Multiobjective Fuzzy Research Articles

MRI Segmentation based on Multiobjective Fuzzy Clustering

Brain image segmentation has a major role in medical image analysis for better interpretation of complex medical diagnosis such as tumor detection. The challenge of brain tumor detection is to detect accurately the tumor portion inside the brain image. In this work, we propose a multiobjective clustering framework to separate tumor regions from a brain image based on the neighbor nearest strategy. Applied to magnetic resonance image brain, our method provides an accurate identification of brain tumor.

An Efficacious Multi-Objective Fuzzy Linear Programming Approach for Optimal Power Flow Considering Distributed Generation

This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality.

Iterative Goal Programming Approach for Solving Multi-objective Intuitionistic Fuzzy Linear Programming Problem

This paper presents an Iterative goal programming approach for solving Multi-objective Intuitionistic Fuzzy Linear Programming Problem (MOIFLPP). The MOIFLP problem involving aspiration level and the right hand side constraints are trapezoidal intuitionistic fuzzy number (TIFN). The concept of ∝-cut of IFN is used to convert the TIFN into crisp one. A solution algorithm is proposed to solve the MOIFLPP and a numerical example is given in detail to explain the solution procedure. Furthermore, the proposed method is easy to apply in real-life situations which give more accurate solution in the sense that the objective values are sufficiently closer to the aspiration levels. Finally, a real life example is used and a compromise solution is found out to satisfy the decision maker.

A Mixed Integer Programming Model for Supplier Selection and Order Allocation Problem with Fuzzy Multiobjective

A mixed integer programming model is proposed to solve supplier selection and order allocation problem for a manufacturer. In this model, quality, delivery performance, and purchasing cost are chosen as three criteria to select suppliers and set as objectives. Inventory level, goods flow balance, service level, supply ability, and marketing demand are considered as constraints. In the proposed model, the three objectives have different weights which are given by experts. However, the experts score the weight by many subjective factors. So, the fuzzy analytic hierarchy process (FAHP) based approach is used to calculate the weighted values. In the end, a case study illustrates the advantage of weighted values solved by FAHP. And the result shows that a weighted model is more advantageous for supplier selection and order allocation.

Robust Routes for the Fuzzy Multi-objective Vehicle Routing Problem

This paper considers a multi-objective variant of vehicle routing problems, in which the customer demands are supposed to be triangular fuzzy numbers and the objective functions are also disrupted by fuzziness. However, the propagation of fuzzy demands to the objectives can affect the reliability of generated solutions. To this end, we propose a robustness approach to deal with fuzziness in the multi-objective context. The new approach tries to achieve robust routes that minimize two fuzzy-valued objectives, the total traveled distance and total tardiness time. Additionally, we suggest to refine our previously proposed algorithms for integrating robustness. An experimental study based on a Monte-Carlo simulation is finally carried out to evaluate the obtained results.

Multi-objective Fuzzy Reliability Optimization Model: A Parametric Geometric Programming Approach

This paper presents a multi-objective reliability optimization model taking system reliability and cost of a series system as objective functions. Due to the vagueness of judgements of the decision maker, the objective as well as constraint goal can involve many uncertain factor and other imprecise parameters with vague in nature in a reliability optimization model. Thus the model is formulated in fuzzy environment by considering cost coefficients and the exponential factor as triangular fuzzy number. Here, the nearest interval approximation method is applied to make the fuzzy model in crisp in nature. There are two types of parametric geometric programming technique is used to solve the proposed model. The performance of these two types of solution approach is evaluated by numerical example at the end of this paper.

An Improved Multiobjective PSO for the Scheduling Problem of Panel Block Construction

Uncertainty is common in ship construction. However, few studies have focused on scheduling problems under uncertainty in shipbuilding. This paper formulates the scheduling problem of panel block construction as a multiobjective fuzzy flow shop scheduling problem (FSSP) with a fuzzy processing time, a fuzzy due date, and the just-in-time (JIT) concept. An improved multiobjective particle swarm optimization called MOPSO-M is developed to solve the scheduling problem. MOPSO-M utilizes a ranked-order-value rule to convert the continuous position of particles into the discrete permutations of jobs, and an available mapping is employed to obtain the precedence-based permutation of the jobs. In addition, to improve the performance of MOPSO-M, archive maintenance is combined with global best position selection, and mutation and a velocity constriction mechanism are introduced into the algorithm. The feasibility and effectiveness of MOPSO-M are assessed in comparison with general MOPSO and nondominated sorting genetic algorithm-II (NSGA-II).

