模糊集合論及其應(yīng)用

內(nèi)容概要

　　《模糊集合論及其應(yīng)用(第4版)》旨在為模糊理論方面的學(xué)者提供一部入門級教程，不僅滿足了學(xué)生學(xué)習(xí)的需要，也很適合相關(guān)的專家學(xué)習(xí)深入研究。為了使本書不僅僅是一部初級教程，讀者范圍更加廣泛，增加了許多參考資料。知識體系新穎，時代氣息十足，不僅是對模糊理論的最現(xiàn)代解釋，也很適合學(xué)習(xí)該理論的應(yīng)用技巧。雖然是模糊集合理論的初期階段，該理論得到了廣泛的發(fā)展，在人工智能，計算機(jī)科學(xué)，控制工程決策論，專家系統(tǒng)，邏輯學(xué)，廣利科學(xué)，運籌學(xué)，機(jī)器人技術(shù)等眾多領(lǐng)域中模糊技術(shù)都有廣泛的應(yīng)用，在理論研究方面也取得了突破性進(jìn)展，作為第四版，有關(guān)概率論，模糊邏輯和近似推理，專家系統(tǒng)，模糊控制，模糊數(shù)據(jù)分析，決策理論和運籌學(xué)中模糊模型等章節(jié)都做了更新和擴(kuò)展，并且包括了不少練習(xí)。目次：模糊集導(dǎo)論；（第一部分）模糊數(shù)學(xué)：模糊集合，基本定義；擴(kuò)展；模糊測度和模糊的測量；擴(kuò)展原理及應(yīng)用；模糊關(guān)系和模糊圖；模糊分析；不確定模型；模糊集合理論應(yīng)用；模糊集合和專家系統(tǒng)；模糊控制；模糊數(shù)據(jù)庫和疑問；模糊數(shù)據(jù)分析；模糊環(huán)境中決策；工程和管理中模糊集合的應(yīng)用；模糊集合理論中的經(jīng)驗研究；展望未來。
　　讀者對象：數(shù)學(xué)專業(yè)研究生，計算機(jī)科學(xué)，人工智能，工程科學(xué)和相關(guān)科研人員。

