New aggregation functions for spherical fuzzy sets and the spherical fuzzy distance within the MULTIMOORA method with applications

Abstract

This article develops a novel approach for multi-objective optimization on the basis of ratio analysis plus the full multiplicative form (MULTIMOORA) using spherical fuzzy sets (SFSs) to obtain proper evaluations. SFSs surpass Pythagorean and intuitionistic fuzzy sets in modeling human cognition since the degree of hesitation is expressed explicitly in a three-dimensional space. In the spherical fuzzy environment, the implementation of the MULTIMOORA encounters two major problems in the aggregation operators and the distance measures that might lead to erroneous results. The extant aggregation operators in some cases can result in a biased evaluation. Therefore, two aggregation functions for SFSs are proposed. These functions guarantee balanced evaluation and avoid false ranking. In the reference point technique, when comparing SFSs, being closer to the ideal solution does not necessarily imply an SFS with a better score. To make up for this drawback, two reference points are employed instead of one, and the distance is not expressed as a crisp value but as an SFS instead. To overcome the disadvantages of the dominance theory in large-scale applications, the results of the three techniques are aggregated to get the overall utility on which the ranking is based. The illustration and validation of the proposed spherical fuzzy MULTIMOORA are examined through two applications, personnel selection, and energy storage technologies selection. The results are compared with the results of other methods to explicate the adequacy of the proposed method and validate the results.

Keywords

Spherical fuzzy sets / Aggregation functions / Multi-criteria decision-making / MULTIMOORA / Personnel selection / Energy storage technologies

References

[1] DeliceE.K., CanG.F.. A new approach for ergonomic risk assessment integrating KEMIRA, best–worst and MCDM methods. Soft Comput., 2020, 24(19):15093-15110

[2] AkramM., LuqmanA., AlcantudJ.C.R.. An integrated ELECTRE-I approach for risk evaluation with hesitant Pythagorean fuzzy information. Expert Syst. Appl., 2022, 200

[3] ChenZ., ZhongP., LiuM., MaQ., SiG.. An integrated expert weight determination method for design concept evaluation. Sci. Rep., 2022, 12(1

[4] AbdulD., WenqiJ., TanveerA.. Prioritization of renewable energy source for electricity generation through AHP-VIKOR integrated methodology. Renew. Energy, 2022, 184: 1018-1032

[5] NguyenV.T., HaiN.H., LanN.T.K.. Spherical fuzzy multicriteria decision-making model for wind turbine supplier selection in a renewable energy project. Energies, 2022, 15 3

[6] IordacheM., PamucarD., DeveciM., ChisalitaD., WuQ., IordacheI.. Prioritizing the alternatives of the natural gas grid conversion to hydrogen using a hybrid interval rough based Dombi MARCOS model. Int. J. Hydrog. Energy, 2022, 47 19):10665-10688

[7] DeveciM., PamucarD., GokasarI., IsikM., CoffmanD.M.. Fuzzy Einstein WASPAS approach for the economic and societal dynamics of the climate change mitigation strategies in urban mobility planning. Struct. Chang. Econ. Dyn., 2022, 61: 1-17

[8] HabibA., AkramM., KahramanC.. Minimum spanning tree hierarchical clustering algorithm: a new Pythagorean fuzzy similarity measure for the analysis of functional brain networks. Expert Syst. Appl., 2022, 201

[9] KaurG., GargH.. A new method for image processing using generalized linguistic neutrosophic cubic aggregation operator. Complex Intell. Syst., 2022

[10] GaraiT., GargH.. Multi-criteria decision making of water resource management problem (in Agriculture field, Purulia district) based on possibility measures under generalized single valued non-linear bipolar neutrosophic environment. Expert Syst. Appl., 2022, 205

[11] ZadehL.A.. Fuzzy sets. Inf. Control, 1965, 8(3):338-353

[12] ZadehL.A.. The concept of a linguistic variable and its applications to approximate reasoning. Inf. Sci., 1975, 8(3):199-249

[13] SamarandacheF.. Neutrosophy: Neutrosophic Probability, Set, and Logic: Analytic Synthesis & Synthetic Analysis, 1998 Rehoboth American Research Press

[14] AtanassovK.T.. Intuitionistic fuzzy sets. Fuzzy Sets Syst., 1986, 20(1):87-96

[15] CuongB.C., KreiovichV.. Picture fuzzy sets-a new concept for computational intelligence problems. 2013 Third World Congress on Information and Communication Technologies (WICT), 2013 1-6

[16] V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision (2009)

[17] TorraV.. Hesitant fuzzy sets. Int. J. Intell. Syst., 2010, 25(6):529-539

[18] YagerR.R., AbbasovA.M.. Pythagorean membership grades, complex numbers, and decision making. Int. J. Intell. Syst., 2013, 28(5):436-452

[19] YagerR.R.. Pythagorean membership grades in multicriteria decision making. IEEE Trans. Fuzzy Syst., 2014, 22(4):958-965

