Abstract

The importance of reservoir sedimentation management as a multi criteria problem in practice with multiple decision makers is evident when one considers that the cost of replacing storage lost annually due to sediment deposition throughout the world is in the order of US$13 billion. If sedimentation can be managed successfully, as it has been in some reservoirs, the loss in reservoir storage space due to this phenomenon can be lowered significantly. The purpose of this research is to develop the ordered weighted averaging (OWA) algorithm and apply it and to select the most preferred alternative with different Orness levels for sediment management in dam reservoirs to satisfy the technical and executive requirements, economic factors, social welfare, and environmental impacts. In this way, we present analytic forms of OWA operator weighting functions, each of which has properties of rank-based weights and a constant level of Orness, irrespective of the number of objectives considered. The model are successfully applied to the Dez hydropower reservoir, which has faced serious sedimentation problems. Results of this study provide a general class of parameterized aggregation operators that include the min, max, and average and have shown themselves to be useful for modeling many different kinds of aggregation problems.

INTRODUCTION

Efficient decision making in sediment management in reservoir problems requires stakeholders' participation, and definition of the multiple criteria in incommensurable units. The increasing complexity of socio-economic environments makes it less and less possible for a single decision maker to consider all relevant aspects of the problem. Therefore one should build intelligent group decision making (GDM) models to combine the often-conflicting preferences. Moving from a single decision maker's setting to multiple decision makers (DMs) introduces a great deal of complexity into the analysis since the analysis must be extended to account, somehow, for group decision makers, each one potentially exhibiting a unique preference structure, perceiving different consequences and responding to a diverse array of aspirations (Yager 1993; Ahn 2014).

GDM includes four stages (Mianabadi & Afshar 2007): (1) specification and evaluation; (2) unification of the opinions; (3) aggregation and selection; (4) evaluation of the consensus measure. Specification and evaluation generally includes: (1) identifying DMs; (2) selecting criteria; (3) defining alternatives; (4) eliciting criteria weights; (5) evaluating the importance of each expert; and (6) assessing the performance of alternatives against the criteria. By collecting different opinions from the DMs about the preferences regarding alternatives, the opinions should be unified. Then, their opinions will be aggregated by an aggregation operator and the most preferred alternative is selected based on the aggregation and final value of each alternative. In a GDM, if the manager strongly avoids the risk of making bad decisions, he/she may combine more stakeholders' preferences in the decision process. This will, however, result in conservative decisions which are different to the results for a neutral or optimistic DM. In fact, a manager would have varying optimism/pessimism insight based on the nature of the problem, especially with different and often contradictory stakeholders. Then the precise modeling of the GDM risks, in these situations, is inevitable.

More work on how to aggregate fuzzy or linguistic information in GDM includes Calvo & Mesiar (2003)’s weighted triangular norms-based aggregation operators, ordered weighted average (OWA) from Yager (1988, 1993) and Chen (2005), Linguistic OWA Combinations (LOWA) from Delgado et al. (1993), Neat OWA Operator (Marimin et al. 2002), Yager's IOWA (1998, 2003), quasi-arithmetic means and quasi-linear means aggregation (Bullen et al. 1988; Marichal et al. 1999), Yager's weighted median (1994), Sugeno integral, (Sugeno 1974) and the Leximin ordering from Dubois et al.(1996) etc. The ordered weighted averaging (OWA) operator, which was introduced by Yager (1988, 1993), has attracted much interest among researchers. The OWA provides flexible aggregation operation ranging between the minimum and the maximum. The motive behind selecting the OWA is its ability to encompass a range of operators from minimum to maximum including various averaging operations, and effectively deal with quantitative and qualitative information (Sadiq et al. 2010). The OWA weight generation provides flexibility to incorporate a decision maker's attitude or tolerance. The OWA operators have been used in a wide range of applications, in fields such as multi criteria and GDM (Wang & Parkan 2007; Ahn 2008; Kouchakinejad & Šipošová 2017), database query management and data mining (Kacprzyk & Zadrozny 2001; Sicilia et al. 2008; Reimann et al. 2017), forecasting (Yager 2008), data smoothing and data mining (Torra 2004), approximate reasoning (Chakraborty & Chakraborty 2004), approximate reasoning, fuzzy system and control (Liu 2006) and so on (Yager et al. 2011; Verma & Sharma 2016). Moreover, the OWA operator is used in fields of water resources management and environmental management problems in this decade. Table 1 summarizes the most important application being developed.

Table 1

Some applications of OWA in water resources management and Environmental management

