Multi-Criteria Fuzzy-Stochastic Diffusion Model of Groundwater Control System Selection

Abstract

When considering data and parameters in hydrogeology, there are often questions of uncertainty, vagueness, and imprecision in terms of the quantity of spatial distribution. To overcome such problems, certain data may be subjectively expressed in the form of expert judgment, whereby a heuristic approach and the use of fuzzy logic are required. In this way, decision-making criteria relating to an optimal groundwater control system do not always have a numerical value. Groundwater control scenarios (alternatives) are identified through hydrodynamic modeling of the aquifer, providing an indication of their effectiveness. The paper develops a fuzzy-stochastic multi-criteria decision-making model to deal with a topical problem: selection of the most suitable groundwater control system for an open-cast mine. Both real numerical and linguistic variables are used to express the values of all criteria that affect the final decision. In particular, it should be pointed out that the values of the criteria are varied over a predefined time horizon. For mathematical calculations, fuzzy dynamic TOPSIS and the stochastic diffusion process—geometric Brownian motion—were used. The proposed method is tested in a case study: the selection of an optimal groundwater control system for an open-cast mine.

Temporal Analysis of Energy Transformation in EU Countries

“…They solved the problem of dynamic evaluation of subcontractors in a construction project using the Evaluation based on Distance from Average Solution (EDAS) method. Polomčić et al [35] used the Fuzzy Dynamic Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to select a groundwater control system for an open-pit mine. In this case, DMCDM allows for changes in the set of criteria, and subsequent periods were aggregated using a weighted average.…”

Energy Security Assessment Based on a New Dynamic Multi-Criteria Decision-Making Framework

“…They extended the MCDM to include the dynamics of the decision problem by calculating the dynamic risk exposure and dynamic discriminative index for subsequent periods. Chen et al [26], Ziemba et al [27], Chen and Li [28], Li et al [29], Yang et al [30], and Polomčić et al [31] proposed a dynamic approach to MCDM in their research by enabling the aggregation of assessments of alternatives over many consecutive periods of time. Moreover, all of these researchers except Polomčić et al [31] postulated the use of different aggregation strategies, depending on which period would be the most important.…”

“…Chen et al [26], Ziemba et al [27], Chen and Li [28], Li et al [29], Yang et al [30], and Polomčić et al [31] proposed a dynamic approach to MCDM in their research by enabling the aggregation of assessments of alternatives over many consecutive periods of time. Moreover, all of these researchers except Polomčić et al [31] postulated the use of different aggregation strategies, depending on which period would be the most important. Chen et al [26] developed an approach to DMCDM in the problem of disaster management.…”

“…Yang et al [30] applied DMCDM in energy metering device selection. Polomčić et al [31] considered the problem of groundwater management scenarios evaluation. Yan et al [32], trying to solve the problem of vendor selection, proposed to study the trend of changes in alternatives over time and take this trend into account when aggregating subsequent periods of time.…”

“…Table 1 presents an overview of the literature related to the various areas of DMCDM application along with the dynamic extensions of the classic MCDM paradigm proposed by the researchers. Project risk management MAUT Calculation of dynamic risk exposure and dynamic discriminative index for different periods [25] Air traffic SAW Changeability of the set of alternatives over time, taking into account historical and present data [24] Automotive manufacturing SAW Changeability of the set of alternatives and the set of criteria over time, taking into account historical, present and projected future data [37] Construction industry Fuzzy EDAS Changeability of the set of alternatives and the set of decision makers over time, aggregation of different periods of time [33] Marketing management PROMETHEE GDSS Aggregation of different periods of time, different aggregation strategies [27] Enterprise Resources Planning system implementation GRA/Fuzzy GRA Changeability of criteria weights over time, aggregation of different periods of time, the use of real numbers for the oldest periods, interval numbers for intermediate periods and triangular fuzzy numbers for the most recent periods [38] Investment management TIFN-WAA Aggregation of different periods of time, different aggregation strategies [28] Investment management Fuzzy TOPSIS Variability of criterion weights over time, aggregation of different periods of time [29] Vendor selection TPIGN Study of the trend of changes in alternatives on the criteria in subsequent periods, aggregation of different periods of time, taking into account the trend of changes [32] Reverse logistics management DIF-MAGDM Variability of criteria weights over time, aggregation of different time periods, aggregation of assessments of many experts [34] Electric energy metering device selection DINFWAA/DINFWGA Aggregation of different periods of time, different aggregation strategies [30] Supplier selection BLTS DMCDM Variability of the set of alternatives and the set of criteria over time, taking into account historical and present data [35] Groundwater management Fuzzy TOPSIS Aggregation of different periods of time [31] Supplier selection IFS DGMCDM Variability of the set of alternatives and the set of criteria over time, taking into account historical and present data [36] DEA-Data Envelopment Analysis, MAUT-Multi-Attribute Utility Theory, SAW-…”