Bivariate grid scale based multiple attribute evaluation technique (GAMETE) with incomplete information on weights
DOI: https://doi.org/10.3846/tede.2025.24346Abstract
In this paper, we have devised a novel Multiple Attribute Decision Making (MADM) method referred to as the bivariate Grid Scale based Multiple Attribute Evaluation Technique (GAMETE) method to deal with MADM decision problems involving tangible and intangible attributes under incomplete weight information. The proposed method innovatively incorporates an Attractiveness GRID Scale (AGRIDS) to evaluate intangible attributes, grounded in cognitive psychological principles – particularly the separability and independence of positive and negative aspects in human judgement. Additionally, a new bidimensional positional advantage operator (bi-pao) is introduced to compute the intangible attractiveness index. Further, linear programming models are formulated in order to construct the pairwise dominance matrix. Afterwards, we rank alternatives using a dominance intensity measure and the Boolean matrix. Furthermore, the proposed method is illustrated through a logistics center location problem. We also perform a comparison with several state-of-the-art linguistic Intuitionistic Fuzzy Sets (LIFS) and linguistic Pythagorean Fuzzy Sets (LPFS) based MADMs with the aim of showing the applicability and feasibility of the method suggested. Notably, GAMETE provides a multidimensional decision-making framework suitable for addressing complex technological and economic challenges where both quantitative and qualitative factors coexist. Its flexibility and interpretability make it a promising tool for real-world strategic decision scenarios.
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dominance measure, intangible attributes, incomplete weight information, Grid scale, Multiple Attribute Decision MakingHow to Cite
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Ali, Z., Hayat, K., & Pamucar, D. (2024). Analysis of coupling in geographic information systems based on WASPAS method for bipolar complex fuzzy linguistic Aczel-Alsina power aggregation operators. PLoS ONE, 19(9), Article e0309900. https://doi.org/10.1371/journal.pone.0309900
Al-Sharqi, F., Al-Quran, A., & Md. Rodzi, Z. (2024). Multi-attribute group decision-making based on aggregation operator and score function of bipolar neutrosophic hypersoft environment. Neutrosophic Sets and Systems, 61, Article 25. https://digitalrepository.unm.edu/nss_journal/vol61/iss1/25
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Ayyildiz, E. (2022). A novel Pythagorean fuzzy multi-criteria decision-making methodology for e-scooter charging station location-selection. Transportation Research Part D: Transport and Environment, 111, Article 103459. https://doi.org/10.1016/j.trd.2022.103459
Cacioppo, J. T., & Berntson, G. G. (1994). Relationship between attitudes and evaluative space: A critical review with emphasis on the separability of positive and negative substrates. Psychological Bulletin, 115(3), 401–423. https://doi.org/10.1037/0033-2909.115.3.401
Cacioppo, J. T., Berntson, G. G., Norris, C. J., & Gollan, J. K. (2012). The evaluative space model. In P. A. M. Van Lange, A. W. Kruglanski, & E. T. Higgins (Eds.), Handbook of theories of social psychology (Vol. 1, pp. 50–73). Sage Publications. https://doi.org/10.4135/9781446249215.n4
Çalış Boyacı, A., & Şişman, A. (2024). Location selection for waste disposal boxes: A geographic information systems based Pythagorean fuzzy multi criteria decision analysis. International Journal of Environmental Science and Technology, 21, 8577–8592. https://doi.org/10.1007/s13762-024-05573-0
Campagner, A., & Ciucci, D. (2017). Measuring uncertainty in orthopairs. In A. Antonucci, L. Cholvy, & Papini, O. (Eds.), Lecture notes in computer science: Vol. 10369. Symbolic and quantitative approaches to reasoning with uncertainty. ECSQARU 2017 (pp. 423–432). Springer. https://doi.org/10.1007/978-3-319-61581-3_38