AuthorsApplications
Despic & Simonovic (2000)  Comparing the OWA with three other methods to select flood control measures in Manitoba, Canada 
Yalcin & Akyurek (2004)  Mapping flood vulnerability in a basin in Turkey 
McPhee & Yeh (2004)  Applying OWA in a multi-objective study to choose scenarios in aquifer management 
Mysiak et al. (2005)  A decision tool in the MULINO decision support system (DSS) for integrated water resources management 
Makropoulos & Butler (2006)  Extending the OWA by applying it in geographic information system (GIS) to produce prioritization maps for pipe replacement in a water distribution network 
Fu et al. (2006)  Aggregating the possible climate change scenarios based on their probabilities by using the OWA approach 
Malczewski (2006)  Using OWA with GIS for multi-criteria evaluation for land-use suitability analysis in Canada 
Zarghami et al. (2008)  Using the OWA operator in group decision making in a conflict among stakeholders in a watershed 
Averna Valente & Vettorazzi (2008)  Integrating OWA with GIS to define the priority areas for forest conservation in a Brazilian river basin in order to increase the regional biodiversity 
Stroppiana et al. (2009)  To aggregate the anomaly scores of a set of contributing factors extracted from the analysis of historical time series, mostly of Earth observations data 
AuthorsApplications
Despic & Simonovic (2000)  Comparing the OWA with three other methods to select flood control measures in Manitoba, Canada 
Yalcin & Akyurek (2004)  Mapping flood vulnerability in a basin in Turkey 
McPhee & Yeh (2004)  Applying OWA in a multi-objective study to choose scenarios in aquifer management 
Mysiak et al. (2005)  A decision tool in the MULINO decision support system (DSS) for integrated water resources management 
Makropoulos & Butler (2006)  Extending the OWA by applying it in geographic information system (GIS) to produce prioritization maps for pipe replacement in a water distribution network 
Fu et al. (2006)  Aggregating the possible climate change scenarios based on their probabilities by using the OWA approach 
Malczewski (2006)  Using OWA with GIS for multi-criteria evaluation for land-use suitability analysis in Canada 
Zarghami et al. (2008)  Using the OWA operator in group decision making in a conflict among stakeholders in a watershed 
Averna Valente & Vettorazzi (2008)  Integrating OWA with GIS to define the priority areas for forest conservation in a Brazilian river basin in order to increase the regional biodiversity 
Stroppiana et al. (2009)  To aggregate the anomaly scores of a set of contributing factors extracted from the analysis of historical time series, mostly of Earth observations data 

In this paper, we will first discuss the most important and most common criteria in sediment management in reservoirs in the scope of sustainable development. Sustainable sediment management is developed and managed to fully contribute to the aims and objectives of the society, for now as well as for the future, while maintaining their ecological, environmental, and hydrological integrity. We used a fuzzy set representation of these linguistic quantifiers to obtain decision functions in the form of OWA aggregations. A methodology is suggested for including importance associated with the individual criteria. Further, rank-based weighting functions having constant values of Orness irrespective of the number of objectives are presented, and a final rank ordering of courses of action is performed by the use of those weighing functions.

MATERIALS AND METHODS

Study area, alternatives and criteria in sediment management

This study was carried out at the Dez reservoir (Figure 1), which is located in southern Iran. The Dez dam is a large hydroelectric dam in Iran, which was built in 1963 by an Italian consortium. At the time of construction, the Dez dam was Iran's largest development project. The Dez dam is a 203 m-high double curvature arch dam, and the level of its crest is 352 m above sea level. The original reservoir volume was 3,315 × 106 m3, and the estimated volume of arriving sediment was 840 × 106 m3 for a 50-year period. The minimum and maximum operating water levels of the reservoir are 300 m and 352 m from sea level, respectively (Dezab Consulting Engineers 2004). Although the project has been well preserved, the project is now more than 40 years old, and is reaching its midlife period. The useful life of the Dez reservoir is threatened by a sediment delta, which is approaching the dam's intake tunnels. A hydrographic study in 2002 showed that sedimentation reduced useful storage of the Dez reservoir from 3,315.6 × 106 m3 to 2,700 × 106 m3 (19% reduction). The difference between the levels of the inlet of the turbine and the bed surface of the deposited sediment is 14 m, and the sedimentation rate near the inlet of the turbine is 2 m/year. Therefore, sediment management in the Dez reservoir is of considerable importance (Khakzad & Elfimov 2014a).

Figure 1

The plan view of the Dez watershed.

Figure 1

The plan view of the Dez watershed.

In the following subsections, various technical and executive requirements, social, economic, and environmental criteria are introduced and discussed. These criteria are essential in securing sustainable development A method of criteria selection to be used in structuring the hierarchy of the criteria will be the subject of this paper.

Watershed rehabilitation: this alternative involves implementing remedial measures in the catchment to control the production and transportation of sediment entering the reservoir. Approximately 15% of the annual sediment yield of the watershed can be controlled by watershed management measures. However, this option would not lead to an immediate reduction of inflow sediment discharge because the construction of check dams and forest planting would take several years.

Irrigation outlet rehabilitation: it is considered essential to rehabilitate the existing Howell Bunger valves to (1) limit the amount of leakage from the valves and (2) provide a means of drawing down the reservoir in an emergency situation. It should be noted that the volume of storage retained has been determined by taking the present value of the volume of sediment that was flushed on an annual basis (50% of the current turbidity supply of 1.8 million m3/year.

Irrigation outlet replacement: instead of simply rehabilitating the existing Howell Bunger valves, their complete replacement with slide gates was considered, as outlined earlier. This would eliminate the present leakage issues, and provide a means of drawing down the reservoir and flushing sediment to maintain the sediment wedge storage. A present value cost was calculated for this alternative and a sediment flushing effectiveness of 100% of the incoming turbidity current sediment was assumed.

Access tunnel flushing: the alternative involved the opening up of the existing upstream cofferdam access tunnel to pass a reasonable discharge and to flush out sediment that accumulated in the area of the power intake.

Reservoir dredging near the dam: this alternative consists of dredging of the wedge of sediment, which deposits immediately upstream of the dam and poses a threat to the power stations if it builds up above the power intake levels. This alternative is incremental to the cost of rehabilitating the irrigation outlets.