[20] GündoğduF.K., KahramanC.. Spherical fuzzy sets and spherical fuzzy TOPSIS method. J. Intell. Fuzzy Syst., 2019, 36(1):337-352

[21] MahmoodT., UllahK., KhanQ., JanN.. An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput. Appl., 2019, 31(11):7041-7053

[22] AshrafS., AbdullahS., MahmoodT., GhaniF., MahmoodT.. Spherical fuzzy sets and their applications in multi-attribute decision making problems. Journal of Intelligent and Fuzzy Systems, 2019 2829-2844

[23] AshrafS., AbdullahS., AslamM., QiyasM., KutbiM.A.. Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms. J. Intell. Fuzzy Syst., 2019, 36(6):6089-6102

[24] AshrafS., AbdullahS.. Spherical aggregation operators and their application in multiattribute group decision-making. Int. J. Intell. Syst., 2019, 34(3):493-523

[25] AshrafS., AbdullahS., MahmoodT.. Spherical fuzzy Dombi aggregation operators and their application in group decision making problems. J. Ambient Intell. Humaniz. Comput., 2020, 11(7):2731-2749

[26] FarrokizadehE., ShishavanS.A.S., DonyatalabY., Kutlu GundogduF., KahramanC.. Spherical fuzzy Bonferroni mean aggregation operators and their applications to multi-attribute decision making. Decision Making with Spherical Fuzzy Sets, 2021 111-134

[27] LiangD., LindaB.E., WangM., XuZ.. Hospital health-care delivery quality evaluation in Ghana: an integrated medical triangular fuzzy MULTIMOORA approach. Inf. Sci., 2022

[28] BrauersW.K.M., ZavadskasE.K.. Project management by multimoora as an instrument for transition economies. Technol. Econ. Dev. Econ., 2010, 16(1):5-24

[29] ZhangC., ChenC., StreimikieneD., BalezentisT.. Intuitionistic fuzzy MULTIMOORA approach for multi-criteria assessment of the energy storage technologies. Appl. Soft Comput., 2019, 79: 410-423

[30] BrauersW., ZavadskasE.K.. The MOORA method and its application to privatization in a transition economy. Control Cybern., 2006, 35(2):445-469 [Online]. Available: https://www.researchgate.net/publication/228345226

[31] DahooieJ.H., ZavadskasE.K., FiroozfarH.R., VanakiA.S., MohammadiN., BrauersW.K.M.. An improved fuzzy MULTIMOORA approach for multi-criteria decision making based on objective weighting method (CCSD) and its application to technological forecasting method selection. Eng. Appl. Artif. Intell., 2019, 79: 114-128

[32] Kutlu GündoğduF.. A spherical fuzzy extension of MULTIMOORA method. J. Intell. Fuzzy Syst., 2020, 38(1):963-978

[33] Kutlu GündoğduF., KahramanC.. A novel VIKOR method using spherical fuzzy sets and its application to warehouse site selection. J. Intell. Fuzzy Syst., 2019, 37(1):1197-1211

[34] LiangD., DarkoA.P., ZengJ.. Interval-valued Pythagorean fuzzy power average-based MULTIMOORA method for multi-criteria decision-making. J. Exp. Theor. Artif. Intell., 2020, 32(5):845-874

[35] BeliakovG., JamesS.. Averaging aggregation functions for preferences expressed as Pythagorean membership grades and fuzzy orthopairs. 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2014 298-305

[36] Kutlu GündoğduF., KahramanC.. A novel spherical fuzzy analytic hierarchy process and its renewable energy application. Soft Comput., 2020, 24(6):4607-4621

[37] SharafI.M., KhalilE.A.H.A.. A spherical fuzzy TODIM approach for green occupational health and safety equipment supplier selection. Int. J. Manag. Sci. Eng. Manag., 2021, 16: 1-13

[38] SharafI.M.. KahramanC., Kutlu GündoğduF.. Global supplier selection with spherical fuzzy analytic hierarchy process. Decision Making with Spherical Fuzzy Sets: Theory and Applications, 2021 Cham Springer 323-348

[39] SharafI.M.. KahramanC., Kutlu GündoğduF.. Spherical fuzzy VIKOR with SWAM and SWGM operators for MCDM. Decision Making with Spherical Fuzzy Sets: Theory and Applications, 2021 Cham Springer 217-240

[40] ÇolakM., Kayaİ.. Multi-criteria evaluation of energy storage technologies based on hesitant fuzzy information: a case study for Turkey. J. Energy Storage, 2020, 28

[41] GuneyM.S., TepeY.. Classification and assessment of energy storage systems. Renewable and Sustainable Energy Reviews, 2017 Amsterdam Elsevier 1187-1197

[42] KhanN., DilshadS., KhalidR., KalairA.R., AbasN.. Review of energy storage and transportation of energy. Energy Storage, 2019, 1 3

[43] StadlerI., SternerM.. Urban energy storage and sector coupling. Urban Energy Transition, 2018 Amsterdam Elsevier 225-244