Improved Score Function Research Articles

Fermatean fuzzy score function and distance measure based group decision making framework for household waste recycling plant location selection

The household waste (HW) disposal and recycling have become a significant challenge due to increasing quantities of generated household wastes and increased levels of urbanization. Selecting locations/sites for building new HW recycling plant comprises numerous sustainability dimensions, thus, this work aims to develop new decision-making model for evaluating and prioritizing the HW recycling plant locations. This paper is categorized into three phases. First, we propose new improved score function to compare the Fermatean fuzzy numbers. Moreover, an example is presented to validate the effectiveness of proposed score function over the extant ones. Second, we introduce new distance measure to estimate the discrimination degree between Fermatean fuzzy sets (FFSs) and further discuss its advantages over the prior developed Fermatean fuzzy distance measures. Third, we introduce an integrated methodology by combining the method with the removal effects of criteria (MEREC), the stepwise weight assessment ratio analysis (SWARA) and the measurement alternatives and the ranking according to compromise solution (MARCOS) approaches with Fermatean fuzzy (FF) information, and named as the “FF-MEREC-SWARA-MARCOS” framework. In this method, the FF-distance measure is used to find the weights of involved decision-making experts. Moreover, an integrated criteria weighting method is presented with the combination of MEREC and SWARA models under the context of FFSs, while the combined FF-MEREC-SWARA-MARCOS model is applied to evaluate and prioritize the locations for HW recycling plant development, which illustrates its feasibility of the developed framework. Comparative study and sensitivity assessment are conducted to validate the obtained outcomes. This work provides a hybrid decision analysis approach, which marks a significant impact to the HW recycling plant location selection process with uncertain information.

A novel fuzzy neural collaborative filtering for recommender systems

In collaborative filtering recommendations, part of studies mainly focus on quantitatively learning user preferences based on explicit rating information. However, due to the uncertainty and complexity of decision-making scenarios, user preferences usually express ambiguity and diversity. Therefore, to fully capture user preferences from both qualitative and quantitative perspectives and improve the accuracy and reliability of recommendations, we propose a novel fuzzy neural collaborative filtering for recommender systems. Firstly, we qualitatively divide user preferences into fine-grained categories based on picture fuzzy set and transform the rating matrix into four preference degree matrices. Then, we employ Bernoulli matrix factorization to independently learn preference features of each submatrix to obtain picture fuzzy numbers. To enhance the adaptability of picture fuzzy set in recommender systems, we design an improved scoring function based on picture fuzzy number to effectively distinguish differences in user preference levels. In addition, we use a simple deep neural framework to quantitatively extract global preferences of users and fuse it with fine-grained preferences of users to thoroughly predict user preferences. Experiments on four benchmark datasets show that the proposed model outperforms other comparison methods in terms of recommendation accuracy. Compared with the closest competitor method, our model has the highest improvements of 5.08% and 4.04% in the metrics HR@10 and NDCG@10, respectively.

Selecting optimal celestial object for space observation in the realm of complex spherical fuzzy systems

The sensible selection of celestial objects for observation by the James Web Space Telescope (JWST) is pivotal for the precise decision-making (DM) process, aligning with scientific priorities and instrument capabilities to maximize valuable data acquisition to address key astronomical questions within the constraints of limited observation time. Aggregation operators are valuable models for condensing and summarizing a finite set of data of imprecise nature. Utilization of these operators is critical when addressing multi-attribute decision-making (MCDM) challenges. The complex spherical fuzzy (CSF) framework effectively captures and represents the uncertainty that arises in a DM problem with more precision. This paper presents two novel aggregation operators, namely the complex spherical fuzzy Yager weighted averaging (CSFYWA) operator and the complex spherical fuzzy Yager weighted geometric (CSFYWG) operator. Many fundamental structural properties of these operators are delineated, and thereby an improved score function is suggested that addresses the limitations of the existing score function within the CSF system. The newly defined operators are applied to formulate an algorithm for MADM problems to tackle the challenges of ambiguous data in the selection process. Moreover, these strategies are effectively applied to handle the MADM problem of selecting the optimal astronomical object for space observation within the CSF context. Additionally, a comparative analysis is also performed to demonstrate the validity and superiority of the proposed techniques compared to the existing strategies.