Excavation of the upper delta: when the Dez reservoir is drawn down to meet irrigation and other water requirement, excavation of the sediment in the delta could be carried out in the dry. This excavation could serve to reduce the rate at which storage is being lost.

Dam raising: the final alternative considered was the raising of the Dez dam to provide additional storage. This raising was limited to 10 m for this evaluation, as outlined previously. The storage created is estimated at approximately 560 million m3 based on an extrapolation of the existing volume-elevation curve.

Dam decommissioning and many of the sediment management techniques that involve the release of reservoir sediments downstream need to be appraised within the framework of environmental and social impacts. Downstream impacts may include: (1) geomorphological changes to the downstream river channel; (2) increases in turbidity; (3) changes in flooding frequency and patterns; (5) reduction of dissolved oxygen in the river; (6) poisoning of the ecosystem, especially where toxic sediments are released. All of the above will have an impact on the natural environment as well as on human activity (Nikolaos et al. 2017). Downstream of Dez dam, at the powerhouse draft tube exit, and upstream and downstream of the regulating dam (at Dezful), turbidity, TSS and conductivity were very similar to that of the mid-depth samples collected in the Dez reservoir prior to flushing. However, after flushing (i.e. after flushing was completed but before the turbidity plume would have completely passed the regulating dam), turbidity and TSS increased by approximately 2 or 3 orders of magnitude (maximum concentrations 3,800 NTUs and 4,260 mg/l, respectively) at the regulating dam. Interestingly, the turbidity and TSS concentration downstream of the regulating dam was approximately three times higher than upstream of the regulating dam. The day following flushing, turbidity and TSS concentrations near the regulating dam remained high relative to the concentrations prior to flushing but diminished by an order of magnitude from those observed shortly after flushing. Turbidity ranged from 28–34 NTUs and TSS ranged from 300–360 mg/l. There were no apparent differences between samples collected upstream and downstream of the regulating dam.

The effects of dredging are dependent on the type of dredger used. Dredging operations often result in increased suspended sediment in the water column. The extent of increased suspended sediment in the water column is highly dependent on the type of dredger used, with a clam-type dredge most likely to increase suspended sediment and an airlift dredger or suction dredge less likely to significantly increase suspended sediment. Since the sediments in the Dez reservoir are not contaminated, loss of sediment to the water column is less of a problem. Dredging can remove aquatic vegetation and other structures that acts as fish habitat. In the case of the Dez reservoir, the sediment dynamics are such that rooted aquatic vegetation beds have not developed and structures such as shoals are in constant flux. Consequently, the effects on fish habitat due to dredging are not considered major.

A full environmental assessment for raising the height of Dez dam is expected to be required at the feasibility level if this option is selected. Based on temperature and oxygen profiles taken in the Dez reservoir, it appears that the reservoir does not stratify and oxygen levels are relatively high throughout the water column. With an increased depth, the reservoir may stratify with a consequent reduction in oxygen concentration in deeper waters. This reduction in oxygen concentration can result in noxious odors and impaired water quality downstream. The current fish community in the Dez reservoir has developed from a river type community to a lake type community and is a significant resource for the local inhabitants. Increasing the depth of the reservoir may alter the existing fish habitat but may replace this habitat with new habitat in the newly flooded areas. If the water quality of the reservoir, however, were to change significantly it could have a deleterious impact on the fish community.

The social welfare of the region is the fundamental objective of every water resources development plan and the social performance of any project has a huge effect in the life of the society (Zarghami & Szidarovszky 2011). Sediment management always requires that some people have to be relocated from their homes, resulting in various mental and emotional tensions. Therefore projects with less resettlement are more preferred. The effects of flushing from any outlet are substantial. Timely warnings to industry, municipalities, irrigation pumping stations and aquaculture facilities that flushing will occur are recommended to allow the parties to prepare for the event and potentially reduce their costs (Khakzad & Elfimov 2015a). In addition, warning signs at bathing beaches that currents and water levels may increase quickly during flushing should be erected and warning sirens should be installed to operate when these changes are imminent. Rapid assessment techniques for suspended solids concentrations should be developed so that the duration of flushing can be managed to prevent the severity index from exceeding 8 and avoid long-term impacts on the fish community (Khakzad & Elfimov 2015b). This could involve developing a relationship between turbidity and suspended solids specific for Dez reservoir sediments and developing a relationship between suspended solids immediately below the Dez dam (after dilution with power and spillway flow) and turbidity. Since turbidity can be measured without laboratory analysis, flushing can be discontinued when the fish severity index would exceed 8 (Khakzad & Elfimov 2014b).

The effects of dredging and offsite disposal are considered insignificant compared to flushing but require some mitigation. Much of the mitigation involves: (1) the selection of an ideal disposal site that does not affect local villages; (2) minimizing the effects of suspended sediment on fish communities within the reservoir by selection of an environmentally sound technique. If a clam-type dredge were utilized, than some means to control the loss of sediment into the water column would need to be developed.

Since most of the land that would be flooded by raising is unproductive and provides little or no wildlife habitat, mitigation would be minimal. The principal areas of concern are the inhabitants of the two villages adjacent to the Dez reservoir that may have to be resettled or compensated for loss of land depending on the extent of dam heightening.

