Linear Programming Technique For Multidimensional Analysis Of Preference Research Articles

Multi-objective optimization of twisted tri-lobed tube geometry for enhanced heat transfer and reduced resistance in turbulent flow

This study presents a detailed multi-objective optimization analysis of turbulent flow and heat transfer within a twisted tri-lobed tube, employing an integrated approach that combines Central Composite Design (CCD), Response Surface Methodology (RSM), Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto frontier analysis, Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The investigation focuses on optimizing key design parameters: Reynolds number (Re), twist pitch (P), and minor circle radius (r), targeting Nusselt number (Nu), Poiseuille number (fRe), and Performance Evaluation Criterion (PEC) as optimization objectives. Our major findings reveal that the developed second-order regression model precisely predicts the influences of these parameters on Nu, fRe, and PEC, with sensitivity analysis showing Re's strong positive impact on Nu and fRe, P's negative effect on fRe, and r's minimal impact. The study notably highlights the significant Nu enhancement with Re increase. Utilizing multi-objective optimization, we identified a Pareto optimal set, and through LINMAP and TOPSIS methods, derived compromise solutions that optimally balance heat transfer efficiency, flow resistance, and overall performance. These outcomes underscore the critical importance of parameter selection to meet specific engineering needs, offering a strategic framework for enhancing twisted tri-lobed tube designs.

A big data quality evaluation method based on group heterogeneity rationality perception information fusion

Big data is complex, and it is difficult to evaluate big data quality with only a few evaluation subjects. This paper designs a universal evaluation method for big data quality based on the idea of group heterogeneity rationality perception information fusion. Group evaluation information is usually large-scale and heterogeneous. The linear programming technique for multidimensional analysis of preference (LINMAP) model has the performance of large-scale evaluation information processing. Because the existing LINMAP models cannot effectively process group evaluation information with heterogeneous rationality, the LINMAP model of heterogeneous rationality (HR-LINMAP) based on group evaluation information is proposed. The research results show: under certain conditions, the LINMAP model of bounded rationality (BR-LINMAP) can be transformed into the LINMAP model of perfect rationality (PR-LINMAP), and the HR-LINMAP is the general form of PR-LINMAP and BR-LINMAP. The scientific research big data resources with mature trading markets are selected as the evaluation objects, and HR-LINMAP is used to analyze the big data quality evaluation cases. The empirical analysis shows that the HR-LINMAP model is feasible and effective, which provides a new idea for big data quality evaluation.

Multi-objective optimization of thermal modules in high heat flux laptops

The thermal module, as an important cooling pathway for chips, is a major factor affecting the performance of laptops. However, thermal analysis and optimization of the whole thermal module of a laptop is absent. Moreover, cost is also a major consideration in the design of a laptop’s thermal module. In this study, based on the thermal module of a high heat flux prototype laptop, we constructed an efficient thermal resistance network model and a cost model to evaluate the impact of different components. Furthermore, we employed NSGA-II (non-dominated sorting genetic algorithm II) to enhance the thermal module's heat dissipation capacity while minimizing cost. By obtaining Pareto solutions that provided optimal thermal resistances for the components in the thermal module, we then utilized LINMAP (linear programming technique for multidimensional analysis of preference) as a decision-making method to determine the best compromise solution. The best compromise solution focuses on reducing the thermal resistances of the thermal interface material on the high heat flux APU side, the shared heat pipe, and heatsinks to enhance the heat dissipation capacity of the thermal module. To control cost, sacrifices were made in the heat transfer performances of the thermal interface material on the GPU side and the independent heat pipes. Comparing the best compromise solution with the prototype, the cooling capacity is improved by 24% and cost is reduced by 9%. The efficient model coupled with optimization method may provide a new theoretical guideline for the laptop designers.