A multi-attribute decision making approach considering economic psychology

The magnitude of the utility of a good depends on the subjective psychological evaluation of the good by the consumer, and the difference in the obtained utility will affect consumer behavior, taking into account that consumers are not completely rational in the actual decision-making process, and that under uncertain conditions, consumers’ perception of loss is much greater than gain. This paper investigates an improved scoring function based on consumer utility and loss aversion, which takes into account the effects of different decision makers’ preferences and loss aversion on the decision outcome. First, the existing score function of intuitionistic fuzzy sets is analyzed in depth, an improved score function is defined, and its properties and special cases are studied in detail. Then, a Multi-Attribute Decision-Making (MADM) method is proposed based on the improved scoring function combined with the intuitionistic fuzzy hybrid average (IFHA) operator. Finally, a real case of new energy-used car transaction decision-making is given, and the proposed method is validated by Spearman’s correlation coefficient, WS ranking similarity coefficient, and RW coefficient to prove its practicality and effectiveness.

A novel LqROPF-Entropy-WASPAS group model based on Frank aggregation operators and improved score function in linguistic q-rung orthopair fuzzy framework

Decision analysis plays a crucial role in our everyday actions. Efficient decision-making models rely heavily on accurately representing human cognitive knowledge. The linguistic q-rung orthopair fuzzy sets (LqROPFSs) offer a versatile means of representing qualitative cognitive information by adapting the parameter q to different scenarios. This study presents a novel scoring function to rank linguistic q-rung orthopair fuzzy numbers (LqROPFNs) with greater precision compared to the current score function. Next, we present novel arithmetic/geometric aggregation operators (AOs) that utilize new Frank operational rules to combine a finite collection of LqROPFNs. The work also examines the several desirable characteristics and special cases of the provided AOs. Furthermore, a novel decision-making model called the LqROPF-Entropy-WASPAS model has been introduced to address the challenges of multiple attribute group decision-making (MAGDM) problems in a linguistic q-rung orthopair fuzzy environment. The model incorporates proposed AOs and a scoring function. The suggested methodology is exemplified by considering a practical decision to select an online teaching platform. The validity of the results is confirmed through an extensive sensitivity analysis and comparative investigation employing various existing MAGDM approaches within the linguistic q-rung orthopair fuzzy framework. The proposed approach offers enhanced flexibility to decision experts, empowering them to analyze decision outcomes across diverse scenarios. This flexibility is achieved by allowing the manipulation of values associated with various parameters, enabling decision-makers to tailor the analysis according to their specific attitudes and requirements. This adaptability ensures a more advanced and personalized analysis of decision outcomes, accommodating decision experts’ distinct viewpoints and preferences in varying situations.

An intuitive fuzzy multi-attribute decision making method based on a herding psychology improved score function for trading decisions

The amount of used new energy vehicle transactions is increasing quickly as the social economy matures, yet prices are typically low, making it increasingly difficult to select a fair trading system. Enhancing the score function is crucial in order to account for how different people’s attitudes affect the outcome of decisions and to choose an acceptable trading strategy that is applicable to other scenarios and has a favorable impact on transaction flow. The choice of a trading scheme for new energy-using vehicles is usually regarded as a multi-attribute decision problem. In this paper, the Intuitionistic Fuzzy Hybrid Averaging (IFHA) operator integration operator with an improved score function is proposed based on the influence of herd mentality on decision-makers. In order to examine the correlation between the score function and the decision outcome using the Spearman rank correlation coefficient, an application to a real situation and some comparative analyses are provided. The outcomes demonstrate that the decision-making process for used car trading schemes can make use of the proposed improved score function.