Economic criteria are the basic measures in evaluating sustainable sediment management alternatives. The general methodology applied to the economic evaluation of the alternatives considered in the current study is based on the discounted cash flow (DCF) technique to compute the present values of future cash flows that an investment would generate. The DCF technique requires that we define cash flow over the planning horizon for the various options being considered. Costs have been broken down into capital costs and operation and maintenance (O&M) costs. Benefit analysis is more complex than cost analysis since benefits accrue from the use of water for agriculture, power, domestic and industrial needs and salinity control. The benefits have been grouped into two categories for the current analysis. The first category is termed ‘fixed benefits’ for this study and includes a predetermined demand for water and an associated reliability requirement. These benefits include agriculture, domestic and industrial needs and salinity control. These benefits are relatively inflexible, in that they must be met or significant and potentially longer term economic, social or environmental impacts may occur (e.g. crop loss). The second category of benefits for this study is termed ‘variable benefits’, in that they are relatively scalable with flow (firm or average) and are composed primarily of power benefits.

Method

Synthesizing the individual opinions in a value representative of a group is usually performed through an aggregation process. Yager introduced a new aggregation technique based on OWA operators. OWA is a soft aggregation operator, suitable for modeling the DM's risk attitude in a GDM problem. The OWA operator is defined as (Yager 1994; Lamata 2004; Mesiar et al. 2015): 
formula
(1)
where bi is the ith largest element in the collection of x1, x2,…, xn.
By choosing different weighting vectors, OWA provides different aggregated results. The range the OWA covers varies from min to max (Figure 2). For example, the following three particular weight vectors generate min, arithmetic average, and max operators respectively. 
formula
(2)
 
formula
(3)
 
formula
(4)
Figure 2

The OWA aggregation.

Figure 2

The OWA aggregation.

Yager introduced another ORness measure for the OWA operator: 
formula
(5)
The ORness value reflects the degree of optimism of DMs. The larger the ORness, the more optimistic the DMs are. OWA operators allow us, through an appropriate selection of parameters, the so-called OWA weights, to model any degree of ORness between 0 (corresponding to a pure and) and 1 (corresponding to a pure OR). Since min and max evaluate the quantifiers ∀ (for all) and ∃ (at least one), respectively, the OWA operators essentially extend the space of quantifiers from the pair {∀, ∃} to the interval [∀, ∃]. For example, 
formula
(6)
 
formula
(7)
 
formula
(8)

The degree of ORness indicates the position of OWA on a continuum between the AND and OR operators. It emphasizes the higher (better) values or the lower (worse) values in a set of attributes associated with the ith alternative. The greater the ORness value, the higher level of the DM's optimism. There is theoretical as well as empirical evidence that individuals with optimistic (or risk-taking) attitudes tend to focus on positive properties of alternatives while pessimistic or risk averse DMs tend to emphasize negative properties of alternatives (Malczewski & Rinner 2005).

Different methods are introduced in the literature for determining the order weights (Xu 2005). In this section fuzzy quantifiers are used to characterize aggregation imperatives, in which the more objects are included, the higher is the satisfaction level. Some examples of these quantifiers are most, half, few or at least one of them. These linguistic inputs are modeled by regular increasing monotonic quantifiers that satisfy the following conditions: 
formula
(9)
Function Q maps the unit interval I = [0, 1] into itself and is really a fuzzy membership function. It can be associated to an n-dimensional OWA operator, where the components of the weighting vector are obtained as: 
formula
(10)
There are many different possibilities for selecting fuzzy membership function Q. A particular form has been chosen as with a given positive parameter . The optimism degree can be calculated by using (10) and (8) and by introducing the new variable and computing the limit as n tends to infinity: 
formula
(11)

The corresponding optimism degree values are shown in Table 2.

Table 2

The corresponding optimism degree values

Linguistic quantifierParameter of quantifier, γOptimism degree
At least one of them γ → 0.0 0.999 
Few of them 0.1 0.909 
Some of them 0.5
1.0
0.667 
Half of them 1.0 0.5 
Many of them 2.0 0.333 
Most of them 10.0 0.091 
All of them γ → ∞ 0.001 
Linguistic quantifierParameter of quantifier, γOptimism degree
At least one of them γ → 0.0 0.999 
Few of them 0.1 0.909 
Some of them 0.5
1.0
0.667 
Half of them 1.0 0.5 
Many of them 2.0 0.333 
Most of them 10.0 0.091 
All of them γ → ∞ 0.001 

RESULTS AND DISCUSSION

We can now determine the combined goodness measures of alternatives for sustainable sediment management in the Dez dam reservoir by using the OWA. Schematic representation of a step-by-step OWA generation process is shown in Figure 3. The calculation procedure is as follows.

Figure 3

Schematic representation of a step-by-step OWA generation process.

Figure 3

Schematic representation of a step-by-step OWA generation process.

Step (1) Every expert in the group expresses his/her evaluation of each alternative in a different preference mentioned formats. In these assessments, ordinal preferences of alternatives are represented by , which defines the preference-ordering evaluation given by DMi to alternative xs. Fuzzy preference relation is expressed by where with membership function and where is a finite set of alternatives. Value defines a ratio of the fuzzy preference intensity of alternative xs to xm. Multiplicative preference relations are represented as Ai where and is a ratio of the fuzzy preference intensity of alternative xs to xm given by DMi. Utility function is shown as Ui where DMi explains his/her Attributes on alternatives as n-tuple utility values. Utility value of alternative xs given by DMi is presented by .

Step (2) Information from step 1 is transformed into a fuzzy preference relationship by an appropriate transformation function. A common transformation between the various preferences is as follows: 
formula
(12)
 
formula
(13)
 
formula
(14)
Step (3) The proposed OWA operator to form the collective preference relation aggregates individual fuzzy relations. 
formula
(15)
where ksm is a ratio of the fuzzy group preference of alternative xs to xm and Q is a fuzzy linguistic quantifier that represents the concept of the fuzzy majority and is used to calculate the weighting vector.

Step (4) Quantifier guided dominance degree (QGDD)i of the alternative xi is calculated. This quantity calculates the dominance of the alternative xi over other alternatives and collective alternative (Equation (16)). Where Pq(xi) defines the preference degree or intensity of alternative xi over others alternatives given by DMq.

Step (5) Difference between individual opinion and group opinion is calculated by using Equation (17). Where Parameter b controls the rigorousness of the consensus process; Sq(Ci) represents the degree of proximity of individual opinion to collective opinion. Pq(xi) and Pg(xi) represent the evaluation given by DMq and collective evaluation to alternative xi, respectively. 
formula
(16)
 
formula
(17)

Step (6) Calculate S(Ci)pis, S(Ci)Nis the minimum and maximum difference between individual opinions with collective opinions, respectively.

Step (7) Aggregated average of disagreement of all DMs on each alternative xi(CM(Ci)) and on all alternatives (CM(C)) is calculated as: 
formula
(18)
 
formula
(19)
Step (8) The consensus measure on each alternative is calculated by using the following expressions: 
formula
(20)
Step (9) The averages of minimum and maximum disagreement of all DMs on all alternatives (GSCL(C)), (GWCL(C)) are calculated by the following functions, respectively: 
formula
(21)
 
formula
(22)
Step (10) The consensus measure on all alternatives (GC) is obtained as follows: 
formula
(23)

Step (11) If GC>CL, the process is finished and the calculated QGDDs in step 4, is assigned as the relative importance of the criteria, because QGDDi is the dominance of criterion ci over other criteria. These values are used as collective weights of attributes for selecting the best possible alternative. Otherwise, go to step 12.

Step (12) In this step, all DMs will be asked to modify their opinions to reach consensus.

Step (13) If the number of rounds of discussion (NRD) is more than the maximum pre-defined cycle (MC), stop the process of discussion and assign QGDDs to criteria. Otherwise, go to step 14.

Step (14) After modifying the experts' opinions, all steps (from step 2 to the end) are recalculated again and this process is continued until GC>CL or NRD > MC.

Step (15) According to the obtained group weights and by using an appropriate multi attribute decision making (MADM) approach, the final and most preferable alternative is selected and all experts are informed by the group manager.

For implementation of OWA for sediment management in Dez hydropower reservoir, a list of potential alternatives and criteria are prepared (Table 3). Twelve DMs have been considered to evaluate the weights of eight criteria. The watershed governing board has requested to find the most robust alternative among these projects with respect to the eight criteria. The criteria and the evaluations of the projects with respect to these criteria were done by a group of experts. There are several factors that may lead to conflict of interest among DMs, which range from the environmental objectives pursued, different rates of socio-economic development for the region, level of engagement and means of participation, and alternative measures to be undertaken.

Table 3

Evaluations of the sediment management alternatives in Dez reservoir with respect to eight criteria

The complexity in the implementation processConstruction & operation timeEconomic costsEconomic benefitsEffects on fishesEffects on water usersEffects on water qualityResettlement
Watershed rehabilitation Medium Medium Very high Low Low Medium Slightly low Slightly high 
Irrigation outlet rehabilitation Low Low Medium Low Medium Slightly high Medium Very low 
Irrigation outlet replacement Slightly high Slightly low Medium Slightly high Medium Medium Medium Very low 
Access tunnel flushing Low Very low Slightly low Low Very high High Very high Medium 
Reservoir dredging near the dam Low Medium High Medium Slightly high Medium Medium Low 
Excavation of the upper delta Slightly low Medium Slightly high Slightly low Slightly high Medium Low Low 
Dam raising Very high Slightly high Slightly low Very high Medium Slightly low Low Medium 
The complexity in the implementation processConstruction & operation timeEconomic costsEconomic benefitsEffects on fishesEffects on water usersEffects on water qualityResettlement
Watershed rehabilitation Medium Medium Very high Low Low Medium Slightly low Slightly high 
Irrigation outlet rehabilitation Low Low Medium Low Medium Slightly high Medium Very low 
Irrigation outlet replacement Slightly high Slightly low Medium Slightly high Medium Medium Medium Very low 
Access tunnel flushing Low Very low Slightly low Low Very high High Very high Medium 
Reservoir dredging near the dam Low Medium High Medium Slightly high Medium Medium Low 
Excavation of the upper delta Slightly low Medium Slightly high Slightly low Slightly high Medium Low Low 
Dam raising Very high Slightly high Slightly low Very high Medium Slightly low Low Medium 

Before applying the method, the original data in Table 3 are synthesized as follows. Step 1. The evaluations of the projects with respect to the criteria are either linguistic or crisp numbers. The linguistic data are transformed into crisp numbers according to the scale shown in Table 4. Step 2. The evaluations of the alternatives with respect to the criteria are normalized into the unit interval [0, 1] by using the linear transformation. Step 3. In the original version of OWA, the criteria weights are considered to be equal. However, in this case the weights are different. Therefore, the normalized evaluations of the alternatives are multiplied by their weights. The final evaluation matrix is shown in Table 5.

