Linear Membership Functions Research Articles

Applying fuzzy multi-objective linear programming to a project management decision with nonlinear fuzzy membership functions

This paper investigates a multi-objective project management problem where the goals of the decision maker are fuzzy. Prior research on this topic has considered linear membership functions to model uncertain project goals. Linear membership functions, however, are not much flexible to model uncertain information of projects in many situations, and therefore, fuzzy models with linear membership functions are not suitable to be applied in many practical situations. Hence, the purpose of this paper is to apply nonlinear membership functions in order to develop a better representation of fuzzy project planning in practice. This approach supports managers in examining different solution strategies and in planning projects more realistically. In doing so, a fuzzy mathematical project planning model with exponential fuzzy goals is developed first which takes account of (a) the time between events, (b) the crashing time for activities, and (c) the available budget. Following, a weighted max---min model is applied for solving the multi-objective project management problem. The performance of the developed solution procedure is compared with the literature that applied linear membership functions to this problem, and it is shown that the model developed in this paper outperforms the existing solution.

Pedestrian movement analysis in transfer station corridor: Velocity-based and acceleration-based

In this paper, pedestrians are classified into aggressive and conservative ones by their temper. Aggressive pedestrians’ walking through crowd in transfer station corridor is analyzed. Treating pedestrians as particles, this paper uses the modified social force model (MSFM) as the building block, where forces involve self-driving force, repulsive force and friction force. The proposed model in this paper is a discrete model combining the MSFM and cellular automata (CA) model, where the updating rules of the CA are redefined with MSFM. Due to the continuity of values generated by the MSFM, we use the fuzzy logic to discretize the continuous values into cells pedestrians can move in one step. With the observation that stimulus around pedestrians influences their acceleration directly, an acceleration-based movement model is presented, compared to the generally reviewed velocity-based movement model. In the acceleration-based model, a discretized version of kinematic equation is presented based on the acceleration discretized with fuzzy logic. In real life, some pedestrians would rather keep their desired speed and this is also mimicked in this paper, which is called inertia. Compared to the simple triangular membership function, a trapezoidal membership function and a piecewise linear membership function are used to capture pedestrians’ inertia. With the trapezoidal and the piecewise linear membership function, many overlapping scenarios should be carefully handled and Dubois and Prade’s four-index method is used to completely describe the relative relationship of fuzzy quantities. Finally, a simulation is constructed to demonstrate the effect of our model.

A Fuzzy Goal Programming Approach for Channel Allocation Problem Using Linear and Non-Linear Membership Functions

A Fuzzy Goal Programming Approach for Channel Allocation Problem Using Linear and Non-Linear Membership Functions

ANFIS-based surface roughness prediction model for EDM of aluminium-based composite material

Surface roughness plays a major role in determining how an original component will interact with its environment. For getting a good surface finish, industries spent huge cost for introducing new technologies. The use of advanced engineering ceramics and composites in the aerospace and defence industries is continuous and increases day by day. Prediction of surface roughness plays a vital role in improving the surface finish in the industries. The present work deals with predicting the surface roughness (SR) of aluminium LM25 SiC 10% composite material in electrical discharge machining (EDM) using adaptive neuro-fuzzy inference system (ANFIS). The discharge voltage, discharge current, pulse on time, pulse off time, gap between tool and work piece and oil pressure are taken as the input parameters, whereas surface roughness is the output machining parameter. Design of experiment is based on Response Surface Methodology (RSM). ANFIS model has been constructed using Gaussian membership function (gaussmf) with two membership functions for each input variables and linear membership function for output. This paper uses the hybrid method for membership function parameter training. Based on the conclusion of ANFIS with hybrid method of membership function parameter training, it provides accurate results.

AN ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM FOR FORECASTING AUSTRALIA’S DOMESTIC LOW COST CARRIER PASSENGER DEMAND

This study has proposed and empirically tested two Adaptive Neuro-Fuzzy Inference System (ANFIS) models for the first time for predicting Australia‘s domestic low cost carriers‘ demand, as measured by enplaned passengers (PAX Model) and revenue passenger kilometres performed (RPKs Model). In the ANFIS, both the learning capabilities of an artificial neural network (ANN) and the reasoning capabilities of fuzzy logic are combined to provide enhanced prediction capabilities, as compared to using a single methodology. Sugeno fuzzy rules were used in the ANFIS structure and the Gaussian membership function and linear membership functions were also developed. The hybrid learning algorithm and the subtractive clustering partition method were used to generate the optimum ANFIS models. Data was normalized in order to increase the model‘s training performance. The results found that the mean absolute percentage error (MAPE) for the overall data set of the PAX and RPKs models was 1.52% and 1.17%, respectively. The highest R2-value for the PAX model was 0.9949 and 0.9953 for the RPKs model, demonstrating that the models have high predictive capabilities.

