertainty, Optimal order quantity, Single-period inventory

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Authors: N.Subramanian, C.Murugesan

Abstract:

This paper is devoted to the study of the general properties of Orlicz space of entire sequence of fuzzy numbers by using infinite matrices.

Keywords: Fuzzy numbers, infinite matrix, Orlicz space, entiresequence.

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Authors: Chao Wang, Yongkun Li

Abstract:

In this paper, the discrete-time fuzzy BAM neural network with delays and impulses is studied. Sufficient conditions are obtained for the existence and global stability of a unique equilibrium of this class of fuzzy BAM neural networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. Some numerical examples are given to demonstrate the effectiveness of the obtained results.

Keywords: Discrete-time fuzzy BAM neural networks, ımpulses, global exponential stability, global asymptotical stability, equilibrium point.

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Authors: Shiuh-Jer Huang, Ming-Tien Su

Abstract:

Since the driving speed and control accuracy of commercial optical disk are increasing significantly, it needs an efficient controller to monitor the track seeking and following operations of the servo system for achieving the desired data extracting response. The nonlinear behaviors of the actuator and servo system of the optical disk drive will influence the laser spot positioning. Here, the model-free fuzzy control scheme is employed to design the track seeking servo controller for a d.c. motor driving optical disk drive system. In addition, the sliding model control strategy is introduced into the fuzzy control structure to construct a 1-D adaptive fuzzy rule intelligent controller for simplifying the implementation problem and improving the control performance. The experimental results show that the steady state error of the track seeking by using this fuzzy controller can maintain within the track width (1.6 μm ). It can be used in the track seeking and track following servo control operations.

Keywords: Fuzzy control, gain tuning and optical disk drive.

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao

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In this paper, by employing a new Lyapunov functional and an elementary inequality analysis technique, some sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solution for fuzzy bi-directional memory (BAM) neural networks with time-varying delays, and all other solutions of the fuzzy BAM neural networks converge the uniqueness periodic solution. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.

Keywords: Fuzzy BAM neural networks, Periodic solution, Global exponential stability, Time-varying delays

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Authors: Mohanad Alata , Moh'd Al-Nimr, Rami Al-Jarrah

Abstract:

The present work demonstrates the design and simulation of a fuzzy control of an air conditioning system at different pressures. The first order Sugeno fuzzy inference system is utilized to model the system and create the controller. In addition, an estimation of the heat transfer rate and water mass flow rate injection into or withdraw from the air conditioning system is determined by the fuzzy IF-THEN rules. The approach starts by generating the input/output data. Then, the subtractive clustering algorithm along with least square estimation (LSE) generates the fuzzy rules that describe the relationship between input/output data. The fuzzy rules are tuned by Adaptive Neuro-Fuzzy Inference System (ANFIS). The results show that when the pressure increases the amount of water flow rate and heat transfer rate decrease within the lower ranges of inlet dry bulb temperatures. On the other hand, and as pressure increases the amount of water flow rate and heat transfer rate increases within the higher ranges of inlet dry bulb temperatures. The inflection in the pressure effect trend occurs at lower temperatures as the inlet air humidity increases.

Keywords: Air Conditioning, ANFIS, Fuzzy Control, Sugeno System.

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Authors: T. P. Lu, B. N. Hwang, T. Z. Liou, Y. L. Lin

Abstract:

Developing a supply chain management (SCM) system is costly, but important. However, because of its complicated nature, not many of such projects are considered successful. Few research publications directly relate to key success factors (KSFs) for implementing a SCM system. Motivated by the above, this research proposes a hierarchy of KSFs for SCM system implementation in the semiconductor industry by using a two-step approach. First, the literature review indicates the initial hierarchy. The second step includes a focus group approach to finalize the proposed KSF hierarchy by extracting valuable experiences from executives and managers that actively participated in a project, which successfully establish a seamless SCM integration between the world's largest semiconductor foundry manufacturing company and the world's largest assembly and testing company. Future project executives may refer the resulting KSF hierarchy as a checklist for SCM system implementation in semiconductor or related industries.

Keywords: Focus group, key success factors, supply chain management, semiconductor industry.

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Authors: A. V. Sai Balasubramanian, N. Ravi Shankar, S. Subbaraman, R. Rengaraj

Abstract:

One of the major cause of eye strain and other problems caused while watching television is the relative illumination between the screen and its surrounding. This can be overcome by adjusting the brightness of the screen with respect to the surrounding light. A controller based on fuzzy logic is proposed in this paper. The fuzzy controller takes in the intensity of light surrounding the screen and the present brightness of the screen as input. The output of the fuzzy controller is the grid voltage corresponding to the required brightness. This voltage is given to CRT and brightness is controller dynamically. For the given test system data, different de-fuzzifier methods have been implemented and the results are compared. In order to validate the effectiveness of the proposed approach, a fuzzy controller has been designed by obtaining a test data from a real time system. The simulations are performed in MATLAB and are verified with standard system data. The proposed approach can be implemented for real time applications.