Table 4

Linguistic variables and equivalent crisp numbers

Linguistic variablesNumber
Very low 0.05 
Low 0.2 
Slightly low 0.35 
Medium 0.5 
Slightly high 0.65 
High 0.8 
Very high 0.95 
Linguistic variablesNumber
Very low 0.05 
Low 0.2 
Slightly low 0.35 
Medium 0.5 
Slightly high 0.65 
High 0.8 
Very high 0.95 
Table 5

The weighted normalized inputs

The complexity in the implementation processConstruction & operation timeEconomic costsEconomic benefitsEffects on fishesEffects on water usersEffects on water qualityResettlement
Watershed rehabilitation 0.5 0.5 0.95 0.2 0.2 0.5 0.35 0.65 
Irrigation outlet rehabilitation 0.2 0.2 0.5 0.2 0.5 0.65 0.5 0.05 
Irrigation outlet replacement 0.65 0.35 0.5 0.65 0.5 0.5 0.5 0.05 
Access tunnel flushing 0.2 0.05 0.35 0.2 0.95 0.8 0.95 0.5 
Reservoir dredging near the dam 0.2 0.5 0.8 0.5 0.65 0.5 0.5 0.2 
Excavation of the upper delta 0.35 0.5 0.65 0.35 0.65 0.5 0.2 0.2 
Dam raising 0.95 0.65 0.35 0.95 0.5 0.35 0.2 0.5 
The complexity in the implementation processConstruction & operation timeEconomic costsEconomic benefitsEffects on fishesEffects on water usersEffects on water qualityResettlement
Watershed rehabilitation 0.5 0.5 0.95 0.2 0.2 0.5 0.35 0.65 
Irrigation outlet rehabilitation 0.2 0.2 0.5 0.2 0.5 0.65 0.5 0.05 
Irrigation outlet replacement 0.65 0.35 0.5 0.65 0.5 0.5 0.5 0.05 
Access tunnel flushing 0.2 0.05 0.35 0.2 0.95 0.8 0.95 0.5 
Reservoir dredging near the dam 0.2 0.5 0.8 0.5 0.65 0.5 0.5 0.2 
Excavation of the upper delta 0.35 0.5 0.65 0.35 0.65 0.5 0.2 0.2 
Dam raising 0.95 0.65 0.35 0.95 0.5 0.35 0.2 0.5 

The disagreement measures on all alternatives (CM(C)) and the average of minimum and maximum disagreement on all alternatives (GSCL(C)), (GWCL(C)). The consensus measures on all alternatives (GC) for each alternative, by using Equations (18)–(23), are computed and then listed in Table 6 for this most likely degree of optimism. The maximum expected values and the variances are also indicated in Table 6 with bold face numbers.

Table 6

Ranking of the alternatives with various degree of optimism

Consensus and disagreement measure on all criteria
Optimism degreeRanking of the alternativesGWCLGSCLCMCGC
0.999 1- Reservoir dredging near the dam
2- Dam raising
3- Access tunnel flushing 
0.7783 0.5315 0.7574 0.0846 
0.909 1- Reservoir dredging near the dam
2- Dam raising
3- Access tunnel flushing 
0.6078 0.3908 0.4618 0.6727 
0.667 1- Reservoir dredging near the dam
2- Dam raising
3-Irrigation outlet replacement 
0.2036 0.1018 0.0495 1.5134 
0.5 1- Dam raising
2- Reservoir dredging near the dam
3-Irrigation outlet replacement 
0.0525 0.0200 0.0029 1.5250 
0.333 1- Dam raising
2- Reservoir dredging near the dam
3-Irrigation outlet replacement 
0.0035938 0.0009375 1.045E-05 1.3490 
0.091 1- Dam raising
2- Reservoir dredging near the dam
3-Irrigation outlet replacement 
2.981E-12 5.681E-13 3.339E-24 1.2354 
0.001 1- Dam raising
2- Reservoir dredging near the dam
3-Irrigation outlet replacement 
1.68E-113 3.21E-114 1.03E-226 1.2353 
Consensus and disagreement measure on all criteria
Optimism degreeRanking of the alternativesGWCLGSCLCMCGC
0.999 1- Reservoir dredging near the dam
2- Dam raising
3- Access tunnel flushing 
0.7783 0.5315 0.7574 0.0846 
0.909 1- Reservoir dredging near the dam
2- Dam raising
3- Access tunnel flushing 
0.6078 0.3908 0.4618 0.6727 
0.667 1- Reservoir dredging near the dam
2- Dam raising
3-Irrigation outlet replacement 
0.2036 0.1018 0.0495 1.5134 
0.5 1- Dam raising
2- Reservoir dredging near the dam
3-Irrigation outlet replacement 
0.0525 0.0200 0.0029 1.5250 
0.333 1- Dam raising
2- Reservoir dredging near the dam
3-Irrigation outlet replacement 
0.0035938 0.0009375 1.045E-05 1.3490 
0.091 1- Dam raising
2- Reservoir dredging near the dam
3-Irrigation outlet replacement 
2.981E-12 5.681E-13 3.339E-24 1.2354 
0.001 1- Dam raising
2- Reservoir dredging near the dam
3-Irrigation outlet replacement 
1.68E-113 3.21E-114 1.03E-226 1.2353 

