A PRACTICAL FUZZY DIGRAPH MODEL FOR MODELING MANUFACTURING FLEXIBILITY

There are many approaches in the literature to model and quantify manufacturing flexibility. Most of these models were developed to quantify several aspects of manufacturing flexibility like machine flexibility, routing flexibility, mix flexibility, volume flexibility, etc. This is mainly due to the fact that developing a generic model, which can be used to measure different types of flexibilities, is not straightforward. Recently, a generic flexibility measure, which is based on digraphs and permanent index, was proposed by the author. The main difficulty with that model like in all other flexibility models is the inability to collect precise data for computing the flexibility. In order to overcome this difficulty, a practical fuzzy linguistic approach is incorporated into the previous digraph model in this article. The extended fuzzy digraph model is explained in detail through an example in the present article.     

Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models

Two-sided assembly lines are especially used at the assembly of large-sized products, such as trucks and buses. In this type of a production line, both sides of the line are used in parallel. In practice, it may be necessary to optimize more than one conflicting objectives simultaneously to obtain effective and realistic solutions. This paper presents a mathematical model, a pre-emptive goal programming model for precise goals and a fuzzy goal programming model for imprecise goals for two-sided assembly line balancing. The mathematical model minimizes the number of mated-stations as the primary objective and it minimizes the number of stations as a secondary objective for a given cycle time. The zoning constraints are also considered in this model, and a set of test problems taken from literature is solved. The proposed goal programming models are the first multiple-criteria decision-making approaches for two-sided assembly line balancing problem with multiple objectives. The number of mated-stations, cycle time and the number of tasks assigned per station are considered as goals. An example problem is solved and a computational study is conducted to illustrate the flexibility and the efficiency of the proposed goal programming models. Based on the decision maker's preferences, the proposed models are capable of improving the value of goals.     

多变量系统的软测量建模研究

研究加氢裂化分馏塔多个产品的质量指标同时预报的一类ＭＩＭＯ软测量建模问题,采用ＲＢＦ网络和Ｆｕｚｚｙ ＡＲＴＭＡＰ网络对该ＭＩＭＯ系统进行建模,并用ＲＢＦ网络建立了每个输出的独立的ＭＩＳＯ软测量模型。应用实例表明,所研究的软测量建模为多变量系统软件测量的工业应用提供了一种有效实用的方法。     

Fuzzy decision making of profit function in production planning using S-curve membership function

Any modern industrial manufacturing unit inevitably faces problems of vagueness in various aspects such as raw material availability, human resource availability, processing capability and constraints and limitations imposed by marketing department. Such a complex problem of vagueness and uncertainty can be handled by the theory of fuzzy linear programming. In this paper, a new fuzzy linear programming based methodology using a modified S-curve membership function is used to solve fuzzy mix product selection problem in Industrial Engineering. Profits and satisfactory level have been computed using fuzzy programming approach. Since there are several decisions to be taken, a performance measure has been defined to identify the decision for high level of profit with high degree of satisfaction.     

A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems

A novel distance measure between two intuitionistic fuzzy sets (IFSs) is proposed in this paper. The introduced measure formulates the information of each set in matrix structure, where matrix norms in conjunction with fuzzy implications can be applied to measure the distance between the IFSs. The advantage of this novel distance measure is its flexibility, which permits different fuzzy implications to be incorporated by extending its applicability to several applications where the most appropriate implication is used. Moreover, the proposed distance might be expressed equivalently by using either intuitionistic fuzzy sets or interval‐valued fuzzy sets. Appropriate experimental configurations have taken place to compare the proposed distance measure with similar distance measures from the literature, by applying them to several pattern recognition problems. The results are very promising because the performance of the new distance measure outperforms the corresponding performance of well‐known IFSs measures, by recognizing the patterns correctly and with high degree of confidence. © 2012 Wiley Periodicals, Inc.     

