# The Development of a Hybrid Model for Dam Site Selection Using a Fuzzy Hypersoft Set and a Plithogenic Multipolar Fuzzy Hypersoft Set

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Aim of this Study

- The construction of a suitability map based on the feasibility of building a dam using several parameters.
- The suggestion of places that would make good dams.
- Computing cross sections and other properties, such as reservoir volume, dam height, and dam breadth, of potential dam locations.
- A hybrid of a fuzzy hypersoft set and a pathogenic multipolar fuzzy hypersoft set being applied to the problem of choosing a dam.

#### 1.2. Research Area

#### 1.3. Literature Review

#### 1.4. Multicriteria Decision Making

#### 1.5. Structure of Paper

## 2. The Preliminaries

#### 2.1. Soft Set

#### 2.2. Hypersoft Set

**Example**

**1.**

#### 2.3. Fuzzy Hypersoft Set

#### 2.4. Plithogenic Hypersoft Set

#### 2.5. Plithogenic Fuzzy Hypersoft Set

#### 2.6. Plithogenic Two-Polar Fuzzy Hypersoft Set

#### 2.7. Plithogenic Multi-Polar Fuzzy Hyper Soft Set

#### 2.8. Distances

- The Hamming distance [62]:$$\begin{array}{c}\hfill {d}_{H}(\mathfrak{Z},\mathfrak{E})=\frac{1}{n}\{{\Sigma}_{i=1}^{n}{\Sigma}_{j=1}^{k}|{p}_{i}o\mathfrak{Z}\left({z}_{k}\right)-{p}_{i}o\mathfrak{E}\left({e}_{j}\right)\left|\right\}\end{array}$$
- The normalized Hamming distance [62]:$$\begin{array}{c}\hfill {d}_{H}(\mathfrak{Z},\mathfrak{E})=\frac{1}{mq}\{{\Sigma}_{i=1}^{n}{\Sigma}_{j=1}^{k}|{p}_{i}o\mathfrak{Z}\left({z}_{k}\right)-{p}_{i}o\mathfrak{E}\left({e}_{j}\right)\left|\right\}\end{array}$$
- The Euclidean distance [62]:$$\begin{array}{c}\hfill {d}_{H}(\mathfrak{Z},\mathfrak{E})=\{\frac{1}{n}{{\Sigma}_{i=1}^{n}{\Sigma}_{j=1}^{k}{({p}_{i}o\mathfrak{Z}\left({z}_{k}\right)-{p}_{i}o\mathfrak{E}({e}_{j}))}^{2}\}}^{\frac{1}{2}}\end{array}$$
- The normalized Euclidean distance [62]:$$\begin{array}{c}\hfill {d}_{N}E(\mathfrak{Z},\mathfrak{E})=\{\frac{1}{nk}{\Sigma}_{i=1}^{n}{\Sigma}_{j=1}^{k}{\Sigma}_{k=1}^{m}{({}^{I}{T}_{X}^{i-}\left({e}_{j}\right)\left({z}_{k}\right)-{}^{I}{T}_{Y}^{i-}\left({e}_{j}\right)\left({z}_{k}\right))\}}^{2}\end{array}$$
- The similarity measures [62]:The similarity measures of two sets $\mathfrak{Z}$ and $\mathfrak{E}$ can be calculated as,$$\begin{array}{c}\hfill S(\mathfrak{Z},\mathfrak{E})=\frac{1}{1+d(\mathfrak{Z},\mathfrak{E})}\end{array}$$