A property perceived service quality evaluation method for public buildings based on multisource heterogeneous information fusion

The basic information of property perceived service quality (PPSQ) evaluation for public buildings is characterized by multisource heterogeneity, which cannot be achieved using the existing evaluation methods. Based on the classical linear programming technique for multidimensional analysis of preference (LINMAP), a multiobjective LINMAP model is constructed, and a new PPSQ evaluation method is proposed to solve the above problem. Constructing the multiobjective LINMAP model is the core of the new PPSQ evaluation method design. The proposed multiobjective LINMAP model includes the following: First, multisource heterogeneous evaluation information is collected by the generalized multi-index multi-scale (MIMS) method, and normalized by the TOPSIS method. Then, the LINMAP model is extended by the objective function, which is constructed with the minimum mean standard deviation (MMSD) between multiple information sources. Finally, the source weight and index weight are determined by the above model, the ranking order of each property service project is calculated, and the comprehensive value of the property service project is obtained. The example study verifies the feasibility and effectiveness of the multiobjective LINMAP model which is suitable for the new requirement of comprehensively and objectively evaluating PPSQ for public buildings.

4E analysis of a two-stage refrigeration system through surrogate models based on response surface methods and hybrid grey wolf optimizer.

Refrigeration systems are complex, non-linear, multi-modal, and multi-dimensional. However, traditional methods are based on a trial and error process to optimize these systems, and a global optimum operating point cannot be guaranteed. Therefore, this work aims to study a two-stage vapor compression refrigeration system (VCRS) through a novel and robust hybrid multi-objective grey wolf optimizer (HMOGWO) algorithm. The system is modeled using response surface methods (RSM) to investigate the impacts of design variables on the set responses. Firstly, the interaction between the system components and their cycle behavior is analyzed by building four surrogate models using RSM. The model fit statistics indicate that they are statistically significant and agree with the design data. Three conflicting scenarios in bi-objective optimization are built focusing on the overall system following the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) decision-making methods. The optimal solutions indicate that for the first to third scenarios, the exergetic efficiency (EE) and capital expenditure (CAPEX) are optimized by 33.4% and 7.5%, and the EE and operational expenditure (OPEX) are improved by 27.4% and 19.0%. The EE and global warming potential (GWP) are also optimized by 27.2% and 19.1%, where the proposed HMOGWO outperforms the MOGWO and NSGA-II. Finally, the K-means clustering technique is applied for Pareto characterization. Based on the research outcomes, the combined RSM and HMOGWO techniques have proved an excellent solution to simulate and optimize two-stage VCRS.

A fairness-concern-based LINMAP method for heterogeneous multi-criteria group decision making with hesitant fuzzy linguistic truth degrees

Heterogeneous multi-criteria group decision making (MCGDM) is a hot topic in the decision analysis field. This paper proposes a fairness-concern-based LINMAP (Linear Programming Technique for Multidimensional Analysis of Preference) method for heterogeneous MCGDM with hesitant fuzzy linguistic (HFL) truth degrees. Heterogeneous evaluation information includes crisp numbers, interval numbers, intuitionistic fuzzy values (IFVs), trapezoidal fuzzy numbers (TrFNs) and hesitant fuzzy sets (HFSs). This paper introduces the fairness concern to calculate the HFL consistency and the HFL inconsistency indices. Based on the framework of LINMAP, a bi-objective HFL programming model is built to derive the criteria weights, the positive ideal fairness vector (PIFV) and the negative ideal fairness vector (NIFV) for each decision maker (DM) simultaneously. Based on the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), a multi-objective programming model is built to obtain DMs’ weights. The alternatives ranking is derived by comprehensive collective relative closeness degrees. Finally, a real example is applied to verify effectiveness and superiority of this heterogeneous MCGDM method. The proposed heterogeneous MCGDM method provides a very useful approach for MCGDM with heterogeneous information.