Fuzzy programming for mixed-integer optimization problems

Mixed-integer optimization problems belong to the group of NP-hard combinatorial problems. Therefore, they are difficult to search for global optimal solutions. Mixed-integer optimization problems are always described by precise mathematical programming models. However, many practical mixed-integer optimization problems have inherited a more or less imprecise nature. Under these circumstances, if we take into account the flexibility of the constraints and the fuzziness of the objectives, the original mixed-integer optimization problems can be formulated as fuzzy mixed-integer optimization problems. Mixed-integer hybrid differential evolution (MIHDE) is an evolutionary search algorithm which has been successfully applied to many complex mixed-integer optimization problems. In this article, a fuzzy mixed-integer mathematical programming model is developed to formulate the fuzzy mixed-integer optimization problem. In addition the MIHDE is introduced to solve the fuzzy mixed-integer programming problem. Finally, the illustrative example shows that satisfactory results can be obtained by the proposed method. This demonstrates that MIHDE can effectively handle fuzzy mixed-integer optimization problems.     

A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers

In the literature, several algorithms are proposed for solving the transportation problems in fuzzy environment but in all the proposed algorithms the parameters are represented by normal fuzzy numbers. Chen [Operations on fuzzy numbers with function principal, Tamkang Journal of Management Science 6 (1985) 13-25] pointed out that in many cases it is not to possible to restrict the membership function to the normal form and proposed the concept of generalized fuzzy numbers. There are several papers in the literature in which generalized fuzzy numbers are used for solving real life problems but to the best of our knowledge, till now no one has used generalized fuzzy numbers for solving the transportation problems. In this paper, a new algorithm is proposed for solving a special type of fuzzy transportation problems by assuming that a decision maker is uncertain about the precise values of transportation cost only but there is no uncertainty about the supply and demand of the product. In the proposed algorithm transportation costs are represented by generalized trapezoidal fuzzy numbers. To illustrate the proposed algorithm a numerical example is solved and the obtained results are compared with the results of existing approaches. Since the proposed approach is a direct extension of classical approach so the proposed approach is very easy to understand and to apply on real life transportation problems for the decision makers.     

Fuzzy knowledge representation study for incremental learning in data streams and classification problems

The extraction of models from data streams has become a hot topic in data mining due to the proliferation of problems in which data are made available online. This has led to the design of several systems that create data models online. A novel approach to online learning of data streams can be found in Fuzzy-UCS, a young Michigan-style fuzzy-classifier system that has recently demonstrated to be highly competitive in extracting classification models from complex domains. Despite the promising results reported for Fuzzy-UCS, there still remain some hot issues that need to be analyzed in detail. This paper carefully studies two key aspects in Fuzzy-UCS: the ability of the system to learn models from data streams where concepts change over time and the behavior of different fuzzy representations. Four fuzzy representations that move through the dimensions of flexibility and interpretability are included in the system. The behavior of the different representations on a problem with concept changes is studied and compared to other machine learning techniques prepared to deal with these types of problems. Thereafter, the comparison is extended to a large collection of real-world problems, and a close examination of which problem characteristics benefit or affect the different representations is conducted. The overall results show that Fuzzy-UCS can effectively deal with problems with concept changes and lead to different interesting conclusions on the particular behavior of each representation.     

基于模糊回归的质量屋决策模型

基于带有对称三角形模糊系数的模糊回归及模糊规划理论，提出关联函数及自 相关函数的数学模型，并在系统考虑资源约束影响的基础上，分别建立了基于质量屋的产品 规划精确模型及模糊模型．仿真研究表明，这些模型适合于各种工程设计问题，尤其是在不 确定的、模糊的条件下，能够有效地确定关联函数及自相关函数，帮助开发人员优化顾客需 求的满意水平，在资源约束下使产品的顾客满意度最大．     

Method for solving unbalanced fully fuzzy multi-objective solid minimal cost flow problems

In fuzzy single and multi-objective minimal cost flow (MCF) problems, it is assumed that there is only one conveyance which can be used for transporting the product. However, in real life problems, more than one conveyance is used for transporting the product. To the best of our knowledge untill now no method is proposed in the literature for solving such fuzzy single and multi-objective MCF problems in which more than one conveyance is used for transporting the product and all the parameters, as well as all the decision variables that are represented by fuzzy numbers. In this paper, these types of fuzzy multi-objective MCF problems are called fully fuzzy multi-objective solid minimal cost flow (SMCF) problems and a new method is proposed for solving these problems. The advantages of the proposed methods are also discussed.     