OPTIMAL OPERATION OF MULTIPURPOSE RESERVOIR FOR IRRIGATION PLANNING WITH CONJUNCTIVE USE OF SURFACE AND GROUNDWATER USING FUZZY RESOURCES

A Fuzzy Linear programming (FLP) model has been developed with the objective of maximizing the net benefits accrued from crops in a year and subjected to constraints on availability of surface water, groundwater, culturable area, and other inputs such as reservoir storages, water requirement of crops, canal capacity and reservoir continuity. It is a conjunctive use model of surface water and ground water to obtain the optimal operating policy for a multipurpose single reservoir by considering the fuzziness involved in the resources i.e. availability of surface water, groundwater and the culturable area. The linear membership function is developed to fuzzify the resources. The developed model is applied to the case study of Jayakwadi reservoir stage-I, built across the river Godavari, Maharashtra state, India. The final model is solved for the maximized degree of satisfaction (λ). The λ obtained is equal to 0.51 and corresponding values of the objective is 3438.439 million rupees.

Fuzzy optimization of linear objective function subject to max-average relational inequality constraints

An optimization problem of a linear objective function subject to a system of fuzzy relational inequalities based on max-average composition and fuzzy inequality is presented. This problem is converted to a new one with ordinary inequalities by using linear membership functions and Bellman-Zadeh decision. Then, dimension of the last problem is reduced and an algorithm is presented to generate the optimal solution of the initial optimization problem. Two numerical examples are given to illustrate the steps of the algorithm. Some aspects of sensitivity analysis of the problem is investigated.

Modified FGP approach for multi-level multi objective linear fractional programming problems

In this paper, we present a new modified method for solving multi-level multi objective linear fractional programming problems (ML-MOLFPPs) based on fuzzy goal programming (FGP) approach with some modifications in the algorithm suggested by Baky (2010) [18] which dealt with multi-level multi objective linear programming problem (ML-MOLPP). In proposed modified approach, numerator and denominator function of each objective at each level are individually transformed into fuzzy goals and their aspiration levels are determined using individual best solutions. Different linear membership functions are defined for numerator and denominator function of each objective function. Then highest degree of each of these membership goals is achieved by minimising the sum of negative deviational variables. The proposed algorithm simplifies the ML-MOLFPP by eliminating solution preferences by the decision makers at each level, thereby avoiding difficulties associate with multi-level programming problems and decision deadlock situations. The aim of this paper is to present simple and efficient technique to obtain compromise optimal solution of ML-MOLFP problems. Numerical examples are illustrated in order to support the proposed modified FGP technique.

Fuzzy decision-making approach in geometric programming for a single item EOQ model

Background and methods : Fuzzy decision-making approach is allowed in geometric programming for a single item EOQ model with dynamic ordering cost and demand-dependent unit cost. The setup cost vari es with the quantity produced/purchased and the modification of objective function with storage area in the presen ce of imprecisely estimated parameters are investigated. It incorpor ates all concepts of a fuzzy arithmetic approach, t he quantity ordered, and demand per unit compares both fuzzy geometric programming technique and other models for linear membership functions. Results and conclusions : Investigation of the properties of an optimal solu tion allows developing an algorithm whose validity is illustrated through an example problem and the results discussed. Sensitivity analysis of the optimal solution is also studied with respect to changes in different p arameter values.

Short Note on Research Findings and Results: An Innovative Fuzzy Computing for Industrial Production Planning

In the first part of this work a logistic membership function, within the non linear membership functions, has been formulated for solving IFLP (Interactive Fuzzy Linear Programming) problem as applied to industrial production system. This membership function is a modified form of the general set of S-curve membership functions. The flexibility of this membership function in applying to real world problem has been proved through an analysis [2,3].

