Decision Making with Spherical Fuzzy Sets: Theory and Applications

551 Pages·2020·8.863 MB·English

by  Cengiz Kahraman, Fatma Kutlu Gündoğdu

Studies in Fuzziness and Soft Computing
Cengiz Kahraman
Fatma Kutlu Gündoğdu   Editors
Decision
Making
with Spherical
Fuzzy Sets
Theory and Applications
Studies in Fuzziness and Soft Computing
Volume 392
Series Editor
Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences,
Warsaw, Poland
The series “Studies in Fuzziness and Soft Computing” contains publications on
various topics in the area of soft computing, which include fuzzy sets, rough sets,
neural networks, evolutionary computation, probabilistic and evidential reasoning,
multi-valuedlogic,andrelatedfields.Thepublicationswithin“StudiesinFuzziness
and Soft Computing” are primarily monographs and edited volumes. They cover
significant recent developments in the field, both of a foundational and applicable
character. An important feature of the series is its short publication time and
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More information about this series at http://www.springer.com/series/2941
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Cengiz Kahraman Fatma Kutlu G ndo du
(cid:129)
Editors
Decision Making
with Spherical Fuzzy Sets
Theory and Applications
123
Editors
CengizKahraman Fatma KutluGündoğdu
Department ofIndustrial Engineering TurkishAir ForceAcademy
Faculty of Management National Defence University
Istanbul TechnicalUniversity Istanbul,Turkey
Istanbul,Turkey
ISSN 1434-9922 ISSN 1860-0808 (electronic)
Studies in FuzzinessandSoft Computing
ISBN978-3-030-45460-9 ISBN978-3-030-45461-6 (eBook)
https://doi.org/10.1007/978-3-030-45461-6
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Preface
The fuzzy set theory, introduced by Lotfi A. Zadeh in 1965, had enclosed a lot of
ground with excellent achievements in almost all branches of science. It found
many application areas in both theoretical and practical studies from engineering
areatoartsandhumanities,fromcomputersciencetohealthsciences,andfromlife
sciencestophysicalsciences.Inthisbook,anewextensionoffuzzysets,entitledas
spherical fuzzy sets, is introduced by pioneer researchers with different points of
view and different research areas. This book consists of an Introduction and three
parts.Thefirstpartinvolvessevenchapterspresentingvaluablecontributionsonthe
elements of spherical fuzzy theory such as spherical fuzzy numbers, operational
laws, new aggregation operators, similarity measures, and spherical fuzzy graphs.
The second part contains 11 chapters. These chapters include spherical fuzzy
decision-making methods and different applications to the real-life problems.
Finally,thelastpartwhichcontainsfourchaptersisonmathematicalprogramming
with spherical fuzzy sets.
Introductiondiscussestheemergenceoffuzzysetsfromahistoricalperspective.
In this Introduction, a comprehensive literature review on the fuzzy set theory is
realized. In the recent years, ordinary fuzzy sets have been extended to new types,
and these extensions have been employed in many areas such as mathematics,
energy, environment, medicine, economics, and decision sciences. This literature
review also analyzes the chronological development of these extensions.
The first chapter in the first part of the book deals with the mathematics of
spherical fuzzy theory. In this chapter, single-valued spherical fuzzy sets and
interval-valued spherical fuzzy sets are introduced with their score and accuracy
functions; arithmetic and aggregation operations such as spherical fuzzy weighted
arithmetic mean operator and interval-valued spherical fuzzy geometric mean
operator. The second chapter is on preliminaries of interval-valued spherical fuzzy
sets. The interval-valued spherical fuzzy sets, operational laws, and aggregation
operators with their properties are introduced in this chapter. The proposed
aggregation operators are also applied toa decision-makingproblem tochoose the
best station which examines the quality of air. The third chapter introduces
spherical trapezoidal fuzzy numbers (STF numbers) and spherical triangular fuzzy
v
vi Preface
numbers (STrF numbers) with laws of their arithmetic operations and their prop-
erties. By utilizing the STF numbers and STrF numbers, two multi-criteria
decision-making methods are developed. The fourth chapter introduces spherical
fuzzy Bonferroni mean (SFBM) and spherical fuzzy normalized weighted
Bonferroni mean (SFNWBM). Based on the proposed aggregation operator
(SFNWBM), it presents an approach for multi-criteria group decision-making
problems under the spherical fuzzy environment. The fifth chapter includes novel
Dice similarity measures of spherical fuzzy sets. This chapter also presents the
generalizedDicesimilaritymeasure-basedmultipleattributegroupdecision-making
models under spherical fuzzy environment. The sixth chapter describes spherical
fuzzy soft sets (SFSSs) with their properties. This chapter shows that DeMorgan’s
lawsarevalidinSFSStheory.Also,itgivesanalgorithmtosolvedecision-making
problems based on adjustable soft discernibility matrix. The seventh chapter pre-
sents certain concepts of spherical fuzzy graphs and describes various methods
oftheirconstruction.Itcomputesdegreeandtotaldegreeofsphericalfuzzygraphs
withtheirimportantproperties.Inaddition,thischaptershowssomeapplicationsof
spherical fuzzy graphs to decision making.