Comprehensive fuzzy multi-objective multi-product multi-site aggregate production planning decisions in a supply chain under uncertainty

The main focus of this paper is to develop a model considering some significant aspects of real-world supply chain production planning approved by industries. To do so, we consider a supply chain (SC) model, which contains multiple suppliers, multiple manufactures and multiple customers. This model is formulated as a fuzzy multi objective mixed-integer nonlinear programming (FMOMINLP) to address a comprehensive multi-site, multi-period and multi-product aggregate production planning (APP) problem under uncertainty. Four conflicting objectives are considered in the presented model simultaneously, which are (i) to minimize the total cost of the SC (production costs, workforce wage, hiring/firing and training costs, transportation cost, inventory holding cost, raw material purchasing cost, and shortage cost), (ii) to improve customer satisfaction, (iii) to minimize the fluctuations in the rate of changes of workforce, and (iv) to maximize the total value of purchasing in order to consider the impact of qualitative performance criteria. This model is converted to multi-objective mixed-integer linear programming (MOMILP) through three steps of the developed method and then the MOMILP model is solved by two different methods. Additionally, comparison of these two methods is presented and the results are analyzed. Finally, the efficiency of the model is investigated by a real industry SC case study.

Application of Fuzzy Multi-Objective Programming in Optimization of Crop Production Planning

Planning for the optimal use of productive resources in agricultural systems leads to the conservation in addition to the promotion of farmers’ socio-economical conditions. Being certain or precise in any decision making in agricultural planning is impossible. Fuzzy mathematical programming techniques, developed in recent decades, are the most appropriate and applicable approaches to include the uncertainty in crop planning and productive resources management. Using the multi-objective Fuzzy Goal Programming (FGP) approach, the farming system of a rural region located in the central of Iran has investigated in this study in order to identify the optimal cropping pattern and land use planning under uncertainty. For this purpose, several objectives like maximizing the area under cultivation, net return and employment opportunities and simultaneously the land, capital, monthly water and labor force requirements and availabilities, crop rotation and a crop lower bound production constraint imprecisely considered as fuzzy goals. The needed data gathered through fieldwork operations. In multi-objective programming context, as the results revealed, the constraints of the productive resources are more determinant in land allocation than the objective functions. To illustrate the precedence of the cited FGP model, the results were quantitatively compared with the existing situation and a crisp goal programming model containing the same objectives and constraints. The precedence mainly pertained to the goals of objective functions. The crop-mix in FGP pattern change achieved considerable conservation of water and capital resources and improvement of income generation of the agricultural system, with almost no variation in the cultivation area.

Fuzzy Multi Objective Linear Programming Problem with Imprecise Aspiration Level and Parameters

This paper considers the multi-objective linear programming problems with fuzzygoal for each of the objective functions and constraints. Most existing works deal withlinear membership functions for fuzzy goals. In this paper, exponential membershipfunction is used.

A decision model for cost effective design of biomass based green energy supply chains

The core driver of this study is to deal with the design of anaerobic digestion based biomass to energy supply chains in a cost effective manner. In this concern, a decision model is developed. The model is based on fuzzy multi objective decision making in order to simultaneously optimize multiple economic objectives and tackle the inherent uncertainties in the parameters and decision makers’ aspiration levels for the goals. The viability of the decision model is explored with computational experiments on a real-world biomass to energy supply chain and further analyses are performed to observe the effects of different conditions. To this aim, scenario analyses are conducted to investigate the effects of energy crop utilization and operational costs on supply chain structure and performance measures.

Pareto Optimal Filter Design for Nonlinear Stochastic Fuzzy Systems via Multiobjective <inline-formula> <tex-math>$H_{\bf 2} /H_{\bm \infty}$</tex-math></inline-formula> Optimization

This paper is concerned with the multiobjective H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering design problem in nonlinear signal processing, which can be approximated by a Takagi-Sugerno (T-S) fuzzy signal system. We propose a multiobjective filter design to estimate state variables from noisy measurements for nonlinear signal systems, and we focus our effort on achieving optimal concurrent performance for H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering. In general, it is difficult to solve the multiobjective (MO) H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy filter problem directly, and we therefore propose an indirect approach to minimize the upper bounds and transform the MO H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem in to a linear matrix inequality (LMI)-constrained multiobjective problem (MOP). In addition, we propose an LMI-based multiobjective evolution algorithm to efficiently find Pareto optimal solutions for the MOP of multiobjective fuzzy filter design for nonlinear stochastic signal processing. Furthermore, for comparison, we also suggest the MO H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter design problem based on the weighted sum method. Our proposed indirect method can be widely employed to practically address the MO filter design problem in nonlinear signal processing. Finally, a trajectory estimation of reentry vehicle by radar is provided to illustrate the design procedure of the Pareto MO optimal filter.

