Fuzzy Applications in Industrial Engineering

A rational approach toward decision-making should take into account human subjectivity, rather than employing only objective probability measures. This attitude towards the uncertainty of human behavior led to the study of a relatively new decision analysis field: Fuzzy decision-making. Fuzzy systems are suitable for uncertain or approximate reasoning, especially for the system with a mathematical model that is difficult to derive. Fuzzy logic allows decision-making with estimated values under incomplete or uncertain information. A major contribution of fuzzy set theory is its capability of representing vague data. Fuzzy set theory has been used to model systems that are hard to define precisely. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into the model formulation and solution process. Fuzzy set theory represents an attractive tool to aid research in industrial engineering (IE) when the dynamics of the decision environment limit the specification of model objectives, constraints and the precise measurement of model parameters. This chapter provides a survey of the applications of fuzzy set theory in IE.

Even the first control chart was proposed during the 1920’s by Shewhart, today they are still subject to new application areas that deserve further attention. If the quality-related characteristics cannot be represented in numerical form, such as characteristics for appearance, softness, color, etc., then control charts for attributes are used. Except for the special cases, fuzzy control charts are used for attributes control charts such as p or c charts. The theory of classical control charts requires all the data to be exactly known. The major contribution of fuzzy set theory is its capability of representing vague data. Fuzzy logic offers a systematic base in dealing with situations, which are ambiguous or not well defined. Fuzzy control charts based on the fuzzy transformation methods are reviewed and a design for the control charts in the case of vague data using fuzzy sets as real valued interpretations of uncertainty and vagueness is proposed.

Heating, Ventilating and Air Conditioning (HVAC) Systems are equipments usually implemented for maintaining satisfactory comfort conditions in buildings. The design of Fuzzy Logic Controllers (FLCs) for HVAC Systems is usually based on the operator’s experience. However, an initial rule set drawn from the expert’s experience sometimes fail to obtain satisfactory results, since inefficient or redundant rules are usually found in the final Rule Base. Moreover, in our case, the system being controlled is too complex and an optimal controller behavior is required.

Boolean network theory, proposed by Stuart A. Kauffman about 3 decades ago, is more general than the cellular automata theory of von Neumann. This theory has many potential applications, and one especially significant application is in the modeling of genetic networking behavior. In order to understand the genomic regulations of a living cell, one must investigate the chaotic phenomena of some simple Boolean networks.

Safety regulations for nuclear reactor control are very strict, which makes it difficult to implement new control techniques. One such technique could be fuzzy logic control (FLC), which can provide very desirable advantages over classical control, like robustness, adaptation and the capability to include human experience into the controller. Simple fuzzy logic controllers have been implemented for a few nuclear research reactors, among which the Massachusetts Institute of Technology (MIT) research reactor [1] in 1988 and the first Belgian reactor (BR1) [2] in 1998, though only on a temporal basis.

In an uncertain economic decision environment, an expert’s knowledge about dicounting cash flows consists of a lot of vagueness instead of randomness. Cash amounts and interest rates are usually estimated by using educated guesses based on expected values or other statistical techniques to obtain them. Fuzzy numbers can capture the difficulties in estimating these parameters. In this chapter, the formulas for the analyses of fuzzy present value, fuzzy equivalent uniform annual value, fuzzy future value, fuzzy benefit-cost ratio, and fuzzy payback period are developed and some numeric examples are given. Then the examined cash flows are expanded to geometric and trigonometric cash flows and using these cash flows fuzzy present value, fuzzy future value, and fuzzy annual value formulas are developed for both discrete compounding and continuous compounding. Finally, a fuzzy versus stochastic investment analysis is examined by using the probability of a fuzzy event.