## 3. Application in a Recognition Problem

#### 3.1. Factors Influencing Dam Siting

#### 3.2. Criteria Selection

#### 3.2.1. Soil

#### 3.2.2. Slope

#### 3.2.3. Geological Layer

#### 3.2.4. Land Cover

#### 3.3. Problem of Selection of Dam Site: Hybrid of Fuzzy Hypersoft Set and Plithogenic Multipolar Fuzzy Hypersoft Set

#### Algorithm of the Problem:

## 4. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Pathan, A.I.; Agnihotri, P.G.; Patel, D. Integrated approach of AHP and TOPSIS (MCDM) techniques with GIS for dam site suitability mapping: A case study of Navsari City, Gujarat, India. Environ. Earth Sci.
**2022**, 81, 443. [Google Scholar] [CrossRef] - Hayles, C.S. An examination of decision making in post disaster housing reconstruction. Int. J. Disaster Resil. Built Environ.
**2010**, 1, 103–122. [Google Scholar] [CrossRef] - Hladka, M.; Hyanek, V. Explanation of the donor decision-making process in the czech republic through a combination of influences of individual motives. Eur. Financ. Account. J.
**2016**, 11, 23–37. [Google Scholar] [CrossRef] - Liu, P.; Zhang, L.; Liu, X.; Wang, P. Multi-valued Neutrosophic number Bonferroni mean operators with their applications in multiple attribute group decision making. Int. J. Inf. Technol. Decis. Mak.
**2016**, 15, 1181–1210. [Google Scholar] [CrossRef] - Yontar, E.; Derse, O. Evaluation of sustainable energy action plan strategies with a SWOT/TWOS-based AHP/ANP approach: A case study. Environ. Dev. Sustain.
**2022**, 25, 5691–5715. [Google Scholar] [CrossRef] - Joshi, B.P.; Joshi, N.; Gegov, A. TOPSIS based Renewable-Energy-Source-Selection using Moderator Intuitionistic Fuzzy Set. Int. J. Math. Eng. Manag. Sci.
**2023**, 8, 979–990. [Google Scholar] [CrossRef] - Chen, S.M. A new approach to handling Fuzzy decision-making problems. IEEE Trans. Syst. Man Cybern.
**1988**, 18, 1012–1016. [Google Scholar] [CrossRef] - Joshi, B.P.; Sati, M.M.; Rayal, A.; Kumar, A.; Kumar, N. An Approach for Renewable-Energy-Source-Selection Problems Based on Choquet Integral Operator of MIFS. In Proceedings of the 2023 3rd International Conference on Advance Computing and Innovative Technologies in Engineering (ICACITE), Greater Noida, India, 12 May 2023; pp. 643–648. [Google Scholar]
- Saeed, M.; Ahsan, M.; Saeed, M.H.; Mehmood, A.; El-Morsy, S. Assessment of solid waste management strategies using an efficient complex fuzzy hypersoft set algorithm based on entropy and similarity measures. IEEE Access
**2021**, 9, 150700–150714. [Google Scholar] [CrossRef] - Saeed, M.; Ahsan, M.; Saeed, M.H.; El-Morsy, S. An optimized complex fuzzy hypersoft set system based approach for the evaluation of strategic procurement techniques for fuel cell and hydrogen components. IEEE Access
**2022**, 10, 71612–71631. [Google Scholar] [CrossRef] - Saeed, M.; Ahsan, M.; Saeed, M.H.; Rahman, A.U.; Mohammed, M.A.; Nedoma, J.; Martinek, R. An algebraic modeling for tuberculosis disease prognosis and proposed potential treatment methods using fuzzy hypersoft mappings. Biomed. Signal Process. Control
**2023**, 80, 104267. [Google Scholar] [CrossRef] - Hooke, J.M.; Mant, J.M. Geomorphological impacts of a flood event on ephemeral channels in SE Spain. Geomorphology
**2000**, 34, 163–180. [Google Scholar] [CrossRef] - McVicar, T.R.; Bierwirth, P.N. Rapidly assessing the 1997 drought in Papua New Guinea using composite AVHRR imagery. Int. J. Remote Sens.
**2010**, 22, 2109–2128. [Google Scholar] [CrossRef] - Maillet, G.M.; Vella, C.; Berné, S.; Friend, P.L.; Amos, C.L.; Fleury, T.J.; Normand, A. Morphological changes and sedimentary processes induced by the December 2003 flood event at the present mouth of the Grand Rhône River (southern France). Mar. Geol.
**2006**, 234, 159–177. [Google Scholar] [CrossRef] - Mondlane, A.I. Floods and droughts in Mozambique–The paradoxical need of strategies for mitigation and coping with uncertainty. In WIT Transactions on Ecology and the Environment; WIT Press: Southampton, UK, 2004; Volume 77. [Google Scholar]
- Llasat, M.d.C.; Rigo, T.; Barriendos, M. The “Montserrat-2000” flash-flood event: A comparison with the floods that have occurred in the northeastern Iberian Peninsula since the 14th century. Int. J. Climatol.
**2003**, 23, 453–469. [Google Scholar] [CrossRef] - Chen, J.L.; Wilson, C.R.; Tapley, B.D.; Yang, Z.L.; Niu, G.Y. 2005 drought event in the Amazon River basin as measured by GRACE and estimated by climate models. J. Geophys. Res. Solid Earth
**2009**, 114, 1–9. [Google Scholar] [CrossRef] - Piao, S.; Ciais, P.; Huang, Y.; Shen, Z.; Peng, S.; Li, J.; Zhou, L.; Liu, H.; Ma, Y.; Ding, Y.; et al. The impacts of climate change on water resources and agriculture in China. Nature
**2010**, 467, 43–51. [Google Scholar] [CrossRef] - Wang, P.; Li, Z.; Li, H.; Zhang, Z.; Xu, L.; Yue, X. Glaciers in Xinjiang, China: Past changes and current status. Water
**2020**, 12, 2367. [Google Scholar] [CrossRef] - Shen, Y.; Chen, Y. Global perspective on hydrology, water balance, and water resources management in arid basins. Hydrol. Process
**2010**, 135, 129–135. [Google Scholar] [CrossRef] - Xie, Z.; Wang, Y.; Li, F. Effect of plastic mulching on soil water use and spring wheat yield in arid region of northwest China. Agric. Water Manag.
**2005**, 75, 71–83. [Google Scholar] [CrossRef] - Cao, C.; Lv, Z.; Li, L.; Du, L. Geochemical characteristics and implications of shale gas from the Longmaxi Formation, Sichuan Basin, China. J. Nat. Gas Geosci.
**2016**, 1, 131–138. [Google Scholar] [CrossRef] - Liu, J.; Yu, J.; Yao, Y.; Dorjee, D. Spatial distribution and change trend of land surface evaporation and drought in Sichuan Province (China) during 2001 to 2015. Eur. J. Remote Sens.
**2022**, 55, 46–54. [Google Scholar] [CrossRef] - Geng, Y.H.; Min, Q.W.; Cheng, S.K. Water demand of crop plantation in northwest China—A case study of the Jinghe watershed. J. Ecol. Rural. Environ.
**2006**, 22, 30–34. [Google Scholar] - Liu, Y.; Wang, L.; Ni, G.; Cong, Z. Spatial distribution characteristics of irrigation water requirement for main crops in China. Trans. Chin. Soc. Agric. Eng.
**2009**, 25, 6–12. [Google Scholar] - Shen, Y.; Li, S.; Chen, Y.; Qi, Y.; Zhang, S. Estimation of regional irrigation water requirement and water supply risk in the arid region of Northwestern China 1989–2010. Agric. Water Manag.