Technical and economic modeling and optimization of a Ford-Philips engine for power production

In this study, for the first time, the effects of various parameters including engine rotational speed, engine pressure, heater temperature, and piston stroke on technical (energy and exergy) and economic (cost savings and payback period) performance of a Ford-Philips 4-215 engine is investigated. Considering the different engine losses, a thermodynamic model of the engine is employed and validated with available experimental data. The results reveal that the increase in engine pressure and heater temperature, augments the capacity and efficiency of the engine, respectively, and increasing the engine rotational speed and piston stroke first shortens the payback period and thereafter makes it longer. Moreover, the engine parameters are designed from six different technical and economic standpoints, and the optimal parameters are selected using two well-known decision methods, namely, the linear programming technique for multidimensional analysis of preference (LINMAP) and the technique for order preference by similarity to ideal solution (TOPSIS). In one of the cases, from energy and economic viewpoints, engine parameters have been designed and the maximum electric power and minimum payback period have been gauged at 260.46 kW and 6.10 years, respectively. In another case, from the exergy perspective, the maximum exergy efficiency and minimum exergy destruction are 65.17 % and 6.81 kW, respectively. Finally, by performing a three-objective optimization (energy, exergy, and economic), the maximum output power and exergy efficiency are evaluated 258 kW and 44.5%, respectively at a 5-year payback period.

Assessing Human Performance Influencing Factors through LINMAP and Bayesian Belief Networks

This study aims at identifying and ranking the performance influencing factors (PIFs) that cause error in human operations. The failure weight and rate for the tasks carried out by each operator were investigated. Assessing these factors reduces human error, hence increasing safety, efficiency and job satisfaction. The methods of linear programming technique for multidimensional analysis of preference (LINMAP) and Bayesian Belief Networks were used to investigate an aircraft tire manufacturing industry. All operators in the workshops were evaluated. Based on data analysis, the tasks of each operator were weighted and the potential error rate of each task was obtained. PIFs for each workshop were ranked and prioritized so that the factors having most influence can be easily distinguished and the tasks where the operators have the highest rate of failure, can be identified. The probability of human error was obtained and in a predictive model, it can be determined that when an error occurs, which factors are most influential in its occurrence. The method utilized does not include copious pairwise, exhausting and at times confusing comparisons for operators.

A multi-granular linguistic distribution-based group decision making method for renewable energy technology selection

The scarcity of resources requires a decrease in nonrenewable energy consumption, which progressively promotes the development of renewable energy due to its immense potential and environmental friendliness. Hence, the use of renewable energy technology is critical for realizing the economic effect, the environment effect and the social benefit unified. Generally, renewable energy technology selection is treated as a multiple criteria group decision making problem. However, decision makers are not allowed to express multiple preferences via personalized linguistic distribution assessments deliberating on diverse criteria in the existing approaches. This work proposes a multi-granular linguistic distribution-based group decision-making method by linking multi-granular linguistic distribution assessments and LINMAP (Linear Programming Technique for Multidimensional Analysis of Preference) method with a mathematical model that can simultaneously yield the credible weights of the considered criteria and prioritize the sequence of optimal renewable energy technologies. To this end, the linguistic distribution-based Hellinger distance measure and linguistic hierarchy-based multi-granular linguistic distribution transformation method are proposed. The decision framework is applied to a case study of power generation-based technology selection, generating reliable criteria weights and yielding acceptable outcomes based on collected assessments. Eventually, the sensitivity analysis and comparative analysis are conducted to verify the feasibility and practicability of our proposal. This flexible decision support technique is geared towards managers and strives to provide reference and inspiration for renewable energy technology selection.

