Decision making (DM) is an important process encountered in every moment of life. Since it is difficult to interpret life depending on a single criterion, Multi-Criteria Decision Making (MCDM) enables to make decisions easier by creating appropriate choice in situations of uncertainty, complexity, and conflicting objectives. Therefore, we have studied the Analytic Hierarchy Process (AHP) which is one of the MCDM methods based on binary comparison logic. When uncertainties concerning the nature of life are considered, the solution procedure of AHP has been addressed by using Interval Type-2 Fuzzy Numbers (IT2FN)s to obtain more realistic results. The usability of AHP with IT2FN is increased by amplifying hierarchy with sub-levels. Since sub-criterion may also need to be evaluated on sub-criteria in some cases of real multi-criteria problems, it is explicitly essential that each of sub-sub-criterion is included in the hierarchy at the own level in the real sense. In this paper, a new multilevel type-2 fuzzy AHP method is expanded by adding sub-criteria to the Interval Type-2 Fuzzy AHP (IT2FAHP) method developed by Kahraman et al. [C. Kahraman, B. Öztayşi, İ. Sarı and B. Turanoğlu, Fuzzy analytic hierarchy process with interval type-2 fuzzy sets, Knowledge-Based Systems59 (2014), 48–57.]. Thanks to the extended method, another aim is to ensure that even complex situations that have multiple levels can be solved simply. Also, the proposed method is illustrated with a portfolio selection problem. Thus, the AHP method with type-2 fuzzy sets is carried out to the portfolio selection problem, which is in the scope of finance theory, for the first time in the literature.
BransJ.-P., L’ingénierie de la décision: élaboration d’instruments d’aide à la décision. La méthode PROMETHEE, Presses de l’Université Laval, (1982).
2.
BuckleyJ.J., Fuzzy hierarchical analysis, Fuzzy Sets and Systems17 (1985), 233–247.
3.
CelikE. and AkyuzE., An interval type-2 fuzzy AHP and TOPSIS methods for decision-making problems in maritime transportation engineering: The case of ship loader, Ocean Engineering155 (2018), 371–381.
4.
CelikE., GulM., AydinN., GumusA.T. and GuneriA.F., A comprehensive review of multi criteria decision making approaches based on interval type-2 fuzzy sets, Knowledge-Based Systems85 (2015), 329–341.
5.
CelikE., GumusA.T. and ErdoganM., A New Extension of the ELECTRE Method Based Upon Interval Type-2 Fuzzy Sets for Green Logistic Service Providers Evaluation, Journal of Testing and Evaluation44(5) (2016), 1813–1827.
6.
OnarS.C., OztaysiB. and KahramanC., Strategic decision selection using hesitant fuzzy TOPSIS and interval type-2 fuzzy AHP: A case study, International Journal of Computational Intelligence Systems7(5) (2014), 1002–1021.
7.
ChenS.-J. and HwangC.-L., Fuzzy Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag, (1992).
8.
ChenS.-M. and LeeL.-W., Fuzzy multiple attributes group decision making based on the interval type-2 TOPSIS method, Expert Systems with Applications37 (2010), 2790–2798.
9.
ChenT.-Y., An interval type-2 fuzzy LINMAP method with approximate ideal solutions for multiple criteria decision analysis, Information Sciences297 (2015), 50–79.
10.
CorrenteS., GrecoS. and SowinskiR., Multiple Criteria Hierarchy Process with ELECTRE and PROMETHEE, Omega41 (2013), 820–846.
11.
DucksteinL. and OpricovicS., Multiobjective optimization in river basin development, Water Resources Research16 (1980), 14–20.
12.
EcerF., Multi-criteria decision making for green supplier selection using interval type-2 fuzzy AHP: a case study of a home appliance manufacturer. Operational Research (2020). https://doi.org/10.1007/s12351-020-00552-y.
13.
EltonE.J. and GruberM.J., Modern portfolio theory, 1950 to date, Journal of Banking & Finance21 (1997), 1743–1759.
14.
EneaM. and PiazzaT., Project Selection by Constrained Fuzzy AHP, Fuzzy Optimization and Decision Making3 (2004), 39–62.
15.
FontelaE., GabusA., World Problems an Invitation to Further Thought within the Framework of DEMATEL, Battelle Geneva Research Centre Switzerland Geneva (1972).
16.
GomesL.F.A.M. and LimaM.M.P.P., From modeling individual preferences to multicriteria ranking of discrete alternatives: A look at prospect theory and the additive difference model, Foundations of Computing and Decision Sciences17(3) (1992), 171–184.
17.
GomesL.F.A.M. and LimaM.M.P.P., TODIM: Basics and application to multicriteria ranking of projects with environmental impacts, Foundations of Computing and Decision Sciences16(4) (1992), 113–127.
18.
GulgorG., IMKB 30 Endeksinde Klasik ve Bulanik Analitik Hiyerarşi Süreci ile Portföy Seçimi ve Performanslarnn Karşılaştırılması, MSc Dissertation, Eskişehir Osmangazi UÜniversitesi, (2010).
19.
HoW., Integrated analytic hierarchy process and its applications A literature review, European Journal of Operational Research186 (2008), 211–228.
20.
HwangC.-L. and YoonK., Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag, (1981).
21.
KahramanC., CebeciU. and RuanD., Multi-attribute comparison of catering service companies using fuzzy AHP: The case of Turkey, International Journal of Production Economics87 (2004), 171–184.
22.
KahramanC., ÖztayşiB., Sarıİ. and TuranoğluB., Fuzzy analytic hierarchy process with interval type-2 fuzzy sets, Knowledge-Based Systems59 (2014), 48–57.
23.
LaarhovenP.J.M. and PedryczW., A fuzzy extension of Saatys priority theory, Fuzzy Sets and Systems11 (1983), 229–241.
24.
MarkowitzH., Portfolio Selection, The Journal of Finance7(1) (1952), 77–91.
25.
MendelJ., JohnR. and LiuF., Interval type-2 fuzzy logic systems made simple, IEEE Transactions on Fuzzy Systems14(16) (2006), 808–821.
26.
MohajeriN. and AminG.R., Railway station site selection using analytical hierarchy process and data envelopment analysis, Computers & Industrial Engineering59 (2010), 107–114.
27.
OztaysiB., A group decision making approach using interval type-2 fuzzy ahp for enterprise information systems project selection, Journal of Multiple-Valued Logic and Soft Computing24 (2015), 475–500.
28.
PaksoyT., PehlivanN.Y. and KahramanC., Organizational strategy development in distribution channel management using fuzzy AHP and hierarchical fuzzy TOPSIS, Expert Systems with Applications39 (2012), 2822–2841.
29.
QinJ., LiuX. and PedryczW., An extended TODIM multicriteria group decision making method for green supplier selection in interval type-2 fuzzy environment, European Journal of Operational Research258 (2017), 626–638.
30.
RahmanM.A., RustebergB., GoguR.C., FerreiraJ.P.L. and SauterM., A new spatial multi-criteria decision support tool for site selection for implementation of managed aquifer recharge, Journal of Environmental Management99 (2012), 61–75.
31.
RoyB., Classement et choix en présence de points de vue multiples (la méthode ELECTRE),rationelle (RIRO), La Revue d’ Informatique et de Recherche Opérationelle (RIRO)8 (1968), 57–75.
32.
SaatyT.L., The Analytic Hierarchy Process, McGraw-Hill, New York, (1980).
33.
SaatyT.L., The Analytic Network Process, Pittsburgh: RWS Publications, (2001).
34.
SaatyT.L., The ANP for DecisionMaking with Dependence and Feedback, USA: RWS Publications, (1996).
35.
SaatyT.L., RogersP.C. and PellR., Portfolio selection through hierarchies, The Journal of Portfolio Management6(3) (1980), 16–21.
36.
SonerO., CelikE. and AkyuzE., Application of AHP and VIKOR methods under interval type 2 fuzzy environment in maritime transportation, Ocean Engineering129 (2017), 107–116.
37.
SrinivasanV. and ShockerA.D., Linear programming techniques for multidimensional analysis of preference, Psychometrika38 (1973), 337–342.
38.
TiryakiF. and AhlatciogluB., Fuzzy portfolio selection using fuzzy analytic hierarchy process, Information Sciences179 (2009), 53–69.
39.
TyagiS., AgrawalS., YangK. and YingH., An extended Fuzzy-AHP approach to rank the influences of socializationexternalization-combination-internalization modes on the development phase, Applied Soft Computing52(52) (2017), 505–518.
40.
UygunÖ., KaçamakH. and KahramanÜ.A., An integrated DEMATEL and Fuzzy ANP techniques for evaluation and selection of outsourcing provider for a telecommunication company, Computers & Industrial Engineering86 (2015), 137–146.
41.
VaidyaO.M. and KumarS., Analytic hierarchy process: An overview of applications, European Journal of Operational Research169 (2006), 1–29.
42.
YigiterS.Y. and AkkaynakB., Modern Portföy Teorisi: Alternatif Yatrm Araçlar ile Bir Uygulama, Kahramanmaras Sütçü Imam Üniversitesi Sosyal Bilimler Dergisi14 (2017), 285–300.
43.
YuS.-M., WangJ. and WangJ.-Q., An Interval Type-2 Fuzzy Likelihood-Based MABAC Approach and Its Application in Selecting Hotels on a Tourism Website, International Journal of Fuzzy Systems19 (2017), 47–61.
44.
ZadehL.A., Fuzzy Sets, Information and Control8 (1965), 338–353.
45.
ZadehL.A., The concept of a linguistic variable and its application to approximate reasoning-I, Information Sciences8 (1975), 199–249.
46.
ZhangK., ZhanJ. and WuW.-Z., Novel fuzzy rough set models and corresponding applications to multi-criteria decisionmaking, Fuzzy Sets and Systems383 (2020), 92–126.
47.
ZhouP., ZhouP., YükselS., DinçerH. and UluerG.S., Balanced Scorecard-Based Evaluation of Sustainable Energy Investment Projects with IT2 Fuzzy Hybrid Decision Making Approach, Energies13(1) (2019), 1–20.