A Fuzzy Multiobjective Model for Supplier Selection under Considering Stochastic Demand in a Supply Chain

With the development of market competition, company faces more and more pressures. Meanwhile, procurement has a vital effect on achieving competitive advantages in a supply chain. Selecting the appropriate suppliers is one of the most important sections in purchase management. However, in real situation, supplier selection is a multiple objective problem about different items with vagueness and randomness of the data. It is very complex. Hence, research about supplier selection is relatively scarce under considering multiple items, discount price, and fuzzy and stochastic information. In our paper, we develop a fuzzy multiobjective supplier selection model for overcoming uncertainty and multiple items. Stochastic demand, fuzzy objectives, and weights are simultaneously applied to help the managers to select the suitable suppliers about different items. For illustration purpose, a numerical example is presented to verify the effectiveness of the proposed model.

Design of a Multi Objective Fuzzy- Proportional Compensator for a Power-split Hybrid Electric Vehicle

In this research the model of the Toyota Prius vehicle as a power-split Hybrid Electric Vehicle is chosen from ADVISOR and the information required about a vehicle and drive cycle are extracted from it. In order to have better energy management, a fuzzy compensator is used beside the planetary gear set, which is responsible for sharing power between energy sources. This compensator helps the planetary gear set on supplying the requested speed and torque from final drive and better sharing power between energy sources considering how the requested power instantaneous changes are. Also to provide the requested speed and torque in a better way a P controller is used. At the end, the results of implementation of this controller are compared to those of the primary model. The results show that the designed fuzzy rule based compensator is able to decrease the driving costs.

An Evolutionary Algorithm for Multiobjective Fuzzy Portfolio Selection Models with Transaction Cost and Liquidity

The major issues for mean-variance-skewness models are the errors in estimations that cause corner solutions and low diversity in the portfolio. In this paper, a multiobjective fuzzy portfolio selection model with transaction cost and liquidity is proposed to maintain the diversity of portfolio. In addition, we have designed a multiobjective evolutionary algorithm based on decomposition of the objective space to maintain the diversity of obtained solutions. The algorithm is used to obtain a set of Pareto-optimal portfolios with good diversity and convergence. To demonstrate the effectiveness of the proposed model and algorithm, the performance of the proposed algorithm is compared with the classic MOEA/D and NSGA-II through some numerical examples based on the data of the Shanghai Stock Exchange Market. Simulation results show that our proposed algorithm is able to obtain better diversity and more evenly distributed Pareto front than the other two algorithms and the proposed model can maintain quite well the diversity of portfolio. The purpose of this paper is to deal with portfolio problems in the weighted possibilistic mean-variance-skewness (MVS) and possibilistic mean-variance-skewness-entropy (MVS-E) frameworks with transaction cost and liquidity and to provide different Pareto-optimal investment strategies as diversified as possible for investors at a time, rather than one strategy for investors at a time.

Improvement of Financial Efficiency and Cost Effectiveness of Financial Institution for ‘Financial Inclusion’ in India

Finance has become an integral part of an economy. Banking institutions play a vital role in facilitating the development of financial system as well as to achieve ‘financial inclusion’ which is the prime objective of policy makers in our economy. The term ‘financial inclusion’ has gained popularity in all emerging economies especially in Indian economy after financial sector reforms. Financial inclusion has become an essential pre-requisite for achieving ‘Inclusive Growth’ in Indian economy and for accelerating economic and social life of all people. The basic financial services at affordable prices to the weaker section of the society are an essential task for policy makers in recent era. Without changing it’s main regular functions, how a financial institution can grow through applying different environmental friendly policies throughout the India is a big question? Due to the various constraints like lack of infrastructural problem, environmental problem, geographical problem, basic education and local political problem, financial institution are not able to reach the needy people in rural areas. Therefore the development of rural financial market with minimum cost and maximum benefit to the people is the prime concern of central authority to reach the mass. Keeping the alarming situation in mind it is time for India to improve the financial efficiency and cost effectiveness of financial institution through minimization of wastage and maximization of sales & profit. On the basis of this background this paper attempts to make a comprehensive study of financial institutional parameters to minimize the cost of operation and maximized profit by using Multi-objective Fuzzy Nonlinear Goal Programming. On the basis of secondary data collected from the annual report and RBI data regarding six financial institutions parameters which can use as a decision making variables for performance measurement of an institution. Regression Analysis method is used to identify the main indicator of financial performance, using SPSS (20) software and LINGO software used to study the Multi-objective Fuzzy Non-linear Goal Programming. The study found that both Internal and external parameters are responsible for doing financial institutions performance and to achieve “Inclusive Growth”. Indian financial backbone can be improved and reach global platform by using an alternative policy like reducing nonperforming assets and increase in managerial performance for customer satisfaction in all levels.