Multi-objective optimization of tensile properties of the corrugated composite sheet

Corrugated sheets with optimized mechanical properties are crucial for lightweight design in industrial applications. This study considered and optimized a corrugated sheet with a sinusoidal profile to enhance elastic modulus, tensile-bending coupling, and weight reduction. For this aim, first, flat specimens consisting of E-glass woven fiber and epoxy resin were made by hand lay-up method, following ASTM D3039. The tensile test determined young’s modulus of flat samples. Afterward, two molds with supports were fabricated. The corrugated specimens were constructed and exposed to a standard tensile test. The finite element analysis was used to simulate the tensile test of corrugated samples. The numerical force-displacement curve is derived from numerical analysis and verified by experimental results. After that, two multi-objective optimization problems, mass-constraint and global optimization, were implemented. Analytical formulations were verified by numerical and experimental results and utilized for optimization purposes. The genetic algorithm was used to examine and confirm trade-off behavior between objective functions. The Pareto fronts diagrams for mentioned two multi-objective optimization problem were obtained. Finally, the optimum parameters are calculated by using the LINMAP (Linear Programming Technique for Multi-dimensional Analysis of Preference) method.

A CRITERION UTILITY CONVERSION TECHNIQUE FOR PROBABILISTIC LINGUISTIC MULTIPLE CRITERIA ANALYSIS IN EMERGENCY MANAGEMENT

In multiple criteria decision making (MCDM), the even swaps method uses the relationships of criteria to make trade-offs but the burdens of experts are heavy; the linear programming technique for multidimensional analysis of preference (LINMAP) method cannot deal with the inter-dependencies among criteria but the cognitive burdens of experts are low. Taking the advantages of both these methods, this study proposes a criterion utility conversion (CUC) technique to solve probabilistic linguistic MCDM problems given that the probabilistic linguistic term set (PLTS) can reflect the psychology of experts when making evaluations. The utility conversion process is first proposed based on the marginal utilities of criteria. Then, the criterion preference ratios of experts are refined from the utility conversion process. Based on the criterion preference ratios and the operations of PLTSs, the adjusted probabilistic linguistic expected values of alternatives are calculated. The consistency and inconsistency indexes of alternatives and criteria are defined to set up the linear programming used to work out the criterion preference ratios. An illustration about the selection of emergency logistics supplier is given to validate the proposed method. The comparative analysis indicates the low cognitive burden, high stability, and strong applicability of the proposed method.

Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Diesel Cycle.

Applying finite time thermodynamics theory and the non-dominated sorting genetic algorithm-II (NSGA-II), thermodynamic analysis and multi-objective optimization of an irreversible Diesel cycle are performed. Through numerical calculations, the impact of the cycle temperature ratio on the power density of the cycle is analyzed. The characteristic relationships among the cycle power density versus the compression ratio and thermal efficiency are obtained with three different loss issues. The thermal efficiency, the maximum specific volume (the size of the total volume of the cylinder), and the maximum pressure ratio are compared under the maximum power output and the maximum power density criteria. Using NSGA-II, single-, bi-, tri-, and quadru-objective optimizations are performed for an irreversible Diesel cycle by introducing dimensionless power output, thermal efficiency, dimensionless ecological function, and dimensionless power density as objectives, respectively. The optimal design plan is obtained by using three solution methods, that is, the linear programming technique for multidimensional analysis of preference (LINMAP), the technique for order preferences by similarity to ideal solution (TOPSIS), and Shannon entropy, to compare the results under different objective function combinations. The comparison results indicate that the deviation index of multi-objective optimization is small. When taking the dimensionless power output, dimensionless ecological function, and dimensionless power density as the objective function to perform tri-objective optimization, the LINMAP solution is used to obtain the minimum deviation index. The deviation index at this time is 0.1333, and the design scheme is closer to the ideal scheme.

