Fuzzy Reasoning in Decision Making and Optimization

This book starts with the basic concepts of fuzzy arithmetics and progresses through the analysis of sup-t-norm-extended arithmetic operations, possibilistic linear systems and fuzzy reasoning approaches to fuzzy optimization. Four applications of (interdependent) fuzzy optimization and fuzzy reasoning to strategic planning, project management with real options, strategic management and supply chain management are presented and carefully discussed. The book ends with a detailed description of some intelligent software agents, where fuzzy reasoning schemes are used to enhance their functionality. It can be useful for researchers and students working in soft computing, applied mathematics, operations research, management science, information systems, intelligent agents and artificial intelligence.

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Many decision-making tasks are too complex to be understood quantitatively, however, humans succeed by using knowledge that is imprecise rather than precise. Fuzzy logic resembles human reasoning in its use of imprecise informa­ tion to generate decisions. Unlike classical logic which requires a deep under­ standing of a system, exact equations, and precise numeric values, fuzzy logic incorporates an alternative way of thinking, which allows modeling complex systems using a higher level of abstraction originating from our knowledge and experience. Fuzzy logic allows expressing this knowledge with subjective concepts such as very big and a long time which are mapped into exact numeric ranges. Since knowledge can be expressed in a more natural by using fuzzy sets, many decision (and engineering) problems can be greatly simplified. Fuzzy logic provides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems. The theory of fuzzy logic provides a mathematical strength to capture the un­ certainties associated with human cognitive processes, such as thinking and reasoning. The conventional approaches to knowledge representation lack the means for representating the meaning of fuzzy concepts. As a consequence, the approaches based on first order logic do not provide an appropriate con­ ceptual framework for dealing with the representation of commonsense knowl­ edge, since such knowledge is by its nature both lexically imprecise and non­ categorical.

Contenu

1. Fuzzy Sets and Fuzzy Logic.- 1.1 Fuzzy sets.- 1.2 Operations on fuzzy sets.- 1.3 The extension principle.- 1.4 t-norm-based operations on fuzzy numbers.- 1.5 Product-sum of triangular fuzzy numbers.- 1.6 Hamacher-sum of triangular fuzzy numbers.- 1.7 t-norm-based addition of fuzzy numbers.- 1.8 A functional relationship between t-norm-based addition and multiplication.- 1.9 On generalization of Nguyen's theorems.- 1.10 Measures of possibility and necessity.- 1.11 A law of large numbers for fuzzy numbers.- 1.12 Metrics for fuzzy numbers.- 1.13 Possibilistic mean value and variance of fuzzy numbers.- 1.14 Auxiliary lemmas.- 1.15 Fuzzy implications.- 1.16 Linguistic variables.- 2. Fuzzy Multicriteria Decision Making.- 2.1 Averaging operators.- 2.2 Obtaining maximal entropy OWA operator weights.- 2.3 OWA Operators for Ph.D. student selection.- 2.4 Possibility and necessity in weighted aggregation.- 2.5 Benchmarking in linguistic importance weighted aggregations.- 3. Fuzzy Reasoning.- 3.1 The theory of approximate reasoning.- 3.2 Aggregation in fuzzy system modeling.- 3.3 Multiple fuzzy reasoning schemes.- 3.4 Some properties of the compositional rule of inference.- 3.5 Computation of the compositional rule of inference under t-norms.- 3.6 On the generalized method-of-case inference rule.- 4. Fuzzy Optimization.- 4.1 Possibilistic linear equality systems.- 4.2 Sensitivity analysis of ãx = b? and ã?x = b??..- 4.3 Possibilistic systems with trapezoid fuzzy numbers.- 4.4 Flexible linear programming.- 4.5 Fuzzy linear programming with crisp relations.- 4.6 Possibilistic linear programming.- 4.7 Possibilistic quadratic programming.- 4.8 Multiobjective possibilistic linear programming.- 5. Fuzzy Reasoning for Fuzzy Optimization.- 5.1 Fuzzy reasoning for FMP.- 5.1.1 Extension to nonlinear FMP.- 5.1.2 Relation to classical LP problems.- 5.1.3 Crisp objective and fuzzy coefficients in constraints.- 5.1.4 Fuzzy objective function and crisp constraints.- 5.1.5 Relation to Zimmermann's soft constraints.- 5.1.6 Relation to Buckley's possibilistic LP.- 5.2 Optimization with linguistic variables.- 5.3 Multiobjective optimization with lingusitic variables.- 5.4 Interdependent multiple criteria decision making.- 5.4.1 The linear case.- 5.4.2 Application functions.- 5.5 MOP with interdependent objectives.- 5.6 Additive linear interdependences.- 5.7 Additive nonlinear interdependences.- 5.8 Compound interdependences.- 5.9 Biobjective interdependent decision problems.- 6. Applications in Management.- 6.1 Nordic Paper Inc.- 6.1.1 Outline of a macro algorithm.- 6.2 A fuzzy approach to real option valuation.- 6.2.1 Probabilistic real option valuation.- 6.2.2 A hybrid approach to real option valuation.- 6.3 The Woodstrat project.- 6.3.1 Fuzzy hyperknowledge support systems.- 6.3.2 Cognitive maps for hyperknowledge representation.- 6.3.3 Adaptive FCM for strategy formation.- 6.4 Soft computing methods for reducing the bullwhip effect.- 6.4.1 The bullwhip effect, some additional details.- 6.4.2 Explanations for the bullwhip effect: standard results.- 6.4.3 Demand signal processing.- 6.4.4 Order batching.- 6.4.5 Price variations.- 6.4.6 A fuzzy approach to demand signal processing.- 6.4.7 A fuzzy logic controller to demand signal processing.- 6.4.8 A hybrid soft computing platform for taming the bullwhip effect.- 7. Future Trends in Fuzzy Reasoning and Decision Making.- 7.1 Software agents and agent-based systems.- 7.2 Intelligence and software agents.- 7.3 Scenario agents.- 7.3.1 The scenario agent: basic functionality.- 7.4 Scenarios and scenario planning: key features.- 7.5 Forecasting.- 7.6 Industry foresight.- 7.7 The scenario agent.- 7.7.1 Support for OW scenarios.- 7.7.2 Support for model-based scenarios.- 7.7.3 Support for scenario building and foresight.- 7.8 Interpretation agent.- 7.8.1 The interpretation agent: basic functionality.- 7.9 Coping with imprecision.- 7.10 Interpretation in a business environment.- 7.11 Mental models and cognitive maps.- 7.12 A preliminary description of an interpretation agent.- 7.13 An interpretation agent: details.- 7.13.1 Interpretation support for OW scenarios.- 7.13.2 Interpretation support for model-based scenarios.- 7.13.3 Interpretation support for decision models.- 7.13.4 Interpretation support for data sources.- 7.13.5 Generic interpretation of agent structures.- 7.13.6 Approximate reasoning and sense-making.- 7.13.7 Support for sense-making and interpretation.