scholarly journals Research on Fuzzy Three Stage Tandem Queues

2019 ◽  
Vol 8 (6S4) ◽  
pp. 1478-1481
Keyword(s):  
Membership Function ◽  
Performance Measures ◽  
Service Time ◽  
System Performance ◽  
Arrival Time ◽  
General Procedure ◽  
Membership Functions ◽  
Tandem Queues ◽  
The Membership Function

This project intends a general procedure to obtain the membership function of the performance measures in three stage tandem queues when the inter-arrival time and service time are in fuzzy. The basic idea is to diminish the crisp queue into fuzzy by applying the α-cut approach technique. A pair of parametric program is formulated to depict that family of crisp queue in which the membership functions of the system performance are acquired.

Tollbooth tandem queues with infinite homogeneous servers

2015 ◽  
Vol 52 (4) ◽  
pp. 941-961 ◽  
Author(s):  
Xiuli Chao ◽  
Qi-Ming He ◽  
Sheldon Ross
Keyword(s):  
Performance Measures ◽  
System Performance ◽  
Stochastic Ordering ◽  
Tandem Queues ◽  
Poisson Arrival ◽  
Arrival Processes ◽  
Poisson Arrivals ◽  
Number Of Customers ◽  
Steady State Solutions ◽  
Transient And Steady State

In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before him/her have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Both transient and steady state solutions are derived first for Poisson arrivals, and then extended to cases with batch Poisson and nonstationary Poisson arrival processes. Finally, we report several stochastic ordering results on how system performance measures are affected by arrival and service processes.

scholarly journals Learning Membership Functions in a Function-Based Object Recognition System

1995 ◽  
Vol 3 ◽  
pp. 187-222 ◽  
Author(s):  
K. Woods ◽  
D. Cook ◽  
L. Hall ◽  
K. Bowyer ◽  
L. Stark
Keyword(s):  
Object Recognition ◽  
Membership Function ◽  
Learning Algorithm ◽  
Physical Property ◽  
Recognition System ◽  
Tree Structure ◽  
Membership Functions ◽  
Recognition Systems ◽  
Membership Value ◽  
The Membership Function

Functionality-based recognition systems recognize objects at the category level by reasoning about how well the objects support the expected function. Such systems naturally associate a ``measure of goodness'' or ``membership value'' with a recognized object. This measure of goodness is the result of combining individual measures, or membership values, from potentially many primitive evaluations of different properties of the object's shape. A membership function is used to compute the membership value when evaluating a primitive of a particular physical property of an object. In previous versions of a recognition system known as Gruff, the membership function for each of the primitive evaluations was hand-crafted by the system designer. In this paper, we provide a learning component for the Gruff system, called Omlet, that automatically learns membership functions given a set of example objects labeled with their desired category measure. The learning algorithm is generally applicable to any problem in which low-level membership values are combined through an and-or tree structure to give a final overall membership value.

Perishable Inventory System with Bi-Level Service System

2016 ◽  
pp. 200-217
Author(s):  
D. Gomathi
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Service Time ◽  
System Performance ◽  
Service System ◽  
Joint Probability ◽  
Inventory System ◽  
Service Time Distribution ◽  
Perishable Inventory ◽  
Perishable Inventory System

In this chapter we consider a perishable inventory system under continuous review at a bi-level service system with finite waiting hall of size N. The maximum storage capacity of the inventory is S units. We assumed that a demand for the commodity is of unit size. The arrival time points of customers form a Poisson process. The individual customer is issued a demanded item after a random service time, which is distributed as negative exponential. The effect of the two modes of operations on the system performance measures is also discussed. It is also assumed that lead time for the reorders is distributed as exponential and is independent of the service time distribution. The items are perishable in nature and the life time of each item is assumed to be exponentially distributed. The demands that occur during stock out periods are lost. The joint probability distribution of the number of customers is obtained in the steady-state case. Various system performance measures in the steady state are derived. The results are illustrated numerically.

scholarly journals A Generalized Fuzzy Integer Programming Approach for Environmental Management under Uncertainty

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Y. R. Fan ◽  
G. H. Huang ◽  
K. Huang ◽  
L. Jin ◽  
M. Q. Suo
Keyword(s):  
Integer Programming ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Mixed Integer ◽  
Programming Approach ◽  
Management Problem ◽  
Membership Functions ◽  
Interactive Algorithm ◽  
Waste Flow ◽  
The Membership Function