Multi-generation energy system based on geothermal source to produce power, cooling, heating, and fresh water: Exergoeconomic analysis and optimum selection by LINMAP method

The current study deals with thermodynamic modeling and multi-objective optimization of a new multi-generation energy system using geothermal as the primary energy source. The proposed system includes a Kalina cycle, a refrigeration unit, thermoelectric module, steam turbine, and heating unit. The new aspects of the proposed system are using the thermoelectric system to low temperature heat recovery and using the benefit of the multi-product. The system exergy analysis shows that the reverse osmosis desalination unit with 449.1 kW has the highest exergy destruction rate in the system. Additionally, three components i.e., reverse osmosis unit, heating system, and steam turbine are responsible for 82.8% of exergy destruction of the system. Exergo-economic analysis revealed that the turbine and the thermoelectric module have the highest cost rates of 12.51 US$/h and 3.62 US$/h respectively. It also concludes that the sum of the cost rate of component and associated exergy destruction cost rate, a significant exergo-economic parameter, for the turbine and reverse osmosis unit are the highest values. Parametric analysis of the proposed system for geothermal source pressure, steam turbine backpressure, Kalina turbine backpressure, and ammonia mass fraction of basic solutions are carried out. The unit cost of product and exergy efficiency are objective functions for optimization. Multi-criteria optimization indicates that using the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) method based on suggested design variables, can reduce the unit cost of the product to 0.107 US$/kWh, and the exergy efficiency can be increased up to 15.86%.

Multi-objective optimization of thermochromic glazing based on daylight and energy performance evaluation

Many efforts have been detected to investigate thermochromic (TC) glazing for improving building energy saving, while only a few approaches for daylight performance analysis. In this study, the performance of TC glazing is investigated based on multi-objective optimization for minimizing energy demand while maximizing daylight availability. The effects of five parameters including transition temperature, solar transmittance in clear state, solar transmittance modulation ability, luminous transmittance in clear state, and luminous modulation ability on the building energy consumption and useful daylighting illuminance (UDI300–3000) are examined. Linear Programming Technique for Multi-dimensional Analysis of Preference (LINMAP) is used for the decision-making of Pareto frontier. This research aims to explore the ideal thermochromic glazing by considering the daylight and energy performance of a typical office room, taking the weather condition of Xiamen, China as an example. Although it is impossible to achieve both optimal values of energy consumption and UDI300–3000 simultaneously, the proposed multi-objective optimization method could still provide low energy consumption with sufficient daylight. The non-dominated sorting of Pareto optimal solution (POS) demonstrated that the optimum building energy consumption and UDI300–3000 for single glazed windows are 46.64 kWh/m2 and 70.92%, respectively, while the values for double glazed windows are 44.40 kWh/m2 and 71.88%, respectively. The selected hypothetical TC windows can improve the building energy and daylighting performance simultaneously when compared with traditional clear single and double glazed windows. The presented framework provides a multi-objective optimization method to determine the most suitable TC glazing technologies for designers and architects during the design and retrofit procedure.

Sustainable design of the household water treatment systems using a novel integrated fuzzy QFD and LINMAP approach: a case study of Iran

There is a high possibility that pursuit of water policies goals which could have impacts on water security. Decision makers are interested in developing the water management systems to establish sustainable demand for secured water. The aim of the paper is to analyze the sustainability indicators (SIs) related to designing of the household water treatment system (HWTS). Thirteen criteria like solid waste, liquid waste, air pollution, initial cost, operation and maintenance costs, transport cost, satisfaction, purchasing power, social acceptance, health, reliability, after sales service, and technological capacity in four categories including environmental, economic, social and technical aspects have been considered. These criteria affect HWTS. These criteria are evaluated by taking into account the customer requirements (CRs) and design requirements (DRs) of HWTS. The objective of this study is to design sustainable HWTSs. This is achieved by an analytical approach integrating quality function deployment (QFD) and a linear programming technique for multidimensional analysis of preference (LINMAP) under fuzzy environment for guiding HWTSs manufactures. Fuzzy QFD-LINMAP approach is used to investigate the roles of the study criteria and the interrelationships between them. The HWTSs development in the city of Behbahan, Iran, is considered. The findings indicate that operation and maintenance costs (with value of 0.0522) is the most important sustainability indicator in the CRs and the least important is technical capacity (with value of 0.1096). The most important sustainability indicator in DRs is purchasing power (with value of 0.0207), and the least important is liquid waste (with value of 0.1469). The results show that sustainability strategies are selected for water treatment systems constraints and the model provides compromise solutions to help decision makers evaluate suitable water policy mix.

