Table Of ContentFuzzy Stochastic Optimization
Shuming Wang • Junzo Watada
Fuzzy Stochastic
Optimization
Theory, Models and Applications
123
ShumingWang JunzoWatada
WasedaUniversity WasedaUniversity
Hibikino,Wakamatsu-ku Hibikino,Wakamatsu-ku
Kitakyushu-City2-7 Kitakyushu-City2-7
Fukuoka,Japan Fukuoka,Japan
ISBN978-1-4419-9559-9 ISBN978-1-4419-9560-5(eBook)
DOI10.1007/978-1-4419-9560-5
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2012934832
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Preface
Randomnessandfuzziness(orvagueness)aretwo majorsourcesofuncertaintyin
the real world. In practical applications in areas of industrial engineering, man-
agement, and economics, chances are pretty good that decision makers are being
confrontedwithinformationthataresimultaneouslyprobabilisticallyuncertainand
fuzzily imprecise, and an optimization (decision making) has to be performed
undersuchatwofolduncertainenvironmentofaco-occurrenceofrandomnessand
fuzziness.
FuzzyrandomvariableoriginallypresentedbyH. Kwakernaakisa tailor-made
mathematicaltoolto describethetwofoldorhybriduncertainty.Itownsatwofold
distributionstructurebeingabletocarryajointintegralityofthesimultaneousprob-
abilisticandfuzzyinformationwhichgoesbeyondthejuxtapositionofinformation
contained in random variable in probability theory and fuzzy variable in theory
of fuzzy set and possibility. Naturally, it is regarded as a generalization for both
random variable and fuzzy variable. Being capable of modeling the randomness
and fuzziness as an ensemble, the fuzzy random variable has become the part
and parcel in the optimization under integrated uncertainties of randomness and
fuzziness(fuzzystochasticoptimization).
Fromboththeoreticalandpracticalperspectives,thisbookaimstopresentaself-
contained, systematic, and up-to-date description of fuzzy stochastic optimization
on the basis of the fuzzy random variable being a core mathematical vehicle to
model the integrated fuzzy random uncertainty. It goes along a direction from
theoretical aspects of the fuzzy random variable to fuzzy stochastic optimization
modelsandtheirreal-lifecasestudies.
We now describe in detail the structure of the book. After an introduction in
Chap.1 which outlines the developmentof theory of fuzzy random variables, and
of fuzzy stochastic optimization models, the core work consists of the next eight
chaptersthat form relativelyindependentthree parts: theory,models, and real-life
applications.
vii
viii Preface
Part I:Theory
In this first part, we present mathematical foundations of fuzzy random variable.
Chapter 2 introduces necessary preliminaries on fuzzy random variable and then
presents analytical properties of fuzzy random variable in different aspects. In
Chap.3, we discuss two renewal processes, i.e., fuzzy stochastic renewal process
and fuzzy stochastic renewal reward process, and a fuzzy random elementary
renewal theorem and a fuzzy random renewal reward theorem are described
indepth.
Part II:Models
In the second part we present a series of fuzzy stochastic optimization models
using fuzzy randomvariables to model uncertain parameters.Chapter 4 discusses
two redundancy allocation models with fuzzy random lifetimes for system reli-
ability optimization in different objectives of reliability maximization and cost
minimization.In Chap.5, we discuss a two-stagefacility locationselection model
with fuzzy randomvariable cost and client demand in which the capacity is fixed
and the objective is to maximize the expected profit. In this two-stage problems,
given each first-stage decision (location decision) and each realization of fuzzy
random parameter, we have a number of second-stage optimization subproblems
to solve to determine the objective value at the first-stage decision. In Chap.6
we establish a genetic risk optimization model in the fuzzy random environment,
namely,two-stagefuzzystochasticprogrammingwithValue-at-Risk(VaR).Inthis
chapter,the notationof VaR metric is introducedinto the fuzzy randomcase, and
afuzzyrandomVaRcriterionisdefinedtoformanobjectiveofVaRminimization
in the context of a two-stage model. Applying the generic fuzzy stochastic VaR
modeltothefacilitylocationselectionwithvariablecapacity,inChap.7webuilda
two-stagefuzzystochasticfacilitylocationmodelwithVaRobjectiveandvariable
capacity, in which both the location and capacity are decision variables. Owing
to the solution difficulties that above fuzzy stochastic models bear, in general,
theycannotbe surmountedby classic mathematicalprogrammingapproaches,the
models are therefore solved with the aid of hybrid approaches that fuse some
improvedmetaheuristicalgorithmsandapproximatevehicles.
Part III:Real-Life Applications
The third part consists of two real-life applications of the optimization models
discussed in Part II. Chapter 8 presents a case study on a dam control system
design problem which is an application of the system reliability optimization
Preface ix
models built in Chap.4. In Chap.9 we present a case study on location selection
problem for frozen food plants to which the models in Chaps.5 and 6 are
applied.
Wearegratefultothefollowingscholarsandfriendsfortheinsightfuldiscussions
and suggestions they provided during the creation of the book. They include
ProfessorWitoldPedryczoftheUniversityofAlberta,Canada;ProfessorYan-Kui
LiuofHebeiUniversity,China;ProfessorLakhmiC.JainoftheUniversityofSouth
Australia, Australia;ProfessorHiroakiIshii of Osaka University,Japan;Professor
Baoding Liu of Tsinghua University, China; Professor Vyacheslav Kalashnikov
of the Monterrey Institute of Technology, Mexico; Professor Jaeseok Choi of
GyeongsangNationalUniversity,Korea;ProfessorJeng-ShyangPanoftheNational
Kaohsiung University of Applied Sciences; Professor Huey-Ming Lee of the
Chinese Culture University; and Professor Berlin Wu of the National Chengchi
University,Taiwan.
Also,thefirstauthorwouldliketothankthefinancialsupportfromtheResearch
Fellowship of the Japan Society for the Promotion of Science (JSPS) for Young
Scientists,andtheResearchFellowshipofthe“AmbientSoCGlobalCOEProgram
of Waseda University”of the Ministry of Education,Culture, Sports, Science and
Technology(MEXT),Japan.
Finally, we wish to thank Dr. Brett Kurzman and Ms. Elizabeth Dougherty
at Springer for their much appreciated editorial work throughout the process of
publishingthisbook.
Beijing,China ShumingWang
Kitakyushu,Japan JunzoWatada