Keywords: Fuzzy controller, Grid voltage

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Authors: Masoud Sadeghian, Alireza Fatehi

Abstract:

In this paper, we use nonlinear system identification method to predict and detect process fault of a cement rotary kiln. After selecting proper inputs and output, an input-output model is identified for the plant. To identify the various operation points in the kiln, Locally Linear Neuro-Fuzzy (LLNF) model is used. This model is trained by LOLIMOT algorithm which is an incremental treestructure algorithm. Then, by using this method, we obtained 3 distinct models for the normal and faulty situations in the kiln. One of the models is for normal condition of the kiln with 15 minutes prediction horizon. The other two models are for the two faulty situations in the kiln with 7 minutes prediction horizon are presented. At the end, we detect these faults in validation data. The data collected from White Saveh Cement Company is used for in this study.

Keywords: Cement Rotary Kiln, Fault Detection, Delay Estimation Method, Locally Linear Neuro Fuzzy Model, LOLIMOT.

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Authors: S. Massoum, A. Bentaallah, A. Massoum, F. Benaimeche, P. Wira, A. Meroufel

Abstract:

This paper presents a speed fuzzy sliding mode controller for a vector controlled induction machine (IM) fed by a voltage source inverter (PWM). The sliding mode based fuzzy control method is developed to achieve fast response, a best disturbance rejection and to maintain a good decoupling. The problem with sliding mode control is that there is high frequency switching around the sliding mode surface. The FSMC is the combination of the robustness of Sliding Mode Control (SMC) and the smoothness of Fuzzy Logic (FL). To reduce the torque fluctuations (chattering), the sign function used in the conventional SMC is substituted with a fuzzy logic algorithm. The proposed algorithm was simulated by Matlab/Simulink software and simulation results show that the performance of the control scheme is robust and the chattering problem is solved.

Keywords: IM, FOC, FLC, SMC, and FSMC.

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Authors: Mustafa Resa Becan

Abstract:

Sliding mode control with a fuzzy boundary layer is presented to hydraulic position control problem in this paper. A nonlinear hydraulic servomechanism which has an asymmetric cylinder is modeled and simulated first, then the proposed control scheme is applied to this model versus the conventional sliding mode control. Simulation results proved that the chattering free position control is achieved by tuning the fuzzy scaling factors properly.

Keywords: Hydraulic servomechanism, position control, sliding mode control, chattering, fuzzy boundary layer.

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Authors: C. Ardil

Abstract:

The selection of an Unmanned Aerial Vehicle (UAV) involves complex decision-making due to the evaluation of numerous alternatives and criteria simultaneously. This process necessitates the consideration of various factors such as payload capacity, maximum speed, endurance, altitude, avionics systems, price, economic life, and maximum range. This study aims to determine the most suitable UAV by taking these criteria into account. To achieve this, the standard fuzzy set methodology is employed, enabling decision-makers to define linguistic terms as references. A practical numerical example is provided to demonstrate the applicability of the proposed approach. Through a successful application, a comparison of different UAVs is conducted, culminating in the selection of the most appropriate vehicle during the final stage.

Keywords: Standard fuzzy sets (SFSs), Unmanned Aerial Vehicle (UAV) selection, multiple criteria decision making, MCDM

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Authors: Yi Liu, Yang Xu

Abstract:

Applying the idea of soft set theory to lattice implication algebras, the novel concept of (implicative) filteristic soft lattice implication algebras which related to (implicative) filter(for short, (IF-)F-soft lattice implication algebras) are introduced. Basic properties of (IF-)F-soft lattice implication algebras are derived. Two kinds of fuzzy filters (i.e.(2, 2 _qk)((2, 2 _ qk))-fuzzy (implicative) filter) of L are introduced, which are generalizations of fuzzy (implicative) filters. Some characterizations for a soft set to be a (IF-)F-soft lattice implication algebra are provided. Analogously, this idea can be used in other types of filteristic lattice implication algebras (such as fantastic (positive implicative) filteristic soft lattice implication algebras).

Keywords: Soft set, (implicative) filteristic lattice implication algebras, fuzzy (implicative) filters, ((2, 2 _qk)) (2, 2 _ qk)-fuzzy(implicative) filters.

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Authors: Mehrdad N. Khajavi, Vahid Abdollahi

Abstract:

The purpose of suspension system in automobiles is to improve the ride comfort and road handling. In this research the ride and handling performance of a specific automobile with passive suspension system is compared to a proposed fuzzy logic semi active suspension system designed for that automobile. The bodysuspension- wheel system is modeled as a two degree of freedom quarter car model. MATLAB/SIMULINK [1] was used for simulation and controller design. The fuzzy logic controller is based on two inputs namely suspension velocity and body velocity. The output of the fuzzy controller is the damping coefficient of the variable damper. The result shows improvement over passive suspension method.