The first chapter of the second part of the book is on spherical fuzzy TOPSIS
method,andthismethodisusedinsolvingamultiplecriteriaselectionproblemfor
optimal site selection of electric vehicle charging station to verify the developed
approach. The second chapter proposes a novel spherical fuzzy VIKOR method.
SupplierselectionproblemissolvedbyusingsphericalfuzzyVIKORwiththefour
implementations, and the results are compared with the results of the spherical
fuzzy TOPSIS. The third chapter presents simple additive weighting (SAW) and
weighted product methods (WPM) to their spherical fuzzy versions. Scoring
methods are the most frequently used multi-attribute decision-making methods
because of their easiness and effectiveness. In this chapter, single-valued and
interval-valued spherical SAW and WPM methods are applied to the selection of
insuranceoptions.Thefourthchapterutilizesthesphericalfuzzysets(SFSs)forthe
applicability of the available data for the WASPAS method. In this study, a
multi-criteriadecision-makingmethod,WASPAS,basedonsingle-valuedspherical
fuzzy sets is applied for the prioritization of the manufacturing challenges of a
contract manufacturing company by considering evaluationsof agroup ofexperts.
The fifth chapter is on livability indices which help to understand how a place is
livable. In this chapter, COmbinative Distance-based ASsessment (CODAS)
methodisextendedtoitsSphericalCODASversionforhandlingtheimpreciseness
and vagueness in human thoughts. The applicability of the methodology is illus-
trated through the assessment of livability index of suburban districts. Sensitivity
analysis demonstrates the robustness of the decision-making methodology. The
sixth chapter is on Industry 4.0, which connects new technologies providing flex-
ibility in manufacturing where the conditions change rapidly. Evaluating compa-
nies’ performance based on Industry 4.0 is a complex multi-criteria problem
includingbothquantitativeandqualitativefactors.AnovelfuzzyMULTIMOORA
method based on interval-valued spherical fuzzy sets is proposed to evaluate the
performances of companies using Industry 4.0 technologies. The seventh chapter
Preface vii
extendstheanalytichierarchyprocess(AHP)usingSFSs.Intheproposedmethod,
SFSsareusedtoconstructthepairwisecomparisonmatrices.Theproposedmethod
is used to solve a case study in global supplier selection based on SFSs and
intuitionistic fuzzy sets (IFSs) for comparative purposes. The eighth chapter is on
generalized three-dimensional spherical fuzzy sets introduced by Kutlu Gündoğdu
and Kahraman. The authors propose spherical fuzzy analytic hierarchy process
method, which is extended to interval-valued spherical fuzzy AHP method. The
proposedmethodisusedtocomparetheserviceperformancesofseveralhospitals.
The method is designed to analyze the service quality in the healthcare industry
based on SERVQUAL dimensions. The ninth chapter extends the conventional
PROMETHEE method into its spherical fuzzy version. In the proposed method,
both the weights of the criteria and the preference relations are SFSs. The relative
degree of closeness is used to determine the preference indices. Two examples are
solved to illustrate the applicability and efficiency of the proposed method in
solving MCDM problems. The tenth chapter is on the usage of spherical fuzzy
quality function deployment for the design of delivery drones. The important rat-
ings and global weights of customer requirements and improvement directions of
designrequirementsarerepresentedbySFSs.Sphericalfuzzyaggregationoperators
are used to aggregate the opinions of different decision-makers. The eleventh
chapter is on the design of mobile phone applications based on mobile Internet
usage.Thefactthattheseinvestmentsshouldbeutilizedbymanyusershasbecome
animportantagendaofbusinessplansformanybrands.Anewmethodisproposed
to decide which design parameters are affective for the related mobile application
and to determine the importance degree of the design parameters. The methods
including Kano model, quality function deployment, and spherical fuzzy sets are
integrated into the proposed method.