Evaluating a green supplier selection problem using a hybrid MODM algorithm

The green supplier selection (GSS) problem is a well-known strategy to outsource with respect to environmental protection. Although different applications of GSS have been proposed in the literature, the fuzzy five-objective GSS model has not been studied yet. This paper develops a multi-objective fuzzy linear programming model for a GSS problem, including 17 criteria, formed into 5 clusters while a hybrid fuzzy multi objective decision making (MODM) is employed to solve it. The aim of this paper is to select the best set of suppliers regarding optimal allocation of order quantities while demand and supplier's capacity are restricted. In the proposed hybrid solution algorithm, fuzzy decision making trial and evaluation laboratory approach is used to understand the interrelation among criteria, and fuzzy analytical network process (ANP) provides the criteria weights with respect to their dependencies. Then, a hybrid of fuzzy ANP and fuzzy multi-objective linear programming presents optimal order allocation among the selected suppliers, verified and compared with two other methods. Finally, the conclusion and future research are presented.

Multi-Objective Fuzzy Chance Constrained Fuzzy Goal Programming for Capacitated Transportation Problem

paper presents a multi-objective fuzzy chance constrained capacitated transportation problem based on fuzzy goal programming problem with capacity restrictions on commodities which are shipped from different sources to different destinations. The capacity of each origin and the demand of each destination are considered random in nature with fuzzy normal stochastic parameters following normal distribution with fuzzy mean and fuzzy variance respectively. These inequality constraints are also considered as fuzzy probabilistic in nature assuming to be triangular fuzzy numbers. Further, the supply and demand constraints are converted into equivalent deterministic forms. Then, we define the fuzzy goal tolerance limit of each of the objective functions which are then characterized by the associated membership functions. In the solution process, the fuzzy parameters are defuzzied by applying graded mean integration method which provided a satisfactory result. Further, an illustrative example is solved to demonstrate the effectiveness of the proposed model. Keywordsgoal programming, fuzzy chance constrained programming, capacitated transportation problem, multi objective decision making, graded mean integration method.

Multi-Objective Fuzzy Optimization Design of Truck Differential

Multi-objective optimization technology and Fuzzy theory were applied to design truck differential based on consideration on its force condition. The mathematical model for the multi-objective optimization design was set up under the objective of the minimum volume of the differential, maximal strength of planet gear, with the design variable of planet gear teeth number Z1, axle shaft gear teeth number Z2, section modulus ms and working width b. Then, the fuzzy solution of multi-objective optimization were use to solve the model. Practical example of calculation shows that, the fuzzy optimization result is superior to that of regular optimization and traditional design, differential volume deceased by 32.73% and 1.92% respectively. Comparing with nominal design, the load of planet gear increases 17%, but is far below its permissible value, and also reduced by 9.04% than that of regular optimization.

Multifeature fusion for polarimetric synthetic aperture radar image classification of sea ice

Sea ice conditions are so heterogeneous, and the differences between the different ice types are less varied than that of land targets, so only using polarimetric or textural features would lead to misclassification of polarimetric synthetic aperture radar (PolSAR) data of sea ice. To support the identification of different ice types, the fusion of textural and polarimetric features would be a good solution. Simple discrimination analysis is used to rationalize a preferred features subset. Some features are analyzed, which include entropy H /alpha α /anisotropy A and three kinds of texture statistics (entropy, contrast, and correlation), in the C- and L-band polarimetric mode. After that, a multiobjective fuzzy decision model is proposed for supervised PolSAR data classification of sea ice, and the targets are categorized according to the principle of maximum membership grade. In consideration of the interference of the correlation among features, the model is based on Mahalanobis distance in which the covariances between the selected heterogeneous features could restrain the interference among redundant features. In the end, the effectiveness of the algorithm for PolSAR image classification of sea ice is demonstrated through the analysis of some experimental results.