Fuzzy set theory applications in production management research: a literature survey
01 Jan 1998-Journal of Intelligent Manufacturing (Kluwer Academic Publishers)-Vol. 9, Iss: 1, pp 39-56
TL;DR: This paper provides a survey of the application of fuzzy set theory in production management research, and identifies selected bibliographies on fuzzy sets and applications.
Abstract: 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 production management when the dynamics of the production environment limit the specification of model objectives, constraints and the precise measurement of model parameters. This paper provides a survey of the application of fuzzy set theory in production management research. The literature review that we compiled consists of 73 journal articles and nine books. A classification scheme for fuzzy applications in production management research is defined. We also identify selected bibliographies on fuzzy sets and applications.
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TL;DR: An overview of some fuzzy set-based approaches to scheduling is proposed,phasizing two distinct uses of fuzzy sets: representing preference profiles and modelling uncertainty distributions, and a possibility-theoretic counterpart of PERT.
303 citations
Cites background from "Fuzzy set theory applications in pr..."
...An abundant bibliography on fuzzy set applications in production management is supplied in Guiffrida and Nagi (1998)....
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TL;DR: This work presents a fuzzy TOPSIS model under group decisions for solving the facility location selection problem, where the ratings of various alternative locations under different subjective attributes and the importance weights of all attributes are assessed in linguistic values represented by fuzzy numbers.
Abstract: This work presents a fuzzy TOPSIS model under group decisions for solving the facility location selection problem, where the ratings of various alternative locations under different subjective attributes and the importance weights of all attributes are assessed in linguistic values represented by fuzzy numbers. The objective attributes are transformed into dimensionless indices to ensure compatibility with the linguistic ratings of the subjective attributes. Furthermore, the membership function of the aggregation of the ratings and weights for each alternative location versus each attribute can be developed by interval arithmetic and α -cuts of fuzzy numbers. The ranking method of the mean of the integral values is applied to help derive the ideal and negative-ideal fuzzy solutions to complete the proposed fuzzy TOPSIS model. Finally, a numerical example demonstrates the computational process of the proposed model.
290 citations
TL;DR: The current body of research that has extended the Salameh and Jaber (2000) EOQ model for imperfect items, and the impact of human error on production and inventory systems is summarized.
223 citations
TL;DR: A new fuzzy mathematical programming model for production planning under uncertainty in an industrial environment that considers fuzzy constraints related to the total costs, the market demand and the available capacity and fuzzy coefficients for the costs due to the backlog of demand and for the required capacity.
127 citations
TL;DR: The objective of this paper is to review scheduling study on FMSs and analyse future trend that employed simulation techniques as the analyzing tool and conclude that AI approaches will be dominating in future study.
Abstract: Since the late 1970s when the first collection of papers on scheduling of flexible manufacturing systems (FMSs) has been published, it has been one of the most popular topics for researchers. A number of approaches have been delivered to schedule FMSs including simulation techniques and analytical methods, whereas the former is the most widely used tool for modeling FMSs. The objective of this paper is to review scheduling study on FMSs and analyse future trend that employed simulation techniques as the analyzing tool. Scheduling methodologies are categorized into, namely traditional simulation techniques with single criterion scheduling approaches, traditional simulation techniques with multi-criteria scheduling approaches, and artificial intelligence (AI) approaches in FMSs. It is concluded that AI approaches will be dominating in future study.
119 citations
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Book•
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01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
52,705 citations
Book•
01 Jan 1988
TL;DR: This chapter discusses the use of Fuzzy Sets for the Evaluation and Ranking of Objects, a Quantitative Approach to Multiaspect Choice, and some of the techniques used in this approach.