Optimization of fuzzy partitions for inductive reasoning using genetic algorithms

Fuzzy Inductive Reasoning (FIR) is a data-driven methodology that uses fuzzy and pattern recognition techniques to infer system models and to predict their future behavior. It is well known that variations on fuzzy partitions have a direct effect on the performance of the fuzzy-rule-based systems. The FIR methodology is not an exception. The performance of the model identification and prediction processes of FIR is highly influenced by the discretization parameters of the system variables, i.e. the number of classes of each variable and the membership functions that define its semantics. In this work, we design two new genetic fuzzy systems (GFSs) that improve this modeling and simulation technique. The main goal of the GFSs is to learn the fuzzification parameters of the FIR methodology. The new approaches are applied to two real modeling problems, the human central nervous system and an electrical distribution problem.     

Fuzzy optimization of units products in mix-product selection problem using fuzzy linear programming approach

In this paper, the modified S-curve membership function methodology is used in a real life industrial problem of mix product selection. This problem occurs in the production planning management where by a decision maker plays important role in making decision in an uncertain environment. As analysts, we try to find a good enough solution for the decision maker to make a final decision. An industrial application of fuzzy linear programming (FLP) through the S-curve membership function has been investigated using a set of real life data collected from a Chocolate Manufacturing Company. The problem of fuzzy product mix selection has been defined. The objective of this paper is to find an optimal units of products with higher level of satisfaction with vagueness as a key factor. Since there are several decisions that were to be taken, a table for optimal units of products respect to vagueness and degree of satisfaction has been defined to identify the solution with higher level of units of products and with a higher degree of satisfaction. The fuzzy outcome shows that higher units of products need not lead to higher degree of satisfaction. The findings of this work indicates that the optimal decision is depend on vagueness factor in the fuzzy system of mix product selection problem. Further more the high level of units of products obtained when the vagueness is low.     

Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations

The priority method on the intuitionistic fuzzy preference relation (IFPR) is proposed. In order to avoid the operational difficulty in dealing with the intuitionistic sets, the equivalent interval matrices of the IFPR are introduced. Based on the multiplicative consistent definition of the fuzzy interval preference relation (FIPR), the goal programming models for deriving the priority vector of the IFPR have been put forward by analyzing the relation between the IFNPR and the IFPR. This goal programming method is generalized to the case of group decision making with the weight information defined by each DM. Two numerical examples are provided to illustrate the application of the proposed models.     

Product mix strategy and manufacturing flexibility

The manufacturing industry is facing a turbulent and constantly changing environment, with growing complexity and high levels of customisation. Any investment solution should address these problems for a dynamic market and within limited budget boundaries, so that companies try to remain competitive. The authors propose a real options model to support firms making important investment decisions, specifically decisions associated with the acquisition of new equipment aimed at allowing firms to increase their manufacturing flexibility for the production of both standard and customized products. This paper is partially based on a real operating experience related to visual finishing technology features in an industrial company that conforms to the definitions of the product mix. The authors’ motivation for this work is driven by firms’ desire to satisfy specific customer needs, and to respond to them quickly under uncertain demand. Our goal, using theories from finance, production management, and product offering management, is to conclude that there is a relevant difference between the evaluation of the technology that is to be chosen, and the potential value due to product mix adaptations that are able to provide the maximum return from investment. We address problems related to standard and customized production systems, and the decision to invest in a set of resources that will enable this choice.     

PROJECT TEAM SELECTION USING FUZZY OPTIMIZATION APPROACH

With their high potential, high motivation, great problem-solving ability and flexibility, project teams are important work structures for the business life. The success of these teams is highly dependent upon the people involved in the project team. This makes the project team selection an important factor for project success. The project team selection can be defined as selecting the right team members, which will together perform a particular project/task within a given deadline. In this article, an analytical model for the project team selection problem is proposed by considering several human and nonhuman factors. Because of the imprecise nature of the problem, fuzzy concepts like triangular fuzzy numbers and linguistic variables are used. The proposed model is a fuzzy multiple objective optimization model with fuzzy objectives and crisp constraints. The skill suitability of each team candidate is reflected to the model by suitability values. These values are obtained by using the fuzzy ratings method. The suitability values of the candidates and the size of the each project team are modeled as fuzzy objectives. The proposed algorithm takes into account the time and the budget limitations of each project and interpersonal relations between the team candidates. These issues are modeled as hard-crisp constraints. The proposed model uses fuzzy objectives and crisp constraints to select the most suitable team members to form the best possible team for a given project. A simulated annealing algorithm is developed to solve the proposed fuzzy optimization model. Software based on C + + computer programming language is also developed to experiment on the proposed model in forming project teams.     