A comparison of the aggregated average of disagreement of all criteria on each alternative xi(CM(Ci)) and on all alternatives (CM(C)) and aggregated average of agreement of all criteria, indicates that three alternatives were ranked as high, those being the replacement of the Howell Bunger valves with slide gates, dredging near the dam option and the dam raising alternative. There was a positive net benefit for irrigation outlet replacement since it was judged to be able to flush out the sediment in the wedge without major damage from passing the sediment. This would eliminate the present leakage issues, provide a means of drawing down the reservoir and flushing sediment to maintain the wedge storage. This sediment flushing operation thereby limits the sediment entering the power intakes. Dam raising produces the highest present value of net benefits and directly addresses the loss of storage volume. It would have to be combined with an alternative for rehabilitating or replacing the irrigation outlets to directly address the potential for power intake sedimentation and to maintain the reservoir draw down capabilities. Based on temperature and oxygen profiles taken in the Dez reservoir, it appears that the reservoir does not stratify and oxygen levels are relatively high throughout the water column. There are at least two villages that may require resettlement due to an increased water level in the Dez reservoir. Resettlement of these communities would require that livelihoods of the residents are maintained, and undue hardship is minimized. Dredging is very sensitive to the cost of dredging and produces present values of net benefits, which range from a small positive value. Dredging operations often result in increased suspended sediment in the water column. The extent of increased suspended sediment in the water column is highly dependent on the type of dredger used, with a clam-type dredge most likely to increase suspended sediment and an airlift dredger or suction dredge less likely to significantly increase suspended sediment. Since the sediments in the Dez reservoir are not contaminated, loss of sediment to the water column is less of a problem.

CONCLUSION

The aim of this article was the solution of a hierarchy multi-criteria decision making (MCDM) for sustainable sediment management in dam reservoirs, where the preferences are stated by a fuzzy number. We considered a definition of such a total order, which is based on two subjective aspects: the degree of optimism/pessimism reflected with the OWA operators. This paper adopted a distance measure method to evaluate the measure of consensus. In this study, a significant number of sediment management alternatives in the Dez hydropower reservoir identified and described the successful application of the OWA principles to a major process for ranking sediment management alternatives in the Dez hydropower reservoir. Based on the results, the options of replacement of the Howell Bunger valves with slide gates, dredging near the dam and the dam raising alternative were ranked at a high level. Results show that DMs are more concerned about the environmental and ecological objectives than the socio-economic ones. Results and application of the proposed framework to rank sediment management alternatives showed that this method provides a powerful tool for the selection of the optimum response scenario against the identified risks and could help the DMs in selecting the most preferred alternative considering the preferences of different DMs.