Chakraborty, S., Raut, R. D., Rofin, T. M., & Chakraborty, S. (2024). On solving a healthcare supplier selection problem using MCDM methods in intuitionistic fuzzy environment. OPSEARCH, 61, 680–708. https://doi.org/10.1007/s12597-023-00733-1
Chen, Z., Liu, P., & Pei, Z. (2015). An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. International Journal of Computational Intelligence Systems, 8(4), 747–760. https://doi.org/10.1080/18756891.2015.1061394
Demir, G., & Ulusoy, E. I. (2024). Wind power plant location selection with fuzzy logic and multi-criteria decision-making methods. Computer and Decision Making: An International Journal, 1, 211–234. https://doi.org/10.59543/comdem.v1i.10713
Ecer, F., & Hashemkhani Zolfani, S. (2022). Evaluating economic freedom via a multi-criteria MEREC-DNMA model-based composite system: Case of OPEC countries. Technological and Economic Development of Economy, 28(4), 1158–1181. https://doi.org/10.3846/tede.2022.17152
Filip, F. G., Zamfirescu, C.-B., & Ciurea, C. (2017). Computer-supported collaborative decision-making. Springer. https://doi.org/10.1007/978-3-319-47221-8
Franco, C., Rodríguez, J. T., & Montero, J. (2015). Building the meaning of preference from logical paired structures. Knowledge-Based Systems, 83, 32–41. https://doi.org/10.1016/j.knosys.2015.03.005
Franco, C., Rodríguez, J. T., & Montero, J. (2017). Learning preferences from paired opposite-based semantics. International Journal of Approximate Reasoning, 86, 80–91. https://doi.org/10.1016/j.ijar.2017.04.010
Garg, H. (2018). Linguistic Pythagorean fuzzy sets and its applications in multi-attribute decision-making process. International Journal of Intelligent Systems, 33(6), 1234–1263. https://doi.org/10.1002/int.21979
Han, Q., Li, W., Lu, Y., Zheng, M., Quan, W., & Song, Y. (2020). TOPSIS method based on novel entropy and distance measure for linguistic Pythagorean fuzzy sets with their application in Multiple Attribute Decision Making. IEEE Access, 8, 14401–14412. https://doi.org/10.1109/ACCESS.2019.2963261
Hasheminasab, H., Hashemkhani Zolfani, S., Zavadskas, E. K., Kharrazi, M., & Skare, M. (2021). A circular economy model for fossil fuel sustainable decisions based on MADM techniques. Economic Research – Ekonomska Istraživanja, 35(1), 564–582. https://doi.org/10.1080/1331677X.2021.1926305
Hashemkhani Zolfani, S., Görçün, Ö. F., & Küçükönder, H. (2021). Evaluating logistics villages in Turkey using hybrid improved fuzzy SWARA (IMF SWARA) and fuzzy MABAC techniques. Technological and Economic Development of Economy, 27(6), 1582–1612. https://doi.org/10.3846/tede.2021.16004
Hezam, I. M., Mishra, A. K., Pamucar, D., Rani, P., & Mishra, A. R. (2024). Standard deviation and rank sum-based MARCOS model under intuitionistic fuzzy information for hospital site selection. Kybernetes, 53(10), 3727–3753. https://doi.org/10.1108/K-01-2023-0136
Hisoğlu, S., Çömert, R., Antila, M., Aman, R., & Huovila, A. (2025). Towards solar-energy-assisted electric vehicle charging stations: A literature review on site selection with GIS and MCDM methods. Sustainable Energy Technologies and Assessments, 75, Article 104193. https://doi.org/10.1016/j.seta.2025.104193
Işık, Ö., & Adalar, İ. (2025). A multi-criteria sustainability performance assessment based on the extended CRADIS method under intuitionistic fuzzy environment: A case study of Turkish non-life insurers. Neural Computing and Applications, 37(5), 3317–3342. https://doi.org/10.1007/s00521-024-10803-0_
Katranci, A., Kundakci, N., & Arman, K. (2025). Fuzzy SIWEC and fuzzy RAWEC methods for sustainable waste disposal technology selection. Spectrum of Operational Research, 3, 87–102. https://doi.org/10.31181/sor31202633
Larsen, J. T., Norris, C. J., McGraw, A. P., Hawkley, L. C., & Cacioppo, J. T. (2009). The evaluative space grid: A single-item measure of positivity and negativity. Cognition and Emotion, 23(3), 453–480. https://doi.org/10.1080/02699930801994054
Li, D., Zeng, W., &., Yin, Q. (2018). Novel ranking method of interval numbers based on the Boolean matrix. Soft Computing, 22, 4413–4122. https://doi.org/10.1007/s00500-017-2625-4