A new approach of Romero’s extended lexicographic goal programming: fuzzy extended lexicographic goal programming

Goal programming (GP) is perhaps one of the most widely used approaches in the field of multicriteria decision making. The major advantage of the GP model is its great flexibility which enables the decision maker to easily incorporate numerous variations on constraints and goals. Romero provides a general structure, extended lexicographic goal programming (ELGP) for GP and some multiobjective programming approaches. In this work, we propose the extension of this unifying framework to fuzzy multiobjective programming. Our extension is carried out by several methodologies developed by the authors in the fuzzy GP approach. An interval GP model has been constructed where the feasible set has been defined by means of a relationship between fuzzy numbers. We will apply this model to our fuzzy extended lexicographic goal programming (FELGP). The FELGP is a general primary structure with the same advantages as Romero’s ELGP and moreover it has the capacity of working with imprecise information. An example is given in order to illustrate the proposed method.     

Designing cellular manufacturing systems under dynamic and uncertain conditions

The paper proposes a fuzzy programming based approach to design a cellular manufacturing system under dynamic and uncertain conditions. The dynamic condition indicates a multi-period planning horizon, in which the product mix and demand in each period can be different. As a result, the best cells designed for one period may not be efficient cells for subsequent periods and some of reconfigurations are required. Uncertain condition implicates to the imprecise nature of the part demand and also the availability of the manufacturing facilities in each period planning. An extended mixed-integer programming model of dynamic cellular manufacturing system, in which some of the coefficients in objective function and constraints are fuzzy quantities, is solved by a developed fuzzy programming based approach. The objective is to determine the optimal cell configuration in each period with maximum satisfaction degree of the fuzzy objective and constraint. To illustrate the behavior of the proposed model and verify the performance of the developed approach, a number of numerical examples are solved and the associated computational results are reported.     

Self-organizing fuzzy aggregation models to rank the objects withmultiple attributes

In this paper, a kind of ranking system, called agent-clients evaluation system, is proposed and investigated where there is no such authority with the right to predetermine weights of attributes of the entities evaluated by multiple evaluators for obtaining an aggregated evaluation result from the given fuzzy multiattribute values of these entities. Three models are proposed to evaluate the entities in such a system based on fuzzy inequality relation, possibility, and necessity measures, respectively. In these models, firstly the weights of attributes are automatically sought by fuzzy linear programming (FLP) problems based on the concept of data envelopment analysis (DEA) to make a summing-up assessment from each evaluator. Secondly, the weights for representing each evaluator's credibility are obtained by FLP to make an integrated evaluation of entities from the viewpoints of all evaluators. Lastly, a partially ordered set on a one-dimensional space is obtained so that all entities can be ranked easily. Because the weights of attributes and evaluators are obtained by DEA-based FLP problems, the proposed ranking models can be regarded as fair-competition and self-organizing ones so that the inherent feature of evaluation data can be reflected objectively     

Combining seasonal ARIMA models with computational intelligence techniques for time series forecasting

Seasonal autoregressive integrated moving average (SARIMA) models form one of the most popular and widely used seasonal time series models over the past three decades. However, in several researches it has been argued that they have two basic limitations that detract from their popularity for seasonal time series forecasting tasks. SARIMA models assume that future values of a time series have a linear relationship with current and past values as well as with white noise; therefore, approximations by SARIMA models may not be adequate for complex nonlinear problems. In addition, SARIMA models require a large amount of historical data to produce desired results. However, in real situations, due to uncertainty resulting from the integral environment and rapid development of new technology, future situations must be forecasted using small data sets over a short span of time. Using hybrid models or combining several models has become a common practice to overcome the limitations of single models and improve forecasting accuracy. In this paper, a new hybrid model, which combines the seasonal autoregressive integrated moving average (SARIMA) and computational intelligence techniques such as artificial neural networks and fuzzy models for seasonal time series forecasting is proposed. In the proposed model, these two techniques are applied to simultaneously overcome the linear and data limitations of SARIMA models and yield more accurate results. Empirical results of forecasting two well-known seasonal time series data sets indicate that the proposed model exhibits effectively improved forecasting accuracy, so that it can be used as an appropriate seasonal time series model.