Abstract: 1. Measures of Possibility and Fuzzy Sets.- 1.1. Imprecision and Uncertainty.- 1.2. Traditional Models of Imprecision and Uncertainty.- 1.3. Confidence Measures.- 1.3.1. Measures of Possibility and of Necessity.- 1.3.2. Possibility and Probability.- 1.4. Fuzzy Sets.- 1.5. Elementary Fuzzy Set Operations.- 1.6. Practical Methods for Determining Membership Functions.- 1.6.1. Vague Categories as Perceived by an Individual.- 1.6.2. Fuzzy Sets Constructed from Statistical Data.- 1.6.3. Remarks on the Set of Degrees of Membership.- 1.7. Confidence Measures for a Fuzzy Event.- 1.8. Fuzzy Relations and Cartesian Products of Fuzzy Sets.- References.- 2. The Calculus of Fuzzy Quantities.- 2.1. Definitions and a Fundamental Principle.- 2.1.1. Fuzzy Quantities, Fuzzy Intervals, Fuzzy Numbers.- 2.1.2. The Extension Principle.- 2.2. Calculus of Fuzzy Quantities with Noninteractive Variables.- 2.2.1. Fundamental Result.- 2.2.2. Relation to Interval Analysis.- 2.2.3. Application to Standard Operations.- 2.2.4. The Problem of Equivalent Representations of a Function.- 2.3. Practical Calculation with Fuzzy Intervals.- 2.3.1. Parametric Representation of a Fuzzy Interval.- 2.3.2. Exact Practical Calculation with the Four Arithmetic Operations.- 2.3.3. Approximate Calculation of Functions of Fuzzy Intervals.- 2.4. Further Calculi of Fuzzy Quantities.- 2.4.1. "Pessimistic" Calculus of Fuzzy Quantities with Interactive Variables.- 2.4.2. "Optimistic" Calculus of Fuzzy Quantities with Noninteractive Variables.- 2.5. Illustrative Examples.- 2.5.1. Estimation of Resources in a Budget.- 2.5.2. Calculation of a PERT Analysis with Fuzzy Duration Estimates.- 2.5.3. A Problem in the Control of a Machine Tool.- Appendix: Computer Programs.- References.- 3. The Use of Fuzzy Sets for the Evaluation and Ranking of Objects.- 3.1. A Quantitative Approach to Multiaspect Choice.- 3.1.1. Basic Principles of the Approach.- 3.1.2. Fuzzy Set-Theoretic Operations.- 3.1.3. Application to the Combination of Criteria.- 3.1.4. Identification of Operators.- 3.1.5. Example.- 3.2. Comparison of Imprecise Evaluations.- 3.2.1. Comparison of a Real Number and a Fuzzy Interval.- 3.2.2. Comparison of Two Fuzzy Intervals.- 3.2.3. Ordering of n Fuzzy Intervals.- 3.2.4. Computer Implementation.- 3.2.5. Example.- Appendix: Computer Programs.- References.- 4. Models for Approximate Reasoning in Expert Systems.- 4.1. Remarks on Modeling Imprecision and Uncertainty.- 4.1.1. Credibility and Plausibility.- 4.1.2. Decomposable Measures.- 4.1.3. Vague Propositions.- 4.1.4. Evaluating the Truth Value of a Proposition.- 4.2. Reasoning from Uncertain Premises.- 4.2.1. Deductive Inference with Uncertain Premises.- 4.2.2. Complex Premises.- 4.2.3. Combining Degrees of Uncertainty Relative to the Same Proposition.- 4.3. Inference from Vague or Fuzzy Premises.- 4.3.1. Representation of the Rule "if X is A, then Y is B".- 4.3.2. "Generalized" Modus Ponens.- 4.3.3. Complex Premises.- 4.3.4. Combining Possibility Distributions.- 4.4. Brief Summary of Current Work and Systems.- 4.5. Example.- Appendix A..- Appendix B: Computer Programs.- References.- 5. Heuristic Search in an Imprecise Environment, and Fuzzy Programming.- 5.1. Heuristic Search in an Imprecise Environment.- 5.1.1. A and A* Algorithms.- 5.1.2. The Classical Traveling Salesman Problem (Reminder).- 5.1.3. Heuristic Search with Imprecise Evaluations.- 5.1.4. Heuristic Search with Fuzzy Values.- 5.2. An Example of Fuzzy Programming: Tracing the Execution of an Itinerary Specified in Imprecise Terms.- 5.2.1. Execution and Chaining of Instructions.- 5.2.2. Illustrative Example.- 5.2.3. Problems Arising in Fuzzy Programming.- 5.2.4. Concluding Remarks.- Appendix: Computer Programs.- A.1. Selection of "the Smallest" of N Fuzzy Numbers.- A.2. Tracing Imprecisely Specified Itineraries.- References.- 6. Handling of Incomplete or Uncertain Data and Vague Queries in Database Applications.- 6.1. Representation of Incomplete or Uncertain Data.- 6.1.1. Representing Data by Means of Possibility Distributions.- 6.1.2. Differences and Similarities with Other Fuzzy Approaches.- 6.1.3. Dependencies and Possibilistic Information.- 6.2. The Extended Relational Algebra and the Corresponding Query Language.- 6.2.1. Generalization of ?-Selection.- 6.2.2. Cartesian Product, ?-Join, and Projection.- 6.2.3. Union and Intersection-Redundancy.- 6.2.4. Queries Employing Other Operations.- 6.3. Example.- 6.3.1. Representation of Data.- 6.3.2. Examples of Queries.- 6.4. Conclusion.- Appendix: Computer Program.- A.1. Data Structures.- A.2. Representation of Queries.- A.3. Description of Implemeted Procedures.- References.