書籍目錄

list of figures
list of tables
foreword
preface
preface to the fourth edition
1 introduction to fuzzy sets
1.1 crispness, vagueness, fuzziness, uncertainty
1.2 fuzzy set theory
part i: fuzzy mathematics
2 fuzzy sets--basic definitions
2.1 basic definitions
2.2 basic set-theoretic operations for fuzzy sets
3 extensions
3.1 types of fuzzy sets
3.2 further operations on fuzzy sets
3.2.1 algebraic operations
3.2.2 set-theoretic operations
3.2.3 criteria for selecting appropriate aggregation
operators
4 fuzzy measures and measures of fuzziness
4.1 fuzzy measures
4.2 measures of fuzziness
5 the extension principle and applications
5.1 the extension principle
5.2 operations for type 2 fuzzy sets
5.3 algebraic operations with fuzzy numbers
5.3.1 special extended operations
5.3.2 extended operations for lr-representation of fuzzy sets
6 fuzzy relations and fuzzy graphs
6.1 fuzzy relations on sets and fuzzy sets
6.1.1 compositions of fuzzy relations
6.1.2 properties of the min-max composition
8.2 fuzzy graphs
6.3 special fuzzy relations
7 fuzzy analysis
7.1 fuzzy functions on fuzzy sets
7.2 extrema of fuzzy functions
7.3 integration of fuzzy functions
7.3.1 integration of a fuzzy function over a crisp interval
7.3.2 integration of a (crisp) real-valued function over a fuzzy
interval
7.4 fuzzy differentiation
8 uncertainty modeling
8.1 application-oriented modeling of uncertainty
8.1.1 causes of uncertainty
8.1.2 type of available information
8.1.3 uncertainty methods
8.1.4 uncertainty theories as transformers of information
8.1.5 matching uncertainty theory and uncertain phenomena
8.2 possibility theory
8.2.1 fuzzy sets and possibility distributions
8.2.2 possibility and necessity measures
8.3 probability of fuzzy events
8.3.1 probability of a fuzzy event as a scalar
8.3.2 probability of a fuzzy event as a fuzzy set
8.4 possibility vs. probability
part ii: applications of fuzzy set theory
9 fuzzy logic and approximate reasoning
9.1 linguistic variables
9.2 fuzzy logic
9.2.1 classical logics revisited
9.2.2 linguistic truth tables
9.3 approximate and plausible reasoning
9.4 fuzzy languages
9.5 support logic programming and fril
9.5.1 introduction
9.5.2 fril rules
9.5.3 inference methods in fril
9.5.4 fril inference for a single rule
9.5.5 multiple rule case
9.5.6 interval and point semantic unification
9.5.7 least prejudiced distribution and learning
9.5.8 applications of fril
10 fuzzy sets and expert systems
10.1 introduction to expert systems
10.2 uncertainty modeling in expert systems
10.3 applications
11 fuzzy control
11.1 origin and objective
11.2 automatic control
11.3 the fuzzy controller
11.4 types of fuzzy controllers
11.4.1 the mamdani controller
11.4.2 defuzzification
11.4.3 the sugeno controller
11.5 design parameters
11.5.1 scaling factors
11.5.2 fuzzy sets
11.5.3 rules
11.6 adaptive fuzzy control
11.7 applications
11.7.1 crane control
11.7.2 control of a model car
11.7.3 control of a diesel engine
11.7.4 fuzzy control of a cement kiln
11.8 tools
11.9 stability
11.10 extensions
12 fuzzy data bases and queries
12.1 introduction
12.2 fuzzy relational databases
12.3 fuzzy queries in crisp databases
13 fuzzy data analysis
13.1 introduction
13.2 methods for fuzzy data analysis
13.2.1 algorithmic approaches
13.2.2 knowledge-based approaches
13.2.3 neural net approaches
13.3 dynamic fuzzy data analysis
13.3.1 problem description
13.3.2 similarity of functions
13.3.3 approaches for analysic dynamic systems
13.4 tools for fuzzy data analysis
13.4.1 requirements for fda tools
13.4.2 data engine
13.5 applications of fda
13.5.1 maintenance management in petrochemical plants
13.5.2 acoustic quality control
14 decision making in fuzzy environments
14.1 fuzzy decisions
14.2 fuzzy linear programming
14.2.1 symmetric fuzzy lp
14.2.2 fuzzy lp with crisp objective function
14.3 fuzzy dynamic programming
14.3.1 fuzzy dynamic programming with crisp state transformation
function
14.4 fuzzy multicriteria analysis
14.4.1 multi objective decision making (modm)
14.4.2 multi attributive decision making (madm)
15 applications of fuzzy sets in engineering and management
15.1 introduction
15.2 engineering applications
15.2.1 linguistic evaluation and ranking of machine tools
15.2.2 fault detection in gearboxes
15.3 applications in management
15.3.1 a discrete location model
15.3.2 fuzzy set models in logistics
15.3.2.1 fuzzy approach to the transportation problem
15.3.2.2 fuzzy linear programming in logistics
15.3.3 fuzzy sets in scheduling
15.3.3.1 job-shop scheduling with expert systems
15.3.3.2 a method to control flexible manufacturing systems
15.3.3.3 aggregate production and inventory planning
15.3.3.4 fuzzy mathematical programming for maintenance
scheduling
15.3.3.5 scheduling courses, instructors, and classrooms
15.3.4 fuzzy set models in inventory control
15.3.5 fuzzy sets in marketing
15.3.5.1 customer segmentation in banking and finance
15.3.5.2 bank customer segmentation based on customer
behavior
16 empirical research in fuzzy set theory
16.1 formal theories vs. factual theories vs. decision
technologies
16.1.1 models in operations research and management science
16.1.2 testing factual models
16.2 empirical research on membership functions
16.2.1 type a-membership model
16.2.2 type b-membership model
16.3 empirical research on aggregators
16.4 conclusions
17 future perspectives
abbreviations of frequently cited journals
bibliography
index

章節(jié)摘錄

　　situation and is meant to be a mapping of a problem, a system, or a process. In contrast to a scientific theory, containing scientific laws as hypotheses, a model normally does not assert invariance with respect to time and space but requires modifications whenever the specific context for which the model was constructed changes.　　In the following, we will concentrate on models rather than on theories. Real-izing that there is quite a variety of types of models, we do not think that it is important and necessary for our purposes to distinguish models by their language （mathematics or logic is considered to be a modeling language）, by area, by problem type, by size, and so on. One classification, however, seems to be impor-tant: the distinction of models by their character. Scientific theories were already divided into formal theories and factual theories.　　……

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