Thefirstchapterofthethirdandlastpartofthebookdealswithsphericalfuzzy
linear programming problem (SFLPP) in which the different parameters are rep-
resented by spherical fuzzy numbers. The crisp version of the SFLPP is obtained
with the aid of positive, neutral, and negative membership degrees. Furthermore,
thesphericalfuzzyoptimizationmodelispresentedtosolvetheSFLPP.Thesecond
chapter in this part proposes a new algorithm based on spherical fuzzy sets called
spherical fuzzy multi-objective programming problem (SFMOLPP).
TheSFMOLPPinevitablyinvolvesthedegreeofneutralityalongwithpositiveand
negative membership degrees of the element into the feasible solution set. It also
generalizes the decision set by imposing the restriction that the sum of squares of
each membership function must be less than or equal to one. The attainment of
achievement function is determined by maximizing the positive membership
function and minimization of neutral and negative membership function of each
objective function under the spherical fuzzy decision set. The third chapter is on
spherical fuzzy goal programming problem (SFGP). The SFGP unavoidably
involves the degree of neutrality along with truth and a falsity membership degree
of the element into the feasible decision set. The fourth chapter presents a new
algorithm based on spherical fuzzy sets called spherical fuzzy geometric pro-
gramming problem (SFGPP) together with several numerical examples.
viii Preface
We hope that this book will provide a useful resource of ideas, techniques, and
methods for the development of the spherical fuzzy set theory. We are grateful to
the referees whose valuable and highly appreciated works contributed to select the
high-quality chapters published in this book. We would like to also thank Prof.
JanuszKacprzyk,theeditorofStudiesinFuzzinessandSoftComputingatSpringer
for his supportive role in this process.
Istanbul, Turkey Cengiz Kahraman
Fatma Kutlu Gündoğdu
From Ordinary Fuzzy Sets to Spherical Fuzzy
Sets
Abstract Fuzzysetshaveagreatprogressineveryscientificresearcharea.Itfound
many application areas in both theoretical and practical studies from engineering
areatoartsandhumanities,fromcomputersciencetohealthsciences,andfromlife
sciences to physical sciences. In this paper, a comprehensive literature review on
the fuzzy set theory is realized. In the recent years, ordinary fuzzy sets have been
extended to new types offuzzy sets, and these extensions have been used in many
areas such as energy, medicine, material, economics, and pharmacology sciences.
This literature review also analyzes the chronological development of these
extensions. In the last section of the paper, we present our new theory entitled
spherical fuzzy sets theory.
Introduction
Thepioneerofthefuzzysettheory,LotfiZadehpublishedthefirstpaperonhisnew
theorythatisawayofhandlinguncertaintybyrepresentingeveryelementintheset
together with a membership degree in 1965. In the real world, we encounter situa-
tions that we cannot determine whether the state is true or false. The fuzzy logic
providesa veryvaluable tool for reasoningin these situations.In thisway, we can
representthe truthinessand falsity of any situation. In Boolean system, truth value
1.0representsabsolutetruthvalueand0.0representsabsolutefalsevalue.However,
infuzzylogic,thereisanintermediatevaluetoopresentwhichispartiallytrueand
partiallyfalse.Between1965and1975,Zadehextendedthefoundationofthefuzzy
set theory by launching fuzzy similarity relations, fuzzy decision making, and lin-
guistichedges.In1970s,someresearchgroupsinJapanstartedtostudythefuzzyset
theory.ThesuccessoffuzzylogicwasobservedinJapanatthebeginningof1980s,
and this led to revitalization in fuzzy logic in the USA at the end of 1980s. Along
with the emergence of the fuzzy set theory, many objections to the theory have
appeared. Nevertheless, the fuzzy logic showed its influence through the real tech-
nology applications. There are many technology applications in the real world by
using fuzzy logic and sets. Fuzzy logic is used in the aerospace field for altitude
control of spacecraft and satellite. It has employed in the automotive system for
speedcontrolandtrafficcontrol.Itisalsousedfordecision-makingsupportsystems
ix