**2013**, 128, 55–64. [Google Scholar] [CrossRef] - Shi, Y.; Shen, Y.; Kang, E.; Li, D.; Ding, Y.; Zhang, G.; Hu, R. Recent and future climate change in northwest China. Clim. Chang.
**2007**, 80, 379–393. [Google Scholar] [CrossRef] - Wan, L.; Xia, J.; Hong, S.; Bu, H.; Ning, L.; Chen, J. Decadal climate variability and vulnerability of water resources in arid regions of Northwest China. Environ. Earth Sci.
**2015**, 73, 6539–6552. [Google Scholar] [CrossRef] - Zadeh, L.A.; Klir, G.J.; Yuan, B. Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers; World Scientific: Singapore, 1996; Volume 6. [Google Scholar]
- Molodtsov, D. Soft set theory—First results. Comput. Math. Appl.
**1999**, 37, 19–31. [Google Scholar] [CrossRef] - Chen, S.M. Measures of similarity between vague sets. Fuzzy Sets Syst.
**1995**, 74, 217–223. [Google Scholar] [CrossRef] - Maji, P.K.; Biswas, R.; Roy, A.R. Soft set theory. Comput. Math. Appl.
**2003**, 45, 555–562. [Google Scholar] [CrossRef] - Saeed, M.; Saeed, M.H.; Shafaqat, R.; Sessa, S.; Ishtiaq, U.; di Martino, F. A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making. Symmetry
**2022**, 14, 2639. [Google Scholar] [CrossRef] - Uddin, F.; Ishtiaq, U.; Javed, K.; Aiadi, S.S.; Arshad, M.; Souayah, N.; Mlaiki, N. A New Extension to the Intuitionistic Fuzzy Metric-like Spaces. Symmetry
**2022**, 14, 1400. [Google Scholar] [CrossRef] - Saqlain, M.; Jafar, M.N.; Riaz, M. A new approach of Neutrosophic soft set with generalized Fuzzy TOPSIS in application of smart phone selection. Neutrosophic Sets Syst.
**2020**, 32, 306. [Google Scholar] - Saeed, M.; Majid, S.Z. Development of Hybrid Model for Donations to Deserving Donees Using Multi-Polar Interval-Valued Neutrosophic Soft Set. Punjab Univ. J. Math.
**2022**, 54, 593–605. [Google Scholar] [CrossRef] - Abdel-Basset, M.; Mohamed, M.; Elhoseny, M.; Chiclana, F.; Zaied, A.E.N.H. Cosine similarity measures of bipolar Neutrosophic set for diagnosis of bipolar disorder diseases. Artif. Intell. Med.
**2019**, 101, 101735. [Google Scholar] [CrossRef] [PubMed] - Abdel-Basset, M.; El-Hoseny, M.; Gamal, A.; Smarandache, F. A novel model for evaluation Hospital medical care systems based on plithogenic sets. Artif. Intell. Med.
**2019**, 100, 101710. [Google Scholar] [CrossRef] [PubMed] - Alamri, F.S.; Saeed, M.H.; Saeed, M. A hybrid entropy-based economic evaluation of hydrogen generation techniques using Multi-Criteria Decision Making. Int. J. Hydrogen Energy
**2023**, 49, 711–723. [Google Scholar] [CrossRef] - Jafar, M.N.; Saeed, M.; Khan, K.M.; Alamri, F.S.; Khalifa, H.A.E.W. Distance and similarity measures using max-min operators of neutrosophic hypersoft sets with application in site selection for solid waste management systems. IEEE Access
**2022**, 10, 11220–11235. [Google Scholar] [CrossRef] - Riaz, M.; Farid, H.M.A. Enhancing green supply chain efficiency through linear Diophantine fuzzy soft-max aggregation operators. J. Ind. Intell.
**2023**, 1, 8–29. [Google Scholar] [CrossRef] - Kausar, R.; Farid, H.M.A.; Riaz, M. A numerically validated approach to modeling water hammer phenomena using partial differential equations and switched differential-algebraic equations. J. Ind. Intell.