An adaptive neuro-fuzzy inference system for modelling Australia's regional airline passenger demand

This study has proposed and empirically tested for the first time two adaptive neuro-fuzzy inference system (ANFIS) models for forecasting Australia's regional airline passenger demand, as measured by enplaned passengers (PAX model) and revenue passenger kilometres performed (RPKs model). In ANFIS, both the learning capabilities of an artificial neural network (ANN) and the reasoning capabilities of fuzzy logic are combined to provide enhanced prediction capabilities, as compared to using a single methodology. Sugeno fuzzy rules were used in the ANFIS structure and Gaussian membership function and linear membership functions were also developed. The hybrid learning algorithm and the subtractive clustering partition method were used to generate the optimum ANFIS models. Data was normalised in order to increase the model's training performance. The results found that the mean absolute percentage error (MAPE) for the out of sample testing dataset of the PAX and RPKs models was 5.40% and 6.91%, respectively.

Fuzzy goal programming applied to multi-objective programming problem with FREs as constraints

Article history: Received February 9, 2015 Received in revised format: May 12, 2015 Accepted June 12, 2015 Available online June 15 2015 This paper presents an alternate technique based on fuzzy goal programming (FGP) approach to solve multi-objective programming problem with fuzzy relational equations (FREs) as constraints. The proposed technique is more efficient and requires less computational work than that of algorithm suggested by Jain and Lachhwani (2009) [Jain, & Lachhwani (2009). Multiobjective programming problem with fuzzy relational equations. International Journal of Operations Research, 6(2), 55−63.]. In FGP formulation, objectives are transformed into the fuzzy goals using maximum and minimal solutions elements of FREs feasible solution set. A pseudo code computer algorithm is developed for computation of maximum solution of FREs. Suitable linear membership function is defined for each objective function. Then achievement of the highest membership value of each of the fuzzy goals is formulated by minimizing the sum of negative deviational variables. The aim of this paper is to present a simple and efficient solution procedure to obtain compromise optimal solution of multiobjective optimization problem with FREs as constraints. A comparative analysis is also carried out between two methodologies based on numerical examples. All rights reserved. Growing Science Ltd. 5 © 201

A Constructing Algorithm for Appropriate Piecewise Linear Membership Function based on Statistics and Information Theory

Abstract This paper proposes a constructing algorithm for an appropriate membership function to integrate the fuzzy Shannon entropy with a piecewise linear function into subjective intervals estimation by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in real-world decision making. The main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the initial mathematical programming problem efficiently using previous constructing approaches. In this paper, introducing some natural assumptions in the real-world and performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each appropriate membership value is developed.

An Interactive Algorithm to Construct an Appropriate Nonlinear Membership Function Using Information Theory and Statistical Method

Abstract This paper develops a constructing algorithm for an appropriate membership function as objectively as possible. It is important to set an appropriate membership function for real-world decision making. The main academic contribution of our proposed algorithm is to integrate a general continuous and nonlinear function with fuzzy Shannon entropy into subjective interval estimation by a heuristic method under a given probability density function based on real-world data. Two main steps of our proposed approach are to set membership values a decision maker confidently judges whether an element is included in the given set or not and to obtain other values objectively by solving a mathematical programming problem with fuzzy Shannon entropy. It is difficult to solve the problem efficiently using previous constructing approaches due to nonlinear function. In this paper, the given nonlinear membership function is approximately transformed into a piecewise linear membership function, and the appropriate values are determined. Furthermore, by introducing natural assumptions in the real-world and interactively adjusting the membership values, an algorithm to obtain the optimal condition of each appropriate membership value is developed.

A dispatching rule-based genetic algorithm for multi-objective job shop scheduling using fuzzy satisfaction levels

In this study, a dispatching rule based genetic algorithm with fuzzy satisfaction levels (FRGA) is proposed to solve the multi-objective manufacturing scheduling problem. The objective is to develop a decision making platform which appropriately handles conflicts among different performance measures in a manufacturing system. The proposed method focuses on a job shop scheduling problem with the objective of minimizing makespan, average flow time, maximal tardiness and total tardiness. Chromosome embeds the dispatching rules over the time period to help machine pick up the job from its queue. A two-level fuzzy approach evaluates each chromosome and indicates the overall satisfaction level. Various experiments are carried out to study the impact of FRGA parameters. FRGA manages to find optimal or near-optimal overall satisfaction level. Later, various tolerance levels of fuzzy linear membership functions and fuzzy operators are investigated. FRGA can quickly capture schedule(s) that highly satisfy decision makers based on decision makers’ preferences.