REFERENCES

REFERENCES
Ahn
B. S.
2008
Preference relation approach for obtaining OWA operators weights
.
International Journal of Approximate Reasoning
47
(
2
),
166
178
.
Averna Valente
R. O.
Vettorazzi
C. A.
2008
Definition of priority areas for forest conservation through the ordered weighted averaging method
.
Forest Ecology and Management
256
(
6
),
1408
1417
.
Bullen
P. S.
Mitrinovic
D. S.
Vasic
P. M.
1988
Means and Their Inequalities, Mathematics and its Applications
.
D. Reidel Publishing Co.
,
Dordrecht
, pp.
31
.
Calvo
T.
Mesiar
R.
2003
Weighted triangular norms-based aggregation operators
.
Fuzzy Sets and Systems
137
(
1
),
3
10
.
Chen
Z.
2005
Consensus In Group Decision Making Under Linguistic Assessments
.
PhD thesis
,
Kansas State University
.
Delgado
M.
Verdegay
J. L.
Vila
M. A.
1993
On aggregation operations of linguistic labels
.
International Journal of Intelligent Systems
8
(
3
),
351
370
.
Despic
O.
Simonovic
S. P.
2000
Aggregation operators for soft decision making in water resources
.
Fuzzy Sets and Systems
115
,
11
33
.
Dezab Consulting Engineers in association with ACTRES International
2004
Dez Dam Rehabilitation Project Contract No. 81-5M334
.
Iranian Minister of Energy
,
Tehran
.
Dubois
D.
Fargier
H.
Prade
H.
1996
Refinements of the maximin approach to decision-making in a fuzzy environment
.
Fuzzy Sets and Systems
81
(
1
),
103
122
.
Fu
G.
Hall
J.
Lawry
J.
2006
Beyond Probability: New Methods for Representing Uncertainty in Projections of Future Climate
.
Tyndall Centre for Climate Change Research Working Paper 75
, .
Khakzad
H.
Elfimov
V. I.
2014a
Evaluation of flow regime of turbidity currents entering Dez Reservoir using extended shallow water model
.
Water Science and Engineering
7
(
3
),
267
276
.
Khakzad
H.
Elfimov
V. I.
2014b
Using turbidity to determine total suspend solids – field measurement: Dez dam reservoir
.
Journal of Water Sustainability
4
(
2
),
77
89
.
Khakzad
H.
Elfimov
V. I.
2015b
Estimate of time required for environmental friendly flushing in Dez dam reservoir
.
Water Practice & Technology
10
(
1
),
73
85
.
Kouchakinejad
F.
Šipošová
A.
2017
Ordered weighted averaging operators and their generalizations with applications in decision making
.
Iranian Journal of Operations Research
8
(
2
),
48
57
.
Lamata
M.
2004
Ranking of alternatives with ordered weighted averaging operators
.
International Journal of Intelligent Systems
19
(
5
),
473
482
.
Liu
X.
2006
Some properties of the weighted OWA operator
.
IEEE Transactions on Systems, Man and Cybernetics, Part B
36
(
1
),
118
127
.
Malczewski
J.
2006
Ordered weighted averaging with fuzzy quantifiers: GIS-based multicriteria evaluation for land-use suitability analysis
.
International Journal of Applied Earth Observation and Geoinformation
8
(
4
),
270
277
.
Marichal
J.-L.
Mathonet
P.
Tousset
E.
1999
Characterization of some aggregation functions stable for positive linear transformations
.
Fuzzy Sets and Systems
102
(
2
),
293
314
.
Marimin
M.
Umano
M.
Hatono
I.
Tamura
H.
2002
Hierarchical semi-numeric method for pairwise fuzzy group decision making
.
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
32
(
5
),
691
700
.
McPhee
J.
Yeh
W. W.
2004
Multiobjective optimization for sustainable groundwater management in semiarid regions
.
Journal of Water Resources Planning and Management
130
(
6
),
490
497
.
Mesiar
R.
Stupňanová
A.
Yager
R. R.
2015
Generalizations of OWA operators
.
IEEE Transactions on Fuzzy Systems
23
(
6
),
2154
2162
.
Mianabadi
H.
Afshar
A.
2007
Group decision making, calculation of relative weights of decision makers to select Ph.D students
.
Iranian Journal of Engineering Education
9
(
35
),
31
53
.
Mysiak
J.
Giupponi
C.
Rosato
P.
2005
Towards the development of a decision support system for water resource management
.
Environmental Modelling & Software
20
,
203
214
.
Nikolaos
P. E.
Palt
S.
Annandale
G. W.
Karki
P.
2017
Reservoir Conservation Model Rescon 2 Beta
.
International Bank for Reconstruction and Development/The World Bank
,
Geneva, Switzerland
.
Reimann
O.
Schumacher
C.
Vetschera
R.
2017
How well does the OWA operator represent real preferences?
European Journal of Operational Research
258
(
3
),
993
1003
.
Sadiq
R.
Rodríguez
M. J.
Tesfamariam
S.
2010
Integrating indicators for performance assessment of small water utilities using ordered weighted averaging (OWA) operators
.
Expert Systems with Applications
37
(
7
),
4881
4891
.
Sicilia
M. A.
Garcia-Barriocanal
E.
Sánchez-Alonso
S.
2008
Empirical assessment of a collaborative filtering algorithm based on OWA operators
.
International Journal of Intelligent Systems
23
,
1251
1263
.
Stroppiana
D.
Boschetti
M.
Brivio
P. A.
Carrara
P.
Bordogna
G.
2009
A fuzzy anomaly indicator for environmental monitoring at continental scale
.
Ecological Indicators
9
(
1
),
92
106
.
Sugeno
M.
1974
The Theory of Fuzzy Integrals and Its Applications
.
PhD thesis
,
Tokyo Institute of Technology
.
Torra
V.
2004
OWA operators in data modeling and reidentification
.
IEEE Transactions on Fuzzy Systems
12
(
5
),
652
660
.
Verma
R.
Sharma
B.
2016
Prioritized information fusion method for triangular fuzzy information and its application to multiple attribute decision making
.
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
24
,
265
290
.
Xu
Z.
2005
An overview of methods for determining OWA weights
.
International Journal of Intelligent Systems
20
,
843
865
.
Yager
R. R.
1988
On ordered weighted averaging aggregation operators in multicriteria decision making
.
IEEE Transactions on Systems, Man and Cybernetics
18
(
1
),
183
190
.
Yager
R. R.
1993
Non-numeric multi-criteria multi-person decision making
.
Group Decision and Negotiation
2
,
81
93
.
Yager
R. R.
1994
Interpreting linguistically quantified propositions
.
International Journal of Intelligent Systems
9
(
6
),
541
569
.
Yager
R. R.
1998
Including importances in OWA aggregations using fuzzy systems modeling, Fuzzy Systems
.
IEEE Transactions on
6
(
2
),
286
294
.
Yager
R. R.
2003
Induced aggregation operators
.
Fuzzy Sets and Systems
137
(
1
),
59
69
.
Yager
R. R.
2008
Time series smoothing and OWA aggregation
.
IEEE Transactions on Fuzzy Systems
16
(
4
),
994
1007
.
Yager
R. R.
Kacprzyk
J.
Beliakov
G.
2011
Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice
.
Springer-Verlag
,
Berlin, Heidelberg
.
Yalcin
G.
Akyurek
Z.
2004
Multiple criteria analysis for flood vulnerable areas
. In:
Proc. of 24th Annual ESRI International User Conference
,
August
,
San Diego, USA
, pp.
9
13
.
Zarghami
M.
Szidarovszky
F.
2011
Multicriteria Analysis: Applications to Water and Environment Management
.
Springer-Verlag
,
Berlin, Heidelberg
.
Zarghami
M.
Ardakanian
R.
Memariani
A.
Szidarovszky
F.
2008
Extended OWA operator for group decision making on water resources projects
.
Journal of Water Resources Planning and Management
134
(
3
),
266
275
.