A LINMAP Method Based on the Bounded Rationality of Evaluators for Property Service Quality Evaluation

Property service quality (PSQ) evaluation is the key means of property management. Traditional PSQ evaluation is usually based on the rational hypothesis of the evaluators. The evaluators’ behaviour with bounded rationality is more in line with the characteristics of modern PSQ evaluation practice. At this point, evaluation information is usually incomplete information and heterogeneous data. The existing LINMAP methods have the ability to process incomplete information and heterogeneous information, but cannot adapt to evaluation information processing under bounded rational behaviour. As one of the major achievements of behavioural economics, prospect theory can explain people’s bounded behaviour when making decisions. The purpose of this paper was to develop a linear programming technique for multidimensional analysis of preference (LINMAP) model based on prospect theory for modern PSQ evaluation. First, a data preprocessing method was designed by referring to the TOPSIS method. Then, the value function was used to construct the dominance matrix, and the LINMAP model based on prospect theory was constructed. Finally, all alternatives were ranked in order according to overall performance value, which was solved by the LINMAP model. The feasibility and effectiveness of the proposed method were demonstrated by example analysis. Based on the evaluation results of PSQ of public projects, the important items and excellent property service projects and their reasons were determined, and some suggestions were proposed to improve PSQ.

Pythagorean fuzzy linear programming technique for multidimensional analysis of preference using a squared-distance-based approach for multiple criteria decision analysis

Pythagorean fuzzy (PF) sets involving Pythagorean membership grades can befittingly manipulate inexact and equivocal information in real-life problems involving multiple criteria decision analysis (MCDA). The linear programming technique for multidimensional analysis of preference (LINMAP) is a prototypical compromising model, and it is widely used to carry on decision-making problems in many down-to-earth applications. In LINMAP, the employment of squares of Euclidean distances is a significant technique that is an effective approach to fit measurements. Taking the advantages of a newly developed Euclidean distance model on the grounds of PF sets, this paper initiates a beneficial concept of squared PF Euclidean distances and studies its valuable and desirable properties. This paper aims to establish a squared Euclidean distance (SED)-based outranking approach and develop a novel PF LINMAP methodology for handling an MCDA problem under PF uncertainty. In the SED-based outranking approach, a novel SED-based dominance index is proposed to reflect an overall balance of a PF evaluative rating between the connection and remotest connection with positive- and negative-ideal ratings, respectively. The properties of the proposed index are also analyzed to exhibit its efficaciousness in determining the dominance relations for intracriterion comparisons. Moreover, this paper derives the comprehensive dominance index to determine the overall dominance relation and defines measurements of rank consistency for goodness of fit and rank inconsistency for poorness of fit. The PF LINMAP model is formulated to seek to ascertain the optimal weight vector that maximizes the total comprehensive dominance index and minimizes the poorness of fit under consideration of the lowest acceptable level and specialized degenerate weighting issues. The practical application concerning bridge-superstructure construction methods is conducted to test the feasibility and practicability of the PF LINMAP model. Over and above that, a generalization of the proposed methodology, along with applications to green supplier selection and railway project investment, is investigated to deal with group decision-making issues. Several comparative studies are implemented to further validate its usefulness and advantages. The application and comparison results display the effectuality and flexibility of the developed PF LINMAP methodology. In the end, the directions for future research of this work are represented in the conclusion.