2,427 citations
Book•
01 Oct 1988TL;DR: This paper presents a general view about the Fuzzification of Models in Engineering and Management Science, and some examples of Fuzzy Set Theory and System Modelling, as well as some of its applications in Transportation Optimization and Decision Making.
Abstract: (1990). Fuzzy Mathematical Models in Engineering and Management Science. Technometrics: Vol. 32, No. 2, pp. 238-238.
1,237 citations
"Fuzzy set theory applications in pr..." refers background or methods in this paper
...The fuzzy Delphi method (see Kaufmann and Gupta (1988)) is used to determine the activity time estimates....
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...…distributions Lootsma (1989) Fuzzy PERT compares stochastic PERT and fuzzy PERT McCahon and Lee (1988) Fuzzy PERT triangular activity times Kaufmann and Gupta (1988) Fuzzy CPM tutorial on fuzzy CPM Dubois and Prade (1985) Fuzzy PERT tutorial on fuzzy PERT Chanas and Kamburowski (1981)…...
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...The bibliographies compiled by Gaines and Kohout (1977), Kandel and Yager (1979), Kandel (1986), and Kaufmann and Gupta (1988) address fuzzy set theory and applications in general....
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...Kaufmann and Gupta (1988) report that over 7,000 research papers, reports, monographs, and books on fuzzy set theory and applications have been published since 1965....
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...Kaufmann and Gupta (1988) devote a chapter of their book to the critical path method in which activity times are represented by triangular fuzzy numbers....
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TL;DR: The forecast of the enrollments of the University of Alabama is carried out and a fuzzy time series model is developed using historical data, which is tested on the basis of its robustness andvantages and problems.
1,188 citations
"Fuzzy set theory applications in pr..." refers background or methods in this paper
... Song and Chissom (1994) apply a first-order, time-variant forecasting model to the Song and Chissom (1993b) university enrollment data set....
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...Sullivan and Woodall (1994) provide a detailed review of the time-invariant and time-variant time series models set forth by Song and Chissom (1993a, 1994)....
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...Song et al. (1995) note that the fuzzy time series models defined in Song and Chissom (1993a), and those used to forecast university enrollments in Song and Chissom (1993b, 1994) , require fuzzification of crisp historical data....
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...Song and Chissom (1994) apply a first order, time-variant forecasting model to the Song and Chissom (1993b) university enrollment data set....
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...Tanaka et al. (1982) Regression (five independent variables) Predict prices of prefabricated houses Chen (1996) Time series Forecast University of Alabama enrollment Song et al. (1995) Time series Modification of earlier model Sullivan and Woodall (1994) Markov model and time series Forecast University of Alabama enrollment Song and Chissom (1994) Time-variant time series Forecast University of Alabama enrollment Cummins and Derrig (1993) ......
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Book•
25 Apr 1996
TL;DR: In this paper, the authors present a survey of Fuzzy multiple objective decision-making techniques and their application in various aspects of the real world, such as: 1.1 Introduction.2 Goal Programming.
Abstract: 1 Introduction.- 1.1 Objectives of This Study.- 1.2 (Fuzzy) Multiple Objective Decision Making.- 1.3 Classification of (Fuzzy) Multiple Objective Decision Making.- 1.4 Applications of (Fuzzy) Multiple Objective Decision Making.- 1.5 Literature Survey.- 1.6 Fuzzy Sets.- 2 Multiple Objective Decision Making.- 2.1 Introduction.- 2.2 Goal Programming.- 2.2a A Portfolio Selection Problem.- 2.2b An Audit Sampling Problem.- 2.3 Fuzzy Programming.- 2.3.1 Max-Min Approach.- 2.3.1a A Trade Balance Problem.- 2.3.1b A Media Selection Problem.- 2.3.2 Augmented Max-Min Approach.- Example.- 2.3.2a A Trade Balance Problem.- 2.3.2b A Logistics Planning Model.