**2023**, 1, 75–86. [Google Scholar] [CrossRef] - Farid, H.M.A.; Riaz, M. q-rung orthopair fuzzy Aczel–Alsina aggregation operators with multi-criteria decision-making. Eng. Appl. Artif. Intell.
**2023**, 122, 106105. [Google Scholar] [CrossRef] - Farid, H.M.A.; Riaz, M. Some generalized q-rung orthopair fuzzy Einstein interactive geometric aggregation operators with improved operational laws. Int. J. Intell. Syst.
**2021**, 36, 7239–7273. [Google Scholar] [CrossRef] - Alaibakhsh, M.; Azizi, S.H.; Kheirkhah Zarkesh, M.M. Water resource management with a combination of underground dam/qanat and site selection of suitable sites using GIS. Water Sci. Technol. Water Supply
**2013**, 13, 606–614. [Google Scholar] [CrossRef] - Yu, X.I.N.; Guangxing, Z.; Xin, Z. Climate change in Bortala Mongol Autonomous Prefecture, Xinjiang since recent 46 years. Arid. Land Geogr.
**2006**, 29, 100–105. [Google Scholar] - Tzeng, G.H.; Huang, J.J. Multiple Attribute Decision Making: Methods and Applications; CRC Press: Boca Raton, FL, USA, 2011. [Google Scholar]
- Chakraborty, S.; Chatterjee, P.; Das, P.P. Multi-Criteria Decision-Making Methods in Manufacturing Environments: Models and Applications; CRC Press: Boca Raton, FL, USA, 2023. [Google Scholar]
- Taherdoost, H.; Madanchian, M. Multi-criteria decision making (MCDM) methods and concepts. Encyclopedia
**2023**, 3, 77–87. [Google Scholar] [CrossRef] - Ayan, B.; Abacıoğlu, S.; Basilio, M.P. A Comprehensive Review of the Novel Weighting Methods for Multi-Criteria Decision-Making. Information
**2023**, 14, 285. [Google Scholar] [CrossRef] - Lee, A.H.; Chen, H.H.; Kang, H.Y. A conceptual model for prioritizing dam sites for tidal energy sources. Ocean. Eng.
**2017**, 137, 38–47. [Google Scholar] [CrossRef] - Gao, Y.; Yang, L.; Song, Y.; Tian, J.; Yang, M. Designing water-saving-ecological check dam sites by a system optimization model in a region of the loess plateau, Northwest China. Ecol. Inform.
**2022**, 72, 101887. [Google Scholar] [CrossRef] - Minatour, Y.; Khazaie, J.; Ataei, M.; Javadi, A.A. An integrated decision support system for dam site selection. Scientia Iranica. Trans. Civ. Eng.
**2015**, 22, 319. [Google Scholar] - Jozaghi, A.; Alizadeh, B.; Hatami, M.; Flood, I.; Khorrami, M.; Khodaei, N.; Ghasemi Tousi, E. A comparative study of the AHP and TOPSIS techniques for dam site selection using GIS: A case study of Sistan and Baluchestan Province, Iran. Geosciences
**2018**, 8, 494. [Google Scholar] [CrossRef] - Balkhair, K.S.; Ur Rahman, K. Development and assessment of rainwater harvesting suitability map using analytical hierarchy process, GIS and RS techniques. Geocarto Int.
**2021**, 36, 421–448. [Google Scholar] [CrossRef] - Abushandi, E.; Alatawi, S. Dam Site Selection Using Remote Sensing Techniques and Geographical Information System to Control Flood Events in Tabuk City. Hydrol. Curr. Res.
**2015**, 6, 1–13. [Google Scholar] - Yasser, M.; Jahangir, K.; Mohmmad, A. Earth dam site selection using the analytic hierarchy process (AHP): A case study in the west of Iran. Arab. J. Geosci.
**2013**, 6, 3417–3426. [Google Scholar] [CrossRef] - Ledec, G.; Quintero, J.D. Good Dams and Bad Dams: Environmental Criteria for Site Selection of Hydroelectric Projects; Latin America and the Caribbean Region: Sustainable Development Working Paper No. 16; World Bank: Washington, DC, USA, 2003; p. 21. [Google Scholar]
- Zavadskas, E.K.; Turskis, Z.; Kildiene, S. State of art surveys of overviews on MCDM/MADM methods. Technol. Econ. Dev. Econ.
**2014**, 20, 165–179. [Google Scholar] [CrossRef] - Zionts, S. MCDM-If Not a Roman Numeral, Then What? Interfaces
**1979**, 9, 94–101. [Google Scholar] [CrossRef] - Smarandache, F. Extension of soft set to hyper-soft set, and then to Plithogenic hyper-soft Set. Neutrosophic Sets Syst.
**2018**, 22, 168–170. [Google Scholar] - Akram, M.; Waseem, N. Similarity measures for new hybrid models: MF sets and mF soft sets. Punjab Univ. J. Math.
**2020**, 51, 115–130. [Google Scholar] - ICOLD. International Commission on Large Dams. Purposes of Dams. Available online: https://www.icold-cigb.org/GB/world_register/general_synthesis.asp (accessed on 1 March 2021).
- Emiroglu, M.E. Influences on selection of the type of dam. Int. J. Sci. Technol.
**2008**, 3, 173–189. [Google Scholar] - Uehara, G.; Ikawa, H. Use of Information from Soil Surveys and Classification. Plant Nutrient Management in Hawaii’s Soils, Approaches for Tropical and Subtropical Agriculture; College of Tropical Agriculture and Human Resources, University of Hawai’i at Manoa: Honolulu, HI, USA, 2000; pp. 67–77. [Google Scholar]
- Singh, J.P.; Singh, D.; Litoria, P.K. Selection of suitable sites for water harvesting structures in Soankhad watershed, Punjab using remote sensing and geographical information system (RS&GIS) approach—A case study. J. Indian Soc. Remote Sens.
**2009**, 37, 21–35. [Google Scholar] - Othman, A.A.; Al-Maamar, A.F.; Al-Manmi, D.A.M.A.; Liesenberg, V.; Hasan, S.E.; Obaid, A.K.; Al-Quraishi, A.M.F. GIS-based modeling for selection of dam sites in the Kurdistan Region, Iraq. ISPRS Int. J. Geo-Inf.
**2020**, 9, 244. [Google Scholar] [CrossRef] - Merrouni, A.A.; Elalaoui, F.E.; Mezrhab, A.; Mezrhab, A.; Ghennioui, A. Large scale PV sites selection by combining GIS and Analytical Hierarchy Process. Case study: Eastern Morocco. Renew. Energy
**2018**, 119, 863–873. [Google Scholar] [CrossRef] - Zhang, Z.; Chen, X.; Huang, Y.; Zhang, Y. Effect of catchment properties on runoff coefficient in a karst area of southwest China. Hydrol. Processes
**2014**, 28, 3691–3702. [Google Scholar] [CrossRef] - Wyllie, D.C. Foundation of gravity and embankment dams. In Foundations on Rock: Engineering Practice; CRC Press: Boca Raton, FL, USA, 2003. [Google Scholar]
- Forzieri, G.; Gardenti, M.; Caparrini, F.; Castelli, F. A methodology for the pre-selection of suitable sites for surface and underground small dams in arid areas: A case study in the region of Kidal, Mali. Phys. Chem. Earth Parts A/B/C
**2008**, 33, 74–85. [Google Scholar] [CrossRef] - Baban, S.M.J.; Wan-Yusof, K. Modelling optimum sites for locating reservoirs in tropical environments. Water Resour. Manag.
**2003**, 17, 1–17. [Google Scholar] [CrossRef] - Adinarayana, J.; Krishna, N.R.; Rao, K.G. An Integrated Approach for Prioritization of Watersheds. J. Environ. Manag.
**1995**, 44, 375–384. [Google Scholar] [CrossRef]

Description | Sole-Purpose | Percentage | Multiple-Purpose | Percentage |
---|---|---|---|---|

Flood Control | 2539 | 8.82% | 4911 | 0.19% |

Fish Farming | 42 | 0.15% | 1487 | 0.06% |

Hydro Power | 6115 | 21.24% | 4135 | 0.16% |

Irrigation | 13,850 | 47.17% | 6278 | 0.24% |

Navigation | 96 | 0.33% | 579 | 0.02% |

Recreation | 1361 | 4.73% | 3035 | 0.11% |

Water Supply | 3376 | 11.73% | 4587 | 0.17% |

Talling | 103 | 0.36% | 12 | 0% |

Others | 1579 | 5.48% | 1385 | 0.05% |

**Table 2.**Source: organized from [66] for soil.

Type | Permeability | Land Use | Soil |
---|---|---|---|

RWH | Low | Near Agricultural Land | Slit Loam |

Check Dams | Less | Barren, Shrub, Riverbed | Sandy Clay Loam |

Percolation Tank | High | Barren, Shrub | Silt Loam |

Farm Ponds | Moderate | Barren, Shrub | Sandy Clay Loam |

Soil Type | Prefernce Value | Unified Preference |
---|---|---|

Sand | 1 | 25 |

Sandy Loam | 4 | 50 |

Loam | 3 | 75 |

Clay Loam | 4 | 100 |

**Table 4.**Source: organized from [66] for slope.

Type | Permeability | Land Use | Slope |
---|---|---|---|

RWH | Low | Near Agricultural Land | <15% |

Check Dams | Less | Barren, Shrub, Riverbed | <15% |

Percolation Tank | High | Barren, Shrub | <10% |

Farm Ponds | Moderate | Barren, Shrub | <10% |

Slope | Preference Value | Unified Preference |
---|---|---|

0 to 1 | 5 | 100 |

1 to 2 | 4 | 75 |

2 to 3 | 3 | 50 |

3 to 4 | 2 | 25 |

**Table 6.**Source: organized from [66] for geological layer.

Type | Geological Resistance | Land Use | Soil |
---|---|---|---|

RWH | Low | Near Agricultural Land | Slit Loam |

Check Dams | Less | Barren, Shrub, Riverbed | Sandy Clay Loam |

Percolation Tank | High | Barren, Shrub | Silt Loam |

Farm Ponds | Moderate | Barren, Shrub | Sandy Clay Loam |

Geological Layer | Preference Value | Unified Preference |
---|---|---|

Low Resistance | 1 | 25 |

Slightly Low Resistance | 4 | 50 |

Moderate Resistance | 3 | 75 |

High Resistance | 4 | 100 |

**Table 8.**Source: organized from [66] land cover.

Type | Permeability | Land Use | Slope |
---|---|---|---|

RWH | Low | Near Agricultural Land | <15% |

Check Dams | Less | Barren, Shrub, Riverbed | <15% |

Percolation Tank | High | Forest | <10% |

Farm Ponds | Moderate | Barr and Shrub | <10% |

Land Cover | Prefernce Value | Unified Preference |
---|---|---|

Farm Land | 1 | 25 |

Forest | 2 | 50 |

Shrub and Herb | 3 | 75 |

Bare Land | 4 | 100 |

. | ${\mathfrak{U}}_{1}$ | ${\mathfrak{U}}_{2}$ | ${\mathfrak{U}}_{3}$ | ${\mathfrak{U}}_{4}$ |
---|---|---|---|---|

${\mathfrak{S}}_{1}$ | (0.10 0.40, 0.50, 0.90) | (0.23, 0.47, 0.60, 0.85) | (0.10, 0.40, 0.60, 0.80) | (0.20, 0.40, 0.60, 0.90) |

${\mathfrak{S}}_{2}$ | (0.08, 0.45, 0.63, 0.90) | (0.18, 0.45, 0.63, 0.70) | (0.20, 0.45, 0.62, 0.79) | (0.18, 0.45, 0.63, 0.90) |

${\mathfrak{S}}_{3}$ | (0.21, 0.47, 0.60, 0.85) | (0.10, 0.39, 0.69, 0.90) | (0.23, 0.47, 0.61, 0.85) | (0.21, 0.47, 0.60, 0.85) |

${\mathfrak{S}}_{4}$ | (0.10, 0.40, 0.60, 0.80) | (0.20, 0.40, 0.60, 0.80) | (0.24, 0.47, 0.60, 0.86) | (0.22, 0.48, 0.60, 0.90) |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Majid, S.Z.; Saeed, M.; Ishtiaq, U.; Argyros, I.K.
The Development of a Hybrid Model for Dam Site Selection Using a Fuzzy Hypersoft Set and a Plithogenic Multipolar Fuzzy Hypersoft Set. *Foundations* **2024**, *4*, 32-46.
https://doi.org/10.3390/foundations4010004

**AMA Style**

Majid SZ, Saeed M, Ishtiaq U, Argyros IK.
The Development of a Hybrid Model for Dam Site Selection Using a Fuzzy Hypersoft Set and a Plithogenic Multipolar Fuzzy Hypersoft Set. *Foundations*. 2024; 4(1):32-46.
https://doi.org/10.3390/foundations4010004

**Chicago/Turabian Style**

Majid, Sheikh Zain, Muhammad Saeed, Umar Ishtiaq, and Ioannis K. Argyros.
2024. "The Development of a Hybrid Model for Dam Site Selection Using a Fuzzy Hypersoft Set and a Plithogenic Multipolar Fuzzy Hypersoft Set" *Foundations* 4, no. 1: 32-46.
https://doi.org/10.3390/foundations4010004