Keywords: Suspension System, Ride Comfort, Fuzzy Logic Controller, Passive and Semi Active System.

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Authors: Jianfeng Li, Feng Jin, Xiaoyu Yang

Abstract:

This paper applies fuzzy clustering algorithm in classifying real estate companies in China according to some general financial indexes, such as income per share, share accumulation fund, net profit margins, weighted net assets yield and shareholders' equity. By constructing and normalizing initial partition matrix, getting fuzzy similar matrix with Minkowski metric and gaining the transitive closure, the dynamic fuzzy clustering analysis for real estate companies is shown clearly that different clustered result change gradually with the threshold reducing, and then, it-s shown there is the similar relationship with the prices of those companies in stock market. In this way, it-s great valuable in contrasting the real estate companies- financial condition in order to grasp some good chances of investment, and so on.

Keywords: Fuzzy clustering algorithm, data mining, real estate company, financial analysis.

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Authors: Rozilawati Binti Dollah, Masaki Aono

Abstract:

Classifying biomedical literature is a difficult and challenging task, especially when a large number of biomedical articles should be organized into a hierarchical structure. In this paper, we present an approach for classifying a collection of biomedical text abstracts downloaded from Medline database with the help of ontology alignment. To accomplish our goal, we construct two types of hierarchies, the OHSUMED disease hierarchy and the Medline abstract disease hierarchies from the OHSUMED dataset and the Medline abstracts, respectively. Then, we enrich the OHSUMED disease hierarchy before adapting it to ontology alignment process for finding probable concepts or categories. Subsequently, we compute the cosine similarity between the vector in probable concepts (in the “enriched" OHSUMED disease hierarchy) and the vector in Medline abstract disease hierarchies. Finally, we assign category to the new Medline abstracts based on the similarity score. The results obtained from the experiments show the performance of our proposed approach for hierarchical classification is slightly better than the performance of the multi-class flat classification.

Keywords: Biomedical literature, hierarchical text classification, ontology alignment, text mining.

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Authors: Elif Alaybeyoğlu, Y. Esra Albayrak

Abstract:

Marketing establishes a communication network between producers and consumers. Nowadays, marketing approach is customer-focused and products are directly oriented to meet customer needs. Marketing, which is a long process, needs organization and management. Therefore strategic marketing planning becomes more and more important in today’s competitive conditions. Main focus of this paper is to evaluate pricing strategies and select the best pricing strategy solution while considering internal and external factors influencing the company’s pricing decisions associated with new product development. To reflect the decision maker’s subjective preference information and to determine the weight vector of factors (attributes), the fuzzy linear programming technique for multidimensional analysis of preference (LINMAP) under intuitionistic fuzzy (IF) environments is used.

Keywords: IF Sets, LINMAP, MAGDM, Marketing.

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Authors: Ömer Faruk Baykoç, Ümit Sami Sakalli

Abstract:

In this paper, we propose a fuzzy aggregate production planning (APP) model for blending problem in a brass factory which is the problem of computing optimal amounts of raw materials for the total production of several types of brass in a period. The model has deterministic and imprecise parameters which follows triangular possibility distributions. The brass casting APP model can not always be solved by using common approaches used in the literature. Therefore a mathematical model is presented for solving this problem. In the proposed model, the Lai and Hwang-s fuzzy ranking concept is relaxed by using one constraint instead of three constraints. An application of the brass casting APP model in a brass factory shows that the proposed model successfully solves the multi-blend problem in casting process and determines the optimal raw material purchasing policies.

Keywords: Aggregate production planning, Blending, brasscasting, possibilistic programming.

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Authors: C. Ardil

Abstract:

This paper investigates the application of the determinate fuzzy preference programming method for a more nuanced and comprehensive evaluation of stealth aircraft. Traditional methods often struggle to incorporate subjective factors and uncertainties inherent in complex systems like stealth aircraft. Determinate fuzzy preference programming addresses this limitation by leveraging the strengths of determinate fuzzy sets. The proposed novel multiple criteria decision-making algorithm integrates these concepts to consider aspects and criteria influencing aircraft performance. This approach aims to provide a more holistic assessment by enabling decision-makers to observe positive and negative outranking flows simultaneously. By demonstrating the validity and effectiveness of this approach through a practical example of selecting a stealth aircraft, this paper aims to establish the determinate fuzzy preference programming method as a valuable tool for informed decision-making in this critical domain.