- 2.3.3 Parametric Approach.- Example.- 2.4 Global Criterion Approach.- 2.4.1 Global Criterion Approach.- 2.4.1a A Nutrition Problem.- 2.4.2 TOPSIS for MODM.- 2. .2a A Water Quality Management Problem.- 2.5 Interactive Multiple Objective Decision Making.- 2.5.1 Optimal System Design.- 2.5.1a A Production Planning Problem.- 2.5.2 KSU-STEM.- 2.5.2a A Nutrition Problem.- 2.5.2b A Project Scheduling Problem.- 2.5.3 ISGP-II.- 2.5.3a A Nutrition Problem.- 2.5.3b A Bank Balance Sheet Management Problem.- 2.5.4 Augmented Min-Max Approach.- 2.5.4a A Water Pollution Control Problem.- 2.6 Multiple Objective Linear Fractional Programming.- 2.6.1 Luhandjula's Approach.- Example.- 2.6.2 Lee and Tcha's Approach.- 2.6.2a A Financial Structure Optimization Problem.- 2.7 Multiple Objective Geometric Programming.- Example.- 2.7a A Postal Regulation Problem.- 3 Fuzzy Multiple Objective Decision Making.- 3.1 Fuzzy Goal Programming.- 3.1.1 Fuzzy Goal Programming.- 3.1.1a A Production-Marketing Problem.- 3.1.1b An Optimal Control Problem.- 3.1.1c A Facility Location Problem.- 3.1.2 Preemptive Fuzzy Goal Programming.- Example: The Production-Marketing Problem.- 3.1.3 Interpolated Membership Function.- 3.1.3.1 Hannan's Method.- Example: The Production-Marketing Problem.- 3.1.3.2 Inuiguchi, Ichihashi and Kume's Method.- Example: The Trade Balance Problem.- 3.1.3.3 Yang, Ignizio and Kim's Method.- Example.- 3.1.4 Weighted Additive Model.- 3.1.4.1 Crisp Weights.- 3.1.4.1a Maximin Approach.- Example: The Production-Marketing Problem.- 3.1.4.1b Augmented Maximin Approach.- 3.1.4.1c Supertransitive Approximation.- Example: The Production-Marketing Problem.- 3.1.4.2 Fuzzy Weights.- Example: The Production-Marketing Problem.- 3.1.5 A Preference Structure on Aspiration Levels.- Example: The Production-Marketing Problem.- 3.1.6 Nested Priority.- 3.1.6a A Personnel Selection Problem.- 3.2 Fuzzy Global Criterion.- Example.- 3.3 Interactive Fuzzy Multiple Objective Decision Making.- 3.3.1 Werners's Method.- Example: The Trade Balance Problem.- 3.3.1a An Aggregate Production Planning Problem.- 3.3.2 Lai and Hwang's Method.- 3.3.3 Leung's Method.- Example.- 3.3.4 Fabian, Ciobanu and Stoica's Method.- Example.- 3.3.5 Sasaki, Nakahara, Gen and Ida's Method.- Example.- 3.3.6 Baptistella and Ollero's Method.- 3.3.6a An Optimal Scheduling Problem.- 4 Possibilistic Multiple Objective Decision Making.- 4.1 Introduction.- 4.1.1 Resolution of Imprecise Objective Functions.- 4.1.2 Resolution of Imprecise Constraints.- 4.2 Possibilistic Multiple Objective Decision Making.- 4.2.1 Tanaka and His Col1eragues' Methods.- Example.- 4.2.1.1 Possibilistic Regression.- Example 1.- Example 2.- 4.2.1.2 Possibilistic Group Method of Data Handling.- Example 28.- 4.2.2 Lai and Hwang's Method.- 4.2.3 Negi's Method.- Example.- 4.2.4 Luhandjula's Method.- Example.- 4.2.5 Li and Lee's Method.- Example.- 4.2.6 Wierzchon's Method.- 4.3 Interactive Methods for PMODM.- 4.3.1 Sakawa and Yano's Method.- Example.- 4.3.2 Slowinski's Method.- 4.3.2a A Long-Term Development Planning Problem of a Water Supply System.- 4.3.2b A Land-Use Planning Problem.- 4.3.2c A Farm Structure Optimization Problem.- 4.3.3 Rommelranger's Method.- Example.- 4.4 Hybrid Problems.- 4.4.1 Tanaka, Ichihashi and Asai's Method.- Example.- 4.4.2 Inuiguchi and Ichihashi's Method.- Example.- 4.5 Possibilistic Multiple Objective Linear Fractional Programming.- 4.6 Interactive Possibilistic Regression.- 4.6.1 Crisp Output and Crisp Input.- Example.- 4.6.2 Imprecise Output and Crisp Input.- Example.- 4.6.3 Imprecise Output and Imprecise Input.- Example.- 5 Concluding Remarks.- 5.1 Future Research.- 5.2 Fuzzy Mathematical Programming.- 5.3 Multiple Attribute Decision Making.- 5.4 Fuzzy Multiple Attribute Decision Making.- 5.5 Group Decision Making under Multiple Criteria.- Books, Monographs and Conference Proceedings.- Journal Articles, Technical Reports and Theses.- Appendix: Stochastic Programming.- A.1 Stochastic Programming with a Single Objective Function.- A.1.1 Distribution Problems.- A.1.2 Two-Stage Programming.- A.1.3 Chance-Constrained Programming.- A.2 Stochastic Programming with Multiple Objective Functions.- A.2.1 Distribution Problem.- A.2.2 Goal Programming Problem.- A.2.3 Utility Function Problem.- A.2.4 Interactive Problem.- References.
1,168 citations