Lindquist, K. A., Satpute, A. B., Wager, T. D., Weber, J., & Barrett, L. F. (2016). The brain basis of positive and negative affect: Evidence from a meta-analysis of the human neuroimaging literature. Cerebral Cortex, 26(5), 1910–1922. https://doi.org/10.1093/cercor/bhv001
Lin, M., Wei, J., Xu, Z., & Chen, R. (2018). Multiattribute group decision-making based on linguistic pythagorean fuzzy interaction partitioned Bonferroni mean aggregation operators. Complexity, 2018, Article 9531064. https://doi.org/10.1155/2018/9531064
Lin, M., Huang, C., & Xu, Z. (2019). TOPSIS method based on correlation coefficient and entropy measure for linguistic Pythagorean fuzzy sets and its application to Multiple Attribute Decision Making. Complexity, 2019, Article 6967390. https://doi.org/10.1155/2019/6967390
Liu, P., & Shen, M. (2019). An extended C-TODIM method with linguistic intuitionistic fuzzy numbers. Journal of Intelligent & Fuzzy Systems, 37(3), 3615–3627. https://doi.org/10.3233/JIFS-182554
Luo, J., & Hu, M. (2023). A bipolar three-way decision model and its application in analyzing incomplete data. International Journal of Approximate Reasoning, 152, 94–123. https://doi.org/10.1016/j.ijar.2022.10.011
Meng, F., &. Dong, B. (2022). Linguistic intuitionistic fuzzy PROMETHEE method based on similarity measure for the selection of sustainable building materials. Journal of Ambient Intelligence and Humanized Computing, 13, 4415–4435. https://doi.org/10.1007/s12652-021-03338-y
Montero, J., Bustince, H., Franco, C., Rodriguez, J. T., Gómez, D., Pagola, M., Fernandez, J., & Barrenechea, E. (2014). Paired structures and bipolar knowledge representation (MSAP Working Paper Series No. 06/2014). University of Copenhagen, Department of Food and Resource Economics.
Moroza, N., & Jurgelane-Kaldava, I. (2019). Development and location of logistics centres: A systematic review of literature. Economics and Business, 33, 264–272. https://doi.org/10.2478/eb-2019-0019
Nila, B., & Roy, J. (2024). Analysing the key success factors of Logistics Center 4.0 implementation using improved Pythagorean fuzzy DEMATEL method. Arabian Journal for Science and Engineering, 49, 11883–11905. https://doi.org/10.1007/s13369-023-08398-0
Norris, C. J., Gollan, J., Berntson, G. G., & Cacioppo, J. T. (2010). The current status of research on the structure of evaluative space. Biological Psychology, 84(3), 422–436. https://doi.org/10.1016/j.biopsycho.2010.03.011
Osgood, C. E., Suci, G. J., & Tannenbaum, P. H. (1967). The measurement of meaning. University of Illinois Press.
Ou, Y., Yi, L., Zou, B., & Pei, Z. (2018). The linguistic intuitionistic fuzzy set TOPSIS method for linguistic multi-criteria decision makings. International Journal of Computational Intelligence Systems, 11, 120–132. https://doi.org/10.2991/ijcis.11.1.10
Pamucar, D. S., Tarle, S. P., & Parezanovic, T. (2018). New hybrid multi-criteria decision-making DEMATEL-MAIRCA model: Sustainable selection of a location for the development of multimodal logistics centre. Economic Research-Ekonomska Istraživanja, 31(1), 1641–1665. https://doi.org/10.1080/1331677X.2018.1506706
Pamucar, D., Torkayesh, A. E., Deveci, M., & Simic, V. (2022). Recovery center selection for end-of-life automotive lithium-ion batteries using an integrated fuzzy WASPAS approach. Expert Systems with Applications, 206, Article 117827. https://doi.org/10.1016/j.eswa.2022.117827
Patel, A., Jana, S., & Mahanta, J. (2023). Intuitionistic fuzzy EM-SWARA-TOPSIS approach based on new distance measure to assess the medical waste treatment techniques. Applied Soft Computing, 144, Article 110521. https://doi.org/10.1016/j.asoc.2023.110521
Rani, P., Mishra, A. R., Mardani, A., Cavallaro, F., Štreimikienė, D., & Khan, S. A. R. (2020). Pythagorean fuzzy SWARA–VIKOR framework for performance evaluation of solar panel selection. Sustainability, 12(10), Article 4278. https://doi.org/10.3390/su12104278
Rebai, A. (1994). Canonical fuzzy bags and bag fuzzy measures as a basis for MADM with mixed non cardinal data. European Journal of Operational Research, 78(1), 34–48. https://doi.org/10.1016/0377-2217(94)90120-1
Rebai, A., Aouni, B., & Martel, J.-M. (2006). A multi-attribute method for choosing among potential alternatives with ordinal evaluation. European Journal of Operational Research, 174(1), 360–373. https://doi.org/10.1016/j.ejor.2005.01.045
Rifle, A., Nedeljković, M., Božanić, D., Štilić, A., & Muhsen, Y. R. (2024). Evaluation of agricultural drones based on the COmpromise Ranking from Alternative SOlutions (CORASO) methodology. Engineering Review, 44(4), 77–90. https://doi.org/10.30765/er.2653
Souissi, M., & Hnich, B. (2022). A safe sequential screening technique for solving multi-attribute choice problems under ranked weights. Computational and Applied Mathematics, 41, Article 163. https://doi.org/10.1007/s40314-022-01843-0
Ulutaş, A., Popovic, G., Radanov, P., Stanujkic, D., & Karabasevic, D. (2021). A new hybrid fuzzy PSI-PIPRECIA-CoCoSo MCDM based approach to solving the transportation company selection problem. Technological and Economic Development of Economy, 27(5), 1227–1249. https://doi.org/10.3846/tede.2021.15058
Uyanik, C., Tuzkaya, G., Kalender, Z. T., & Oguztimur, S. (2020). An integrated DEMATEL–IF-TOPSIS methodology for logistics centers’ location selection problem: An application for Istanbul Metropolitan area. Transport, 35, 548–556. https://doi.org/10.3846/transport.2020.12210
Wang, W.-Y., Yang, Y.-C., & Lin, C.-Y. (2022). Integrating the BWM and TOPSIS algorithm to evaluate the optimal token exchanges platform in Taiwan. Technological and Economic Development of Economy, 28(2), 358–380. https://doi.org/10.3846/tede.2021.15935
Wen, Z., Liao, H., & Zavadskas, E. K (2020). MACONT: Mixed aggregation by comprehensive normalization technique for multi-criteria analysis. Informatica, 31(4), 857–880. https://doi.org/10.15388/20-INFOR417
Yager, R. R., & Abbasov, A. M. (2013). Pythagorean membership grades, complex numbers, and decision making. International Journal of Intelligent Systems, 28, 436–452. https://doi.org/10.1002/int.21584
Yalcin Kavus, B., Ayyildiz, E., Gülüm Taş, P., & Taşkın, A. (2023). A hybrid Bayesian BWM and Pythagorean fuzzy WASPAS-based decision-making framework for parcel locker location selection problem. Environmental Science and Pollution Research, 30, 90006–90023. https://doi.org/10.1007/s11356-022-23965-y
Yazdani, M., Muñoz-Ocaña, Y., Fernández-Rodríguez, V., & Torres-Jiménez, M. (2018). Logistics center location decision using a multi-attribute analysis structure. In P. Chatterjee, M. Yazdani, & S. Chakraborty (Eds.), Sustainability modeling in engineering (pp. 1–26). World Scientific. https://doi.org/10.1142/9789813276338_0001
Yesilcayir, N., Ayvazoglu, G., Celik, S., & Peker, I. (2024). Transit warehouse location selection by IF AHP-TOPSIS integrated methods for disaster logistics: A case study of Turkey. Research in Transportation Business & Management, 57, Article 101232. https://doi.org/10.1016/j.rtbm.2024.101232
Zadeh, L. A. (1965) Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zakeri, S., Chatterjee, P., Konstantas, D., & Shojaei Farr, A. (2023). Introducing alternatives ranking with elected nominee (ARWEN) method: A case study of supplier selection. Technological and Economic Development of Economy, 29(3), 1080–1126. https://doi.org/10.3846/tede.2023.18789
Zavadskas, E. K., Mardani, B., Turskis, Z., Jusoh, A., & Nor, K. M. D. (2016). Development of TOPSIS method to solve complicated decision-making problems – an overview on developments from 2000 to 2015. International Journal of Information Technology & Decision Making, 15(3), 645–682. https://doi.org/10.1142/S0219622016300019
Zayas, V., Surenkok, G., & Pandey, G. (2017). Implicit ambivalence of significant others: Significant others trigger positive and negative evaluations. Social and Personality Psychology Compass, 11(11), Article e12360. https://doi.org/10.1111/spc3.12360
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