In this study, a generalized fuzzy integer programming (GFIP) method is developed for planning waste allocation and facility expansion under uncertainty. The developed method can (i) deal with uncertainties expressed as fuzzy sets with known membership functions regardless of the shapes (linear or nonlinear) of these membership functions, (ii) allow uncertainties to be directly communicated into the optimization process and the resulting solutions, and (iii) reflect dynamics in terms of waste-flow allocation and facility-capacity expansion. A stepwise interactive algorithm (SIA) is proposed to solve the GFIP problem and generate solutions expressed as fuzzy sets. The procedures of the SIA method include (i) discretizing the membership function grade of fuzzy parameters into a set ofα-cutlevels; (ii) converting the GFIP problem into an inexact mixed-integer linear programming (IMILP) problem under eachα-cut level; (iii) solving the IMILP problem through an interactive algorithm; and (iv) approximating the membership function for decision variables through statistical regression methods. The developed GFIP method is applied to a municipal solid waste (MSW) management problem to facilitate decision making on waste flow allocation and waste-treatment facilities expansion. The results, which are expressed as discrete or continuous fuzzy sets, can help identify desired alternatives for managing MSW under uncertainty.

scholarly journals FGA Temperature Control for Incubating Egg

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Ismail Yusuf ◽  
Yusram Yusuf ◽  
Nur Iksan
Keyword(s):  
Membership Function ◽  
Selection Process ◽  
Exact Result ◽  
Membership Functions ◽  
Trial And Error ◽  
Fuzzy Logic Controllers ◽  
Design And Implementation ◽  
Human Operators ◽  
Function Selection ◽  
The Membership Function

This paper investigates the use of genetic algorithms (GA) in the design and implementation of fuzzy logic controllers (FLC) for incubating egg. What is the best to determine the membership function is the first question that has been tackled. Thus it is important to select the accurate membership functions, but these methods possess one common weakness where conventional FLC use membership function generated by human operators. The membership function selection process is done with trial and error, and it runs step by step which takes too long in solving the problem. This paper develops a system that may help users to determine the membership function of FLC using the GA optimization for the fastest processing in solving the problems. The data collection is based on the simulation results, and the results refer to the transient response specification which is maximum overshoot. From the results presented, we will get a better and exact result; the value of overshot is decreasing from 1.2800 for FLC without GA to 1.0081 with GA (FGA).

A MATHEMATICAL PROGRAMMING APPROACH TO FUZZY TANDEM QUEUES

2005 ◽  
Vol 13 (04) ◽  
pp. 425-436 ◽  
Author(s):  
SHIH-PIN CHEN
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Programming Approach ◽  
Extension Principle ◽  
Queueing Models ◽  
Membership Functions ◽  
Tandem Queues ◽  
Mathematical Programs ◽  
Mathematical Programming Approach

Tandem queueing models play an important role in many real world systems such as computer systems, production lines, and service systems. This paper proposes a procedure to construct the membership functions of the performance measures in tandem queueing systems, in that the arrival rate and service rates are fuzzy numbers. The basic idea is to transform a fuzzy tandem queue to a family of crisp tandem queues by applying the α -cut approach. Then on the basis of α -cut representation and the extension principle, a pair of mathematical programs is formulated to describe this family of crisp tandem queues, via which the membership functions of the performance measures are derived. Two numerical examples are solved successfully to demonstrate the validity of the proposed approach. Since the performance measures are expressed by membership functions rather than by crisp values, the fuzziness of input information is completely conserved. Thus the proposed approach for fuzzy systems can represent the system more accurately, and more information is provided for designing queueing systems. The successful extension of tandem queues to fuzzy environments permits tandem queueing models to have wider applications.

A METHOD FOR FINDING CRITICAL PATH WITH SYMMETRIC OCTAGONAL INTUITIONISTIC FUZZY NUMBERS

2020 ◽  
Vol 9 (11) ◽  
pp. 9273-9286
Author(s):  
N. Rameshan ◽  
D.S. Dinagar
Keyword(s):  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Membership Functions ◽  
Intuitionistic Fuzzy Number ◽  
Lower And Upper Bounds ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Membership Function

The concept of this paper represents finding fuzzy critical path using octagonal fuzzy number. In project scheduling, a new method has been approached to identify the critical path by using Symmetric Octagonal Intuitionistic Fuzzy Number (SYMOCINTFN). For getting a better solution, we use the fuzzy octagonal number rather than other fuzzy numbers. The membership functions of the earliest and latest times of events are by calculating lower and upper bounds of the earliest and latest times considering octagonal fuzzy duration. The resulting conditions omit the negative and infeasible solution. The membership function takes up an essential role in finding a new solution. Based on membership function, fuzzy number can be identified in different categories such as Triangular, Trapezoidal, pentagonal, hexagonal, octagonal, decagonal, hexa decagonal fuzzy numbers etc.