Prediction of Squeeze Cast Density Using Fuzzy Logic Based Approaches

AbstractIn the present work, efforts are made to develop the input-output relationships for squeeze casting process by utilizing the fuzzy logic based approaches. Casting density in Squeeze casting is expressed as function of process parameters, such as time delay before pressurizing the metal, pressure durations, squeeze pressure, pouring temperature and die temperature. It is to be noted that, Mamdani based model and Takagi and Sugeno's model have been developed to model density in squeeze casting process. Manually constructed Mamdani based fuzzy logic controller and Takagi and Sugeno's based fuzzy logic controller have been used in approach 1 and approach 2 respectively. Training of FLC is carried with the help of five hundred input-output data set generated artificially through regression equations, obtained earlier by the same authors. The performance of the developed models was tested for both the linear and non-linear membership function distributions with the help of ten test cases. Moreover, the test data was collected by conducting the experiments and not used in training of FLCs. It is interesting to note that both approaches are capable to make accurate predictions. However, the performance of approach 2 with G bell shape membership function distribution is found to outperform approach 1 and other type of membership function distributions. The findings are useful to foundry-men, since it provides information on casting density in squeeze casting process for the different combination of process parameters without conducting any experiments.

Fuzzy multi-objective procurement/production planning decision problems for recoverable manufacturing systems

In actual lot-sizing production-to-order problems for recoverable remanufacturing systems, input data or parameters are often imprecise or fuzzy. This study develops a novel fuzzy multi-objective linear programming (FMOLP) model with a piecewise linear membership function to solve integrated, procurement/production, planning decision problems with fuzzy environments and deal with multi-component, multi-vendor, multi-source and multi-machines under recoverable remanufacturing systems. The initial FMOLP model developed in this study attempts to simultaneously minimize total costs and total lead times in relation to supplier capacity, lead time, lot release, machine yield and customer demand. The proposed FMOLP model provides a systematic framework that facilitates a fuzzy decision-making process, enabling a decision maker to interactively adjust search direction during the solution procedure to obtain the preferred satisfactory solution. To test the model's adequacy, an actual implementation of several scenarios was conducted using remanufacturing production systems. The analytical results presented in this study can help decision managers better understand systematic analysis and the potential for improving cost-effectiveness and lead time in terms of recoverable remanufacturing planning.

TOPSIS approach to linear fractional bi-level MODM problem based on fuzzy goal programming

The objective of this paper is to present a technique for order preference by similarity to ideal solution (TOPSIS) algorithm to linear fractional bi-level multi-objective decision-making problem. TOPSIS is used to yield most appropriate alternative from a finite set of alternatives based upon simultaneous shortest distance from positive ideal solution (PIS) and furthest distance from negative ideal solution (NIS). In the proposed approach, first, the PIS and NIS for both levels are determined and the membership functions of distance functions from PIS and NIS of both levels are formulated. Linearization technique is used in order to transform the non-linear membership functions into equivalent linear membership functions and then normalize them. A possible relaxation on decision for both levels is considered for avoiding decision deadlock. Then fuzzy goal programming models are developed to achieve compromise solution of the problem by minimizing the negative deviational variables. Distance function is used to identify the optimal compromise solution. The paper presents a hybrid model of TOPSIS and fuzzy goal programming. An illustrative numerical example is solved to clarify the proposed approach. Finally, to demonstrate the efficiency of the proposed approach, the obtained solution is compared with the solution derived from existing methods in the literature.

Fuzzy Eoq Model for Deteriorating Items with Exponential Membership Function

In this Paper a multi item EOQ model with stock dependent demand for deteriorating items is considered in fuzzy environment. Inventory costs such as holding cost and setup cost have been represented by exponential membership function and profit, deteriorating rate and total investment constraint are represented by linear membership functions. The model has been solved by fuzzy non-linear programming (FNLP) method. Results have been presented along with those of corresponding crisp model and a sensitivity analysis.

Solving Matrix Games with I-fuzzy Payoffs: Pareto-optimal Security Strategies Approach

A recent research work of Clemente et al. [12] on Pareto-optimal security strategies (POSS) in matrix games with fuzzy payoffs is extended to I-fuzzy scenario. Besides, the membership and the non-membership functions of the I-fuzzy values for both players are obtained by employing the technique of multiobjective optimization. The presented approach provides an efficient solution to a class of I-fuzzy matrix games with piecewise linear membership and non-membership functions. This class also includes I-fuzzy matrix games with triangular and trapezoidal I-fuzzy numbers as special cases. Further, POSS approach also provides an approximate solution to I-fuzzy matrix games with payoffs as general I-fuzzy numbers.