A GENERAL MULTI-ATTRIBUTE MULTI-SCALE DECISION MAKING METHOD BASED ON DYNAMIC LINMAP FOR PROPERTY PERCEIVED SERVICE QUALITY EVALUATION

The scientific evaluation of property perceived service quality (PPSQ) needs multi-stage, multi-source and large-group perceived information, which is deemed to be the decision problem for dynamic, heterogeneous and large-scale data processing. Aiming at the problem, we propose a general multi-attribute multi-scale (MAMS) method based on the dynamic linear programming technique for multi-dimensional analysis of preference (LINMAP). In the dynamic LINMAP model, the classic MAMS matrix is introduced and extended into a general form. The dynamic LINMAP model is constructed by defining dynamic consistency and dynamic inconsistency. The time series weight is determined by Orness method. The new method adapts to the requirements of modern PPSQ. Finally, we verify the feasibility and effectiveness of dynamic LINMAP method by analyzing a PPSQ evaluation example. The new method improves the traditional PPSQ evaluation, and provides a perspective for large-scale data processing by the classic decision method.

Optimal design parameters and performance optimization of thermodynamically balanced dish/Stirling concentrated solar power system using multi-objective particle swarm optimization

In this work, a theoretical model based on opto-geometric and thermodynamic analyses of Solar Dish-Stirling System (SDSS) considering opto-geometric sizing criteria and energy balance of different system components has been developed. An optimization algorithm has been also implemented for simultaneously maximizing the output power and total efficiency of the SDSS using the Multi-Objective Particle Swarm Optimization (MOPSO). Nine decision variables have been considered, namely, the interception factor, mirror reflectance of the concentrator, receiver absorbance, receiver transmittance, receiver emissivity, tilt angle of the receiver, the direct solar intensity, the speed of wind, and the temperature of ambient. Pareto optimal frontier (POF) was determined and the optimal solution was selected by applying a decision making approach called the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP). Moreover, a sensitivity analysis was also carried out to identify the impact of the rim angle, the dish concentrator diameter, the mirror soiling coefficient of concentrator, and the ratio of design concentration on the SDSS performance optimization. The results showed that the proposed MOPSO shows a feasible approach to achieve a maximal power output of 23.46 kW with an optimal final total efficiency of 30.15% that approaches the ideal solution. Moreover, the sensitivity results indicated that SDSS with concentrator diameters of (2.5–15 m) can produce final optimal output powers of (1.43–53.34 kW) with insignificant variation in the overall efficiency (29.80–30.20%), at the obtained optimal solutions for the optimized dish concentrator configurations. Moreover, the results also emphasize how mirror soiling factor of the concentrator, has a dramatic effect on the optimal electric power and total efficiency of SDSS. It can be concluded that the proposed MOPSO approach can lead to more desired results and allow the technical feasibility for design of SDSS according to the need of such output power required for a certain application.

A Novel Three-Phase LINMAP Method for Hybrid Multi-Criteria Group Decision Making With Dual Hesitant Fuzzy Truth Degrees

Based on the idea of linear programming technique for multidimensional analysis of preference (LINMAP), a novel three-phase LINMAP method is presented here for solving hybrid multi-criteria group decision making (MCGDM) with dual hesitant fuzzy (DHF) truth degrees and incomplete criteria weights information. Firstly, by simultaneously taking into account the difference between each alternative and all the others for the decision maker (DM), the difference of each alternative between the individual DM and the decision group, and the difference of each alternative between the individual DM and all the others, a tri-objective nonlinear programming model is created to determine the DMs' weights. Secondly, to derive the criteria weights, objective positive ideal solution (OPIS), and the objective negative ideal solution (ONIS), a new four-objective DHF mathematical programming model is established by minimizing inconsistency and maximizing consistency based on OPIS and ONIS, and a pair of parametric nonlinear programming models are technically established by unequal weighted summation approach for solving the four-objective DHF mathematical programming model, which can provide DMs with more agility and flexible space to change their preference. Thirdly, by considering the distances of each alternative from the OPIS and ONIS for individual DM and the decision group, a minimizing deviation optimal model is established to derive the group ranking order of alternatives. Finally, a new method is put forward for solving hybrid MCGDM with DHF truth degrees, and the validity and practicability of the proposed method is analyzed through a case of water quality monitoring system (WQMS) selection.