A novel B&B recommendation method based on improved intuitionistic fuzzy sets

PurposeThis paper aims to propose a bed and breakfast (B&B) recommendation method that takes into account review timeliness and user preferences to help consumers choose the most satisfactory B&B.Design/methodology/approachThis paper proposes a B&B ranking method based on improved intuitionistic fuzzy sets. First, text mining and cluster analysis are combined to identify the concerns of consumers and construct an attribute set. Second, an attribute-level-based text sentiment analysis is established. The authors propose an improved intuitionistic fuzzy set, which is more in line with the actual situation of sentiment analysis of online reviews. Next, subjective-objective combinatorial assignments are applied, considering the consumers’ preferences. Finally, the vlsekriterijumska optimizacija i kompromisno resenje (VIKOR) algorithm, based on the improved score function, is advised to evaluate B&Bs.FindingsA case study is presented to illustrate the use of the proposed method. Comparative analysis with other multi-attribute decision-making (MADM) methods proves the effectiveness and superiority of the VIKOR algorithm based on the improved intuitionistic fuzzy sets proposed in this paper.Originality/valueProposing a B&B recommendation method that takes into account review timeliness and user customization is the innovation of this paper. In this approach, the authors propose improved intuitionistic fuzzy sets. Compared with the traditional intuitionistic fuzzy set, the improved intuitionistic fuzzy set increases the abstention membership, which is more in line with the actual situation of attribute-level sentiment analysis of online reviews.

A probability-based fuzzy algorithm for multi-attribute decision-analysis with application to aviation disaster decision-making

This research addresses the challenges of multi-attribute group decision-making in a hesitant fuzzy environment, where randomness and uncertainty introduce biases into practical making choices. A probability-based double uncertain fuzzy (PDHF) algorithm is proposed to overcome these challenges. The algorithm constructs probability-based double hesitant fuzzy information matrices for each decision expert. The maximum deviation and entropy methods determine objective weights for decision experts and attribute indicators. Combining an improved scoring function and deviation function generates a comprehensive decision evaluation information matrix for decision experts. Subsequently, a decision algorithm that integrates probability-based double hesitant fuzzy sets with the preference ranking organization method (PROM) is employed to obtain the final decision result. As part of a case study, the algorithm is used to evaluate emergency action plans for aviation disaster accidents. Comparing the results with those from the TOPSIS, VIKOR, and PDHFS decision-making algorithms shows that the suggested PDHF algorithm works well and can be trusted for the multi-attribute group decision-making problems in hesitant fuzzy environments.

Selecting an Optimal Approach to Reduce Drivers of Climate Change in a Complex Intuitionistic Fuzzy Environment

The sustainability of the climate is a critical concern in the modern world. A variety of acts are included in sustainability that strive to lessen our carbon footprint and maintain the fragile balance of our world. To preserve a sustainable future for future generations, we must cooperate in adopting renewable energy sources, supporting green transportation, and implementing responsible land use. In this article, we propose the concepts of complex intuitionistic fuzzy Dombi hybrid averaging (CIFDHA) and complex intuitionistic fuzzy Dombi hybrid geometric (CIFDHG) operators within the framework of a complex intuitionistic fuzzy environment. Furthermore, we explore several additional important features of these operators. To overcome the limitations of the existing score function within the CIF knowledge context, we present a new and improved score function. Additionally, we apply the proposed score function and newly defined operators to select an optimal strategy for mitigating the drivers of climate change and saving the planet’s valuable resources for a more livable and resilient planet. In order to demonstrate the validity and practicality of the suggested strategies, we conducted a comparative study of these novel techniques with existing methods.

On Selection of the Efficient Water Purification Strategy at Commercial Scale Using Complex Intuitionistic Fuzzy Dombi Environment

The primary objective of the water purification process is to remove harmful chemical compounds and microorganisms from water sources in order to produce water suitable for human consumption. Water purification satisfies the demand for drinkable water, which is a requirