Membership function

About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.

Fuzzy sets, decision making, and expert systems

Abstract: 1 Introduction.- The Logic of Decisions, Behavioral Decision Theory, and Decision Technology.- Optimization, Outranking, Evaluation.- Basics of Fuzzy Set Theory.- 2 Individual Decision Making in Fuzzy Environments.- Symmetrical Models.- Nonsymmetrical Models.- Fuzzy Utilities.- 3 Multi-Person Decision Making in Fuzzy Environments.- Basic Models.- Fuzzy Games.- Fuzzy Team Theory.- Fuzzy Group Decision Making.- 4 Fuzzy Mathematical Programming.- Fuzzy Linear and Nonlinear Programming.- Fuzzy Multi-Stage Programming.- 5 Multi-Criteria Decision Making in Ill-Structured Situations.- Fuzzy Multi-Criteria Programming.- Multi-Attribute Decision Making (MADM).- Fuzzy Outranking.- 6 Operators and Membership Functions in Decision Models.- Axiomatic, Pragmatic, and Empirical Justification.- The Measurement of Membership Functions.- Selecting Appropriate Operators in Decision Models.- 7 Decision Support Systems.- Knowledge-Based vs. Data-Based Systems.- Linguistic Variables, Fuzzy Logic, Approximate Reasoning.- An Interactive Decision Support System for Fuzzy and Semi-fuzzy Multi-Objective Problems.- Expert Systems and Fuzzy Sets.

Cluster Validity with Fuzzy Sets

Abstract: Given a finite, unlabelled set of real vectors X, one often presumes the existence of (c) subsets (clusters) in X, the members of which somehow bear more similarity to each other than to members of adjoining clusters. In this paper, we use membership function matrices associated with fuzzy c-partitions of X, together with their values in the Euclidean (matrix) norm, to formulate an a posteriori method for evaluating algorithmically suggested clusterings of X. Several numerical examples are offered in support of the proposed technique.

Fuzzy Multiple Objective Decision Making: Methods And Applications

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.