Capital budgeting is based on the analysis of some financial parameters of considered investment projects. It is clear that estimation of investment efficiency, as well as any forecasting, is rather an uncertain problem. In a case of stock investment one can to some extent predict future profits using stock history and statistical methods, but only in a short time horizon. In the capital investment one usually deals with a business-plan which takes a long time — as a rule, some years — for its realization. In such cases, a description of uncertainty within a framework of traditional probability methods usually is impossible due to the absence of objective information about probabilities of future events. This is a reason for the growing for the last two decades interest in applications of interval and fuzzy methods in budgeting. In this paper a technique for fuzzy-interval evaluation of financial parameters is presented. The results of technique application in a form of fuzzy-interval and weighted non-fuzzy values for main financial parameters NPV and IRR as well as the quantitative estimation of risk of an investment are presented.Another problem is that one usually must consider a set of different local criteria based on financial parameters of investments. As its possible solution, a numerical method for optimization of future cash-flows based on the generalized project’s quality criterion in a form of compromise between local criteria of profit maximisation and financial risk minimisation is proposed.

A mathematical model for European/American options with uncertainty is presented. The uncertainty is represented by both randomness and fuzziness. The randomness and fuzziness are evaluated respectively by probabilistic expectation and fuzzy expectation defined by a possibility measure from the viewpoint of decision-maker’s subjective judgment. Prices of European call/put options with uncertainty are presented, and their valuation and properties are discussed under a reasonable assumption. The hedging strategies are also considered for marketability of the European options in portfolio selection. Further, the American options model with uncertainty is discussed by a numerical approach and is compared with the analytical case of the infinite terminal time. The buyer’s/seller’s rational range of the optimal expected price in each option is presented and the meaning and properties of the optimal expected prices are discussed.

The explosion in the use of Internet has contributed to arise a lot of web sites that offer many kind of services (products, information, etc). At the beginning the quality of these web sites was not too important because the most important fact was that people knew that there was a web site because there was not a big competence. But recently, there are many web sites related to the same topics in Internet and the quality of their services has become a critical factor. Different evaluation approaches for different types of web sites have been developing [2, 22, 35] in which the users provide their opinions in a predefined numerical scale to evaluate their services. Nevertheless, the information provided by users is related to their own perceptions. Usually, human perceptions are subjective and not objective, therefore to assess perceptions with precise information is not very suitable and the results are not accurate. Therefore, in this chapter we propose a linguistic quality evaluation model to evaluate the services offered by the web sites. The use of the fuzzy linguistic approach has provided good results managing human perceptions. Our proposal will consist of a hierarchical model to evaluate the services offered by general purpose web sites, such that, it will choose a few quality dimensions to be evaluated, where each one has different criteria. The users will provide their knowledge about these criteria by means of linguistic assessments. But different users can have different knowledge about the web site’s criteria, so the evaluation model should take into account this point. Therefore, our model will be defined in a multi-granular linguistic information context, such that, different users can express their opinions in different linguistic term sets according to their knowledge. In order to develop this evaluation model we shall use different tools and resolution schemes based on decision techniques that are able to deal with multi-granular linguistic information.

In many industrial engineering problems, we must select a design, select parameters of a process, or, in general, make a decision. Informally, this decision must be optimal, the best for the users. In traditional operations research, we assume that we know the objective function f(x) whose values describe the consequence of a decision x for the user. Optimization of well-defined functions is what started calculus in the first place: once we know the objective function f(x), we can use differentiation to find its maximum, e.g., as the point x at which the derivative of f with respect to x is equal to 0.

Even if the given data are crisp, there exists uncertainty in decision making process and inconsistency based on human judgements. The purpose of this paper is to obtain the evaluations which reflect such an uncertainty and inconsistency of the given information. Based on the idea that intervals are more suitable than crisp values to represent evaluations in uncertain situations, we introduce this interval analysis concept into two well-known decision making models, DEA and AHP. In the conventional DEA, the relative efficiency values are measured and in the proposed interval DEA, the efficiency values are defined as intervals considering various viewpoints of evaluations. In the conventional AHP, the priority weights of alternatives are obtained and in the proposed interval AHP, the priority weights are also defined as intervals reflecting the inconsistency among the given judgements.

A general form of a collective choice rule in group decision making under fuzzy preferences and a fuzzy majority is proposed. It encompasses some well-known choice rules. Our point of departure is the fuzzy majority based linguistic aggregation rule (solution concept) proposed by Kacprzyk [11–13]. This rule is viewed here from a more general perspective, and the fuzzy majority – meant as a fuzzy linguistic quantifier – is dealt with by using Yager’s [42] OWA operators. The particular collective choice rules derived via the general scheme proposed are shown to be applicable in the case of nonfuzzy preferences too. Moreover, a relation to Zadeh’s concept of a protoform is mentioned in this context.