Keywords: Determinate fuzzy set, stealth aircraft selection, distance function, decision making, uncertainty, preference programming. MCDM

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Authors: Taghreed Abu-Salim

Abstract:

This paper develops and investigates a framework for the assessment of customer involvement in the service design process of result oriented product-service systems in order to improve the service offering in a business-to-business (B2B) context. The framework comprises five main criteria and fifteen sub-criteria that contribute to customer involvement in a hierarchy using a maturity grid to highlight the strengths and weaknesses for each criterion. To develop the customer involvement framework, an extensive literature review related to service design, result oriented product-service system (PSS) and customer involvement in service design was carried out. Key factors that significantly influence customer involvement from industry and literature were identified to develop the framework. A major contribution of the developed framework includes a hierarchy of appropriate criteria for assessing customer involvement in the service design process within results oriented PSS; the definition of four maturity levels which are suitable to describe the whole spectrum of customer involvement in the service design process; and finally, The paper concludes by enabling service providers to: take proactive decisions; screen and evaluate new services; improve perceived service quality; and provide barriers against imitation.

Keywords: Customer involvement, maturity grid, new service development, result oriented product-service system, service design.

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Authors: Mohsen Pirdashti, Masoomeh Omidi, Hemmatollah Pidashti

Abstract:

Today, advantage of biotechnology especially in environmental issues compared to other technologies is irrefragable. Kimia Gharb Gostar Industries Company, as a largest producer of citric acid in Middle East, applies biotechnology for this goal. Citrogypsum is a by–product of citric acid production and it considered as a valid residuum of this company. At this paper summary of acid citric production and condition of Citrogypsum production in company were introduced in addition to defmition of Citrogypsum production and its applications in world. According to these information and evaluation of present conditions about Iran needing to Citrogypsum, the best priority was introduced and emphasized on strategy selection and proper programming for self-sufficiency. The Delphi technique was used to elicit expert opinions about criteria for evaluating the usages. The criteria identified by the experts were profitability, capacity of production, the degree of investment, marketable, production ease and time production. The Analytical Hierarchy Process (ARP) and Expert Choice software were used to compare the alternatives on the criteria derived from the Delphi process.

Keywords: Analytical Hierarchy Process, ARP, Delphi, Multi- criteria decision making, Citrogypsum

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Authors: Joseph C. Chen, Venkata Mohan Kudapa

Abstract:

Development of two real-time surface roughness (Ra) prediction systems for milling operations was attempted. The systems used not only cutting parameters, such as feed rate and spindle speed, but also the cutting current generated and corrected by a clamp type energy sensor. Two different approaches were developed. First, a fuzzy inference system (FIS), in which the fuzzy logic rules are generated by experts in the milling processes, was used to conduct prediction modeling using current cutting data. Second, a neuro-fuzzy system (ANFIS) was explored. Neuro-fuzzy systems are adaptive techniques in which data are collected on the network, processed, and rules are generated by the system. The inference system then uses these rules to predict Ra as the output. Experimental results showed that the parameters of spindle speed, feed rate, depth of cut, and input current variation could predict Ra. These two systems enable the prediction of Ra during the milling operation with an average of 91.83% and 94.48% accuracy by FIS and ANFIS systems, respectively. Statistically, the ANFIS system provided better prediction accuracy than that of the FIS system.

Keywords: Surface roughness, input current, fuzzy logic, neuro-fuzzy, milling operations.

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Authors: Vassilis S. Kodogiannis, John N. Lygouras

Abstract:

In this research study, an intelligent detection system to support medical diagnosis and detection of abnormal lesions by processing endoscopic images is presented. The images used in this study have been obtained using the M2A Swallowable Imaging Capsule - a patented, video color-imaging disposable capsule. Schemes have been developed to extract texture features from the fuzzy texture spectra in the chromatic and achromatic domains for a selected region of interest from each color component histogram of endoscopic images. The implementation of an advanced fuzzy inference neural network which combines fuzzy systems and artificial neural networks and the concept of fusion of multiple classifiers dedicated to specific feature parameters have been also adopted in this paper. The achieved high detection accuracy of the proposed system has provided thus an indication that such intelligent schemes could be used as a supplementary diagnostic tool in endoscopy.

Keywords: Medical imaging, Computer aided diagnosis, Endoscopy, Neuro-fuzzy networks, Fuzzy integral.

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Authors: C. Ardil

Abstract:

This article presents a new approach to uncertainty, vagueness, and imprecision analysis for ranking alternatives with fuzzy data for decision making using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). In the proposed approach, fuzzy decision information related to the aircraft selection problem is taken into account in ranking the alternatives and selecting the best one. The basic procedural step is to transform the fuzzy decision matrices into matrices of alternatives evaluated according to all decision criteria. A numerical example illustrates the proposed approach for the military combat aircraft selection problem.

Keywords: trapezoidal fuzzy numbers, multiple criteria decision making analysis, decision making, aircraft selection, MCDMA, fuzzy TOPSIS

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