Fuzzy Reasoning in Decision Making and Optimization

by Carlsson, Christer; Fuller, Robert

• ISBN13: 9783790814286
• ISBN10: 3790814288
• Format: Hardcover
• Copyright: 2002-03-01
• Publisher: Physica Verlag

Summary

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.

Table of Contents

Fuzzy Sets and Fuzzy Logic
Fuzzy sets	1	(6)
Operations on fuzzy sets	7	(5)
The extension principle	12	(7)
t-norm-based operations on fuzzy numbers	19	(2)
Product-sum of triangular fuzzy numbers	21	(3)
Hamacher-sum of triangular fuzzy numbers	24	(4)
t-norm-basd addition of fuzzy numbers	28	(2)
A functional relationshipo between t-norm-based addition and multiplication	30	(3)
On generalization of Nguyen's theorems	33	(2)
Measures of possibility and necessity	35	(3)
A law of large numbers for fuzzy numbers	38	(6)
Metrics for fuzzy numbers	44	(2)
Possibilistic mean value and variance of fuzzy numbers	46	(7)
Auxiliary lemmas	53	(4)
Fuzzy implications	57	(3)
Linguistic variables	60	(5)
Fuzzy Multicriteria Decision Making
Averaging operators	65	(8)
Obtaining maximal entropy OWA operator weights	73	(5)
OWA Operators for Ph. D. student selection	78	(7)
Possibility and necessity in weighted aggregation	85	(7)
Benchmarking in linguistic importance weighted aggregations	92	(9)
Fuzzy Reasoning
The theory of approximate reasoning	101	(3)
Aggregation in fuzzy system modeling	104	(3)
Multiple fuzzy reasoning schemes	107	(4)
Some properties of the compositional rule of inference	111	(4)
Computation of the compositional rule of inference under t-norms	115	(4)
On the generalized method-of-case inference rule	119	(4)
Fuzzy Optimization
Possibilistic linear equality systems	123	(7)
Sensitivity analysis of ax = b and aδ x = bδ	130	(4)
Possibilistic systems with trapezoid fuzzy numbers	134	(2)
Flexible linear programming	136	(6)
Fuzzy linear programming with crisp relations	142	(2)
Possibilistic linear programming	144	(4)
Possibilistic quadratic programming	148	(2)
Multiobjective possibilistic linear programming	150	(7)
Fuzzy Reasoning for Fuzzy Optimization
Fuzzy reasoning for FMP	157	(13)
Extension to nonlinear FMP	161	(1)
Relation to classical LP problems	162	(1)
Crisp objective and fuzzy coefficients in constraints	163	(1)
Fuzzy objective function and crisp constraints	164	(1)
Relation to Zimmermann's soft constraints	164	(2)
Relation to Buckley's possibilistic LP	166	(4)
Optimization with linguistic variables	170	(7)
Multiobjective optimization with linguistic variables	177	(2)
Interdependent multiple criteria decision making	179	(11)
The linear case	184	(2)
Application functions	186	(4)
MOP with interdependent objectives	190	(3)
Additive linear interdependences	193	(6)
Additive nonlinear interdependences	199	(2)
Compound interdependences	201	(2)
Biobjective interdependent decision problems	203	(4)
Applications in Management
Nordic Paper Inc.	207	(5)
Outline of a macro algorithm	209	(3)
A fuzzy approach to real option valuation	212	(7)
Probabilistic real option valuation	213	(2)
A hybrid approach to real option valuation	215	(4)
The Woodstrat project	219	(17)
Fuzzy hyperknowledge support systems	220	(11)
Cognitive maps for hyperknowledge representation	231	(1)
Adaptive FCM for strategy formation	232	(4)
Soft computing methods for reducing the bullwhip effect	236	(19)
The bullwhip effect, some additional details	240	(2)
Explanations for the bullwhip effect: standard results	242	(1)
Demand signal processing	243	(1)
Order batching	244	(2)
Price variations	246	(1)
A fuzzy approach to demand signal processing	247	(1)
A fuzzy logic controller to demand signal processing	248	(2)
A hybrid soft computing platform for taming the bull-whip effect	250	(5)
Future Trends in Fuzzy Reasoning and Decision Making
Software agents and agent-based systems	255	(6)
Intelligence and software agents	261	(3)
Scenario agents	264	(4)
The scenario agent: basic functionality	267	(1)
Scenarios and scenario planning: key features	268	(4)
Forecasting	272	(3)
Industry foresight	275	(3)
The scenario agent	278	(9)
Support for OW scenarios	279	(2)
Support for model-based scenarios	281	(4)
Support for scenario building and foresight	285	(2)
Interpretation agent	287	(3)
The interpretation agent: basic functionality	288	(2)
Coping with imprecision	290	(3)
Interpretation in a business environment	293	(2)
Mental models and cognitive maps	295	(1)
A preliminary description of an interpretation agent	296	(4)
An interpretation agent: details	300	(19)
Interpretation support for OW scenarios	302	(3)
Interpretation support for model-based scenarios	305	(4)
Interpretation support for decision models	309	(3)
Interpretation support for data sources	312	(1)
Generic interpretation of agent structures	313	(1)
Approximate reasoning and sense-making	313	(1)
Support for sense-making and interpretation	314	(5)
Bibliography	319	(18)
Index	337