Electromyographic signals and spinal forces in trunk muscles during lifting motion can be used to describe the dynamics of muscular activities. Yet spinal forces can not be measured directly, and EMG signals are often difficult to measure in industry due to environmental hostilities. EMG waves, however, can be treated and analyzed as responses of a system that takes kinematics measurements and other auxiliary factors as inputs. By establishing the kinematics-EMG-force relationship using neural and fuzzy approaches, we propose models for EMG and spinal force estimation. Key variables affecting EMG and forces in lifting tasks are identified using fuzzy average with fuzzy cluster distribution method. An EMG signal estimation model with a novel structure of feedforward neural network is then built. And the spinal forces are estimated by a recurrent fuzzy neural network model. The proposed neural and fuzzy approaches can prune the input variables and estimate EMG and forces effectively.

The intelligent human-machine interaction domain is huge and rich in concepts, methods, models and tools. Fuzzy logic can be exploited for designing current approaches contributing to intelligent interfaces. As an illustration, this chapter describes the development of a intelligent human-machine interface which is tolerant of human error during the control of a simple industrial process. Human- error-tolerant interfaces (HETI) should be applied to industrial processes in order to keep the human operators sufficiently vigilant to enable them to handle unexpected events. With this goal, a global architecture is proposed; it integrates a human operator model (concerned with possible human actions and potential errors). For the design of this model, preliminary human behaviours and errors during the control of a simulated process have been analysed. This enables to devise general rules, to be used when programming such an interface, using fuzzy logic. The Human-error-tolerant interface design and evaluation are described.

The ease allowance is an important criterion in garment sales. It is often taken into account in the process of construction of garment patterns. However, the existing pattern generation methods can not provide a suitable estimation of ease allowance, which is strongly related to wearer’s body shapes and movements and used fabrics. They can only produce 2D patterns for a fixed standard value of ease allowance. In this chapter, we propose a new method of estimating ease allowance of a garment using fuzzy logic and sensory evaluation. Based on these values of ease allowance, we develop a new method of automatic pattern generation, permitting to improve the wearer’s fitting perception of a garment. The effectiveness of our method has been validated in the design of trousers of jean type. It can also be applied for designing other types of garment.

This chapter is on scope and problems of manufacturing management (MM), contexts and uncertainty in MM, intelligent approaches in project management, inventory management, and production logistics. The other subject included is intelligent production planning and control.

Job shop scheduling (JSS) problem is NP-hard in its simplest case and we generally need to add new constraints when we want to solve a JSS in any practical application area. Therefore, as its complexity increases we need algorithms that can solve the problem in a reasonable time period and can be modified easily for new constraints. In the literature, there are many metaheuristic methods to solve JSS problem. In this chapter, the proposed Ant algorithm can solve JSS problems in reasonable time and it is very easy to modify the artificial ants for new constraints. In addition, it is very easy to modify artificial ants for multiobjective cases.

A distributed and a supervisory scheduling architecture for manufacturing systems and their realization in MATLAB are presented. The distributed architecture uses a set of lower level fuzzy control modules that reduce Work-In- Process (WIP) and synchronize the production system’s operation. The production rate in each stage is controlled so as to satisfy demand, avoid overloading and eliminate machine starvation or blocking. Performance tuning of the distributed controllers has been assigned to a supervisory control architecture. The scheduling objective is to keep the WIP as low as possible maintaining, at the same time, quality of service by keeping backlog into acceptable levels. It is also shown, in this chapter, how MATLAB’s SIMULINK may be used to construct effective production systems simulators. SIMULINK has become very popular in academia and industry and provides a number of powerfull tools, that is almost impossible to find in a dedicated tool for discrete event systems simulation.

Traditional methods for modelling and defining Management Information System (MIS) decision-making tasks, have tended to centre around a systems science view of the world. This is largely in terms of modelling the individual, group, organisation, or system in relation to process and environmental boundaries. Whilst such approaches are excellent for citing the situational context of such decision-making tasks, this and other orthodox Operational Research (OR) techniques do not necessarily highlight or show those causal interdependencies which are dependent upon vague or ill-defined, ambiguous information. Fuzzy Logic, at its core, provides the researcher (be they academic or practitioner) with a multitude of techniques for handling uncertainty in this respect. As such, this article discusses and outlines the development of the application of Fuzzy Cognitive Mapping (FCM) to the MIS decision-making task of Information Systems Evaluation (ISE), in terms of the on-going research interests of the authors. Through defining the nature of ISE, the authors present two models of such investment appraisal techniques, and through the generation and simulation of their respective FCMs, provide further insight into this MIS decision making task. Finally the chapter concludes by discussing and analysing the development of this fuzzy technique as a valuable OR tool.

This paper makes a deeper study of a multi-thread based cooperative strategy, previously proposed by us, to solve combinatorial optimization problems. In this strategy, each thread stands for a different optimization algorithm (or the same one with different settings) and they are all controlled by a coordinator. Both, the solvers threads and the coordinator thread have been modeled by soft computing techniques. We evaluate the performance of the strategy according to the number of threads using instances of the knapsack problem.

A fuzzy optimization problem arising in some import-export companies in the south of Spain is presented. In Fuzzy Optimization is desirable that fuzzy solutions can be really attained because then the decision maker will be able of making a decision “a posteriori” according to the current decision environment. In this way, no more runs of the optimization technique are needed when decision environment changes or when decision maker requires check out several decisions in order to establish the more appropriates. Multi-objective optimization can obtain the solution of a fuzzy optimization problem, since capturing the Pareto front we are able composing the solution fuzzy. Multi-objective Evolutionary algorithms have been shown in the last few years as powerful techniques to solve multi-objective optimization problems because they can search for multiple Pareto solutions in a single run of the algorithm. In this contribution we first introduce a multi-objective approach for nonlinear constrained optimization problems with fuzzy costs, and then an “ad hoc” multi-objective evolutionary algorithm to solve the former problem. A case-study of a fuzzy optimization problem is analyzed and the proposed solutions from the evolutionary algorithm here considered are shown.

Performance of a faculty is vital both for students and school, and must be measured and evaluated for positive reinforcement to faculty. Faculty performance evaluation problem is a difficult and sensitive issue which has quantitative and qualitative aspects, complexity and imprecision. In literature many different approaches are proposed in order to evaluate faculty performance. To deal with imprecision and vagueness of evaluation measures, fuzzy multi-attribute evaluation techniques can be used. In this paper, a comprehensive hierarchical evaluation model with many main and sub-attributes is constructed and a new algorithm for fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) that enables taking into account the hierarchy in the evaluation model is proposed. The obtained results from this new fuzzy TOPSIS approach are compared with fuzzy Analytic Hierarchy Process (AHP) on an application in an engineering department of a university and some sensitivity analyses are presented.

In recent years, association rules from large databases have received considerable attention and have been applied to various areas such as marketing, retail and finance, et al. While conventional approaches usually deal with databases with binary values, this chapter introduces an approach to discovering association rules from quantitative datasets. To remedy possible boundary problems due to sharp partitioning and to represent linguistic knowledge, fuzzy logic is used to “discretize” quantitative domains. A method of finding fuzzy sets for each quantitative attribute by using clustering is proposed based on different overlapping degrees. This proposed method is then applied to two real datasets housing and credit.

Fuzzy regression is a fuzzy variation of classical regression analysis. It has beenstudied and applied to various areas. Two types of fuzzy regression models are Tanaka’s linear programming approach and the fuzzy least-squares approach. In this chapter, a wide literature review including both theoretical and application papers on fuzzy regression has been given. Fuzzy regression models for nonfuzzy input/nonfuzzy output, nonfuzzy input/fuzzy output, and possibilistic regression model have been summarized. An illustrative example has been given. Fuzzy hypothesis testing for the coefficients of a linear regression function has been explained with two numerical examples.