scholarly journals Approximation of real data by fuzzy sets for the classification problem

2019 ◽  
pp. 22-26
Author(s):  
Kostiantyn Sukhanov
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Real Data ◽  
Training Data ◽  
Learning Object ◽  
Membership Functions ◽  
One Dimensional ◽  
Set Membership ◽  
The Membership Function

The article deals with the method of classification of real data using the apparatus of fuzzy sets and fuzzy logic as a flexible tool for learning and recognition of natural objects on the example of oil and gas prospecting sections of the Dnieper-Donetsk basin. The real data in this approach are the values for the membership function that are obtained not through subjective expert judgment but from objective measurements. It is suggested to approximate the fuzzy set membership functions by using training data to use the approximation results obtained during the learning phase at the stage of identifying unknown objects. In the first step of learning, each traditional future of a learning data is matched by a primary traditional one-dimensional set whose membership function can only take values from a binary set — 0 if the learning object does not belong to the set, and 1 if the learning object belongs to the set. In the second step, the primary set is mapped to a fuzzy set, and the parameters of the membership function of this fuzzy set are determined by approximating this function of the traditional set membership. In the third step, the set of one-dimensional fuzzy sets that correspond to a single feature of the object is mapped to a fuzzy set that corresponds to all the features of the object in the training data set. Such a set is the intersection of fuzzy sets of individual features, to which the blurring and concentration operations of fuzzy set theory are applied in the last step. Thus, the function of belonging to a fuzzy set of a class is the operation of choosing a minimum value from the functions of fuzzy sets of individual features of objects, which are reduced to a certain degree corresponding to the operation of blurring or concentration. The task of assigning the object under study to a particular class is to compare the values of the membership functions of a multidimensional fuzzy set and to select the class in which the membership function takes the highest value. Additionally, after the training stage, it is possible to determine the degree of significance of an object future, which is an indistinctness index, to remove non-essential data (object futures) from the analysis.

scholarly journals A Reliability-Based Multisensor Data Fusion with Application in Target Classification

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2192
Author(s):  
Gabriel Awogbami ◽  
Abdollah Homaifar
Keyword(s):  
Data Fusion ◽  
Membership Function ◽  
Fuzzy Membership ◽  
Membership Functions ◽  
Target Classification ◽  
Decision Accuracy ◽  
Multisensor Data Fusion ◽  
Fuzzy Membership Functions ◽  
Multisensor Data ◽  
The Membership Function

The theory of belief functions has been extensively utilized in many practical applications involving decision making. One such application is the classification of target based on the pieces of information extracted from the individual attributes describing the target. Each piece of information is usually modeled as the basic probability assignment (BPA), also known as the mass function. The determination of the BPA has remained an open problem. Although fuzzy membership functions such as triangular and Gaussian functions have been widely used to model the likelihood estimation function based on the historical data, it has been observed that less emphasis has been placed on the impact of the spread of the membership function on the decision accuracy of the reasoning process. Conflict in the combination of BPAs may arise due to poor characterization of fuzzy membership functions to induce belief mass. In this work, we propose a multisensor data fusion within the framework of belief theory for target classification where shape/spread of the membership function is adjusted during the training/modeling stage to improve on the classification accuracy while removing the need for the computation of the credibility. To further enhance the performance of the proposed method, the reliability factor is deployed not only to effectively manage the possible conflict among participating bodies of evidence for better decision accuracy but also to reduce the number of sources for improved efficiency. The effectiveness of the proposed method was evaluated using both the real-world and the artificial datasets.

Tollbooth tandem queues with infinite homogeneous servers

2015 ◽  
Vol 52 (04) ◽  
pp. 941-961 ◽  
Author(s):  
Xiuli Chao ◽  
Qi-Ming He ◽  
Sheldon Ross
Keyword(s):  
Performance Measures ◽  
System Performance ◽  
Stochastic Ordering ◽  
Tandem Queues ◽  
Poisson Arrival ◽  
Arrival Processes ◽  
Poisson Arrivals ◽  
Number Of Customers ◽  
Steady State Solutions ◽  
Transient And Steady State

In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before him/her have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Both transient and steady state solutions are derived first for Poisson arrivals, and then extended to cases with batch Poisson and nonstationary Poisson arrival processes. Finally, we report several stochastic ordering results on how system performance measures are affected by arrival and service processes.

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