Type-2 Fuzzy Decision-Making Theories, Methodologies and Applications

282 Pages·2019·4.636 MB·English

by  Jindong Qin, Xinwang Liu

Uncertainty and Operations Research
Jindong Qin
Xinwang Liu
Type-2 Fuzzy
Decision-
Making Theories,
Methodologies
and Applications
Uncertainty and Operations Research
Editor-in-Chief
Xiang Li, Beijing University of Chemical Technology, Beijing, China
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More information about this series at http://www.springer.com/series/11709
Jindong Qin Xinwang Liu
(cid:129)
Type-2 Fuzzy
Decision-Making Theories,
Methodologies
and Applications
123
Jindong Qin XinwangLiu
Schoolof Management Schoolof Economics andManagement
WuhanUniversity ofTechnology Southeast University
Wuhan, Hubei, China Nanjing, Jiangsu,China
ISSN 2195-996X ISSN 2195-9978 (electronic)
Uncertainty andOperationsResearch
ISBN978-981-13-9890-2 ISBN978-981-13-9891-9 (eBook)
https://doi.org/10.1007/978-981-13-9891-9
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Foreword
In a nutshell, this book authored by Profs. Jindong Qin and Xinwang Liu entitled
Type-2 Fuzzy Decision-Making Theories, Methodologies and Applications is a
comprehensive, well-written monograph on a timely and important area of
decision-makingrealizedintheformalframeworkoftype-2fuzzysets.Thetopicis
important for several reasons. Undoubtedly, real-world decision-making processes
realized in ever-growing complex environments with numerous conflicting objec-
tives and diverse constraints are present in almost every endeavor of human
activities embracing areas of finance, management, engineering, transportation,
health care, and many others. In the plethora of methodologies supporting
decision-making, fuzzy sets along with their generalizations occupy a visible
position. It is not surprising at all bearing in mind that non-numeric and granular
informationcanbeconvenientlyformalizedbymeansoffuzzysets.Thegraduality
of membership values is a highly appealing feature which is in rapport with the
descriptors of objectives, constraints, and priorities being quite often conveyed in
natural language. Type-2 fuzzy sets help address existing variability within the
scope of membership functions of individual fuzzy sets by admitting that such
grades are no longer single numeric values but rather information granules them-
selves. This gives rise to granular fuzzy sets. In particular, if these granular
descriptorsarefuzzysetsdefinedin[0,1]orareregardedasintervalsin[0,1],we
refertothemasfuzzysetsoftype-2.Type-2fuzzysetshaveestablishedthemselves
as one of the most actively exercised directions in the theory and applications of
fuzzy sets. It is quite likely that this direction of research will continue to grow
intensively in the coming years.
Qin’s and Liu’s monograph contributes to this rapidly growing area and brings
newandessentialresultsinthedisciplineoftype-2fuzzysets.Theauthorsofferan
authoritativetreatiseontheessentialtopics,bothatthetheoreticalandappliedend.
In a systematic and logically organized way, this book exposes the reader to the
essentials of the theory of type-2 fuzzy sets, methodology, algorithms, and their
applications. The theoretical investigations bring us the essentials of the concept
and processing of type-2 fuzzy sets including operations, type reduction, and var-
ious ranking methods. In the sequel, the topic of multiple criteria decision-making
v
vi Foreword
is covered, followed by an extensive discussion on aggregation operations
(including various types of means). Numerous techniques of decision-making are
carefully generalized by bringing the ideas of type-2 fuzzy sets; this concerns
well-known methods including TOPSIS, analytical network process, TODIM, and
VIKOR. The application part of this book is well aligned with the methodological
andalgorithmicconsiderations.Compellingcasestudiesindecisionproblemssuch
asurbanrailtransitevaluation,supplierselection,high-techinvestment,evaluation
of emergency material supplier selection are covered in depth.
Theauthorshaveachievedalot:Alongwiththeextensivecoverageofthearea,
this book comes with convincing motivation and solid, well-supported arguments.
Algorithmic aspects are lucidly presented. Furthermore, an important balance
between the theory and the applied aspects has been achieved.
In sum, this is a timely publication that will appeal to all researchers and
practitioners interested in both theoretically inclined and application-oriented
studies on type-2 fuzzy sets.
Edmonton, Canada Witold Pedrycz
Preface
Type-2 fuzzy set theory was originally introduced by Zadeh (1975) and further
developedbyMendel(1999),whichcanberegardedasoneofthemostusefuland
efficientmethodologiestohandlecomplexorhigher-orderuncertaintyinformation.
It opens new perspectives for research on multiple criteria decision-making under
type-2fuzzyenvironments.Recently,type-2fuzzydecision-makinghasbeenahot
branch in uncertainty decision analysis area.
Inthisbook,wegiveathoroughandsystematicintroductiontothelateststudies
on type-2 fuzzy decision-making theory and also used these methods to various
decision applications, such as supplier selection and group recommendation sys-
tems. This book is organized into eleven chapters, which are listed as follows:
Chapter1firstintroducesthebasicconceptoftype-2fuzzysetsanditsoperations
and then reviews some classical type reduction methodologies like Karnik and
Mendel(KM)algorithm.Inaddition,therankingmethodsfortype-2fuzzysetsare
alsointroducedsuchasKMcentroidrankingmethod,signed-baseddistanceranking
method,and ranking method based onpossibility mean and variation coefficient.
Chapter2mainlyintroducesmultiplecriteriadecision-makingwithtype-2fuzzy
information. First, we give the comparison of multiple criteria decision-making
(MCDM)andmultipleobjectivedecision-making(MODM).Andthen,somebasic
informationaggregationoperatorsfortype-2fuzzyinformationarereviewed,which
include linguistic weighted average (LWA), analytical solution for LWA, interval
type-2 fuzzy ordered weighted averaging (OWA). Finally, the research on type-2
fuzzydecision-makingiselaboratedandthetrendontype-2fuzzydecision-making
is analyzed.
Chapter 3 introduces interval type-2 fuzzy aggregation operators based on
Maclaurin means and its extensions, such as interval type-2 fuzzy Maclaurin
symmetric mean (MSM) operator, interval type-2 fuzzy dual Maclaurin symmetric
mean (DMSM) operator, interval type-2 fuzzy exponential Maclaurin symmetric
mean operator. In addition, the properties and theorems of those operators are
given. Furthermore, we apply these aggregation operators to MCDM with interval
type-2 fuzzy information. And two examples on paper quality evaluation of
Sciencepaper online and personalized tourism recommendation are proposed.
vii
viii Preface
Chapter 4 introduces a new method to handle multiple attribute group
decision-makingproblemsbasedoncombinedrankingvalue(CRV)underinterval
type-2 fuzzy environment. We put forward three ranking methods to calculate the
ranking value of IT2FSs based on arithmetic average (AA) operator, geometric
average (GA) operator, and harmonic average (HA) operator, respectively, and
discuss some of its properties. By proposing the three types of ranking value
methodsanditscorrespondingintervaltype-2fuzzyentropy,anewapproachbased
on the principle of combinatorial optimization with ranking entropy and the least
squares for determining attribute weight is given. Finally, a practical example of
urban rail transit evaluation is provided to illustrate the practicality and effective-
ness of the proposed method, and comparative analyses are performed.
Chapter 5 proposes an analytical solution to fuzzy TOPSIS method based on
KM algorithm. Some properties are discussed, and the computation procedure for
the proposed analytical solution is given as well. Compared with the existing
TOPSIS method for personnel selection problem, it obtains accurate fuzzy relative
closeness instead of the crisp point or approximate fuzzy relative closeness esti-
mate.Itcanbothavoidinformationlossandkeepcomputationalefficiencytosome
extent. Moreover, the global picture offuzzy relative closeness provides a way to
furtherdiscusstheinnerpropertiesoffuzzyTOPSISmethod.Detailedcomparisons
with approximate fuzzy relative closeness method are provided in personnel
selection application.
Chapter 6 integrates the analytical network process (ANP) method and the
VIKOR method under interval type-2 fuzzy environment to solve supplier evalu-
ation problems in sustainable supplier chain management. The proposed method
consists of two stages. First, we obtained the weights of criteria via the ANP
method. And then, based on the weights of criteria presented in stage 1, a com-
promise solution will be proposed by using the VIKOR method. A numerical
example is presented to show the detailed decision process. In addition, a com-
parativeanalysiswithintervaltype-2fuzzyANPmethodandintervaltype-2fuzzy
TOPSIS method is also presented to verify the validity of the proposed method.
Chapter 7 extends the TODIM (an acronym in Portuguese of interactive and
multi-criteria decision-making)technique tosolve multiple criteria group decision-
making (MCGDM) problems within the context of interval type-2 fuzzy sets and
present its application to green supplier selection problem. First, we introduce a
new distance measure based on the fuzzy logic and a-cut level. Then, an extended
novel TODIM method based on prospect theory to solve MCGDM problem under
IT2FSs environment is developed. Finally, a green supplier selection example is
provided to demonstrate the usefulness of the proposed method. Furthermore, a
sensitivity analysis carried out with the aid of granular computing and the com-
parative analysis with TOPSIS technique are also performed.
Chapter 8 extends the linear programming techniques to multidimensional
analysis of preference (LINMAP) method to solve MCGDM problems within the
context of interval type-2 fuzzy sets, in which all the attributes and the preference
relations are represented by interval type-2 fuzzy sets and its weights of attributes
information are incomplete known. First, we introduce a new distance measure
Preface ix
basedonthecentroidinterval.Then,weconstructthelinearprogrammingmodelto
determinetheintervaltype-2fuzzypositiveidealsolutionandcorrespondingcriteria
weight vector. Based on which, an extended LINMAP method to interval type-2
fuzzyenvironmentisdeveloped.Finally,asupplierselectionexampleisprovidedto
demonstrate theusefulness of theproposed method.
Chapter9introducestheintervaltype-2fuzzydecision-makingmethodbasedon
prospect theory and the VIKOR method. Motivated by the idea of the VIKOR
methodandtheprospecttheory,anextendedintervaltype-2fuzzyVIKORmethod
based ontheprospecttheorytohandle MADM withinintervaltype-2fuzzy sets is
developed. We define a new distance measure for interval type-2 fuzzy sets and
developanovelintervaltype-2fuzzyVIKORmethodbasedontheprospecttheory.
In addition, a numerical example that concerns high-tech investment evaluation to
illustrate the practicality and validity of the proposed method is included.
Chapter 10 introduces an interval type-2 fuzzy decision-making method based
ongranularcomputing.Then,ascoringmatrixfillingmethodbasedoninformation
granular optimization is proposed. Finally, we give a new interval type-2 fuzzy
multi-criteria recommendation algorithm based on best worst method (BWM) and
MULTIMOORA.
Chapter11introducesanovelintervaltype-2fuzzyemergencydecision-making
method,whichintegratesBWMandtheCOPRAStodealwithemergencymaterial
supplierselection.First,animprovedBWMweightsolutionmodelwithanoptimal
allocation of information granularity is developed. Then, a two-stage combined
ranking method based on aggregation operator for interval type-2 fuzzy set is pro-
posed. Third, an extended COPRAS method for emergency material supplier
selectionisdeveloped.Finally,anumericalexampleconcerningemergencymaterial
supplier selection isshown to prove the applicability ofthe proposed method.
Thisbookissuitablefortheengineers,technicians,andresearchersinthefields
offuzzy mathematics, operations research, decision analysis, information science,
management science and engineering, etc. It can also be used as a textbook for
postgraduate and senior-year undergraduate students of the relevant professional
institutions of higher learning.
The work was supported by the National Natural Science Foundation of China
(NSFC)underProject71701158,MinistryofEducationinChina(MOE)Projectof
HumanitiesandSocialSciences(17YJC630114),FundamentalResearchFundsfor
the Central Universities under the Projects 2017VI010 and 2018IVB036.
Special thanks to Prof. Witold Pedrycz at the University of Alberta for lots of
insightful ideas and great suggestions.
Wuhan, China Jindong Qin
Nanjing, China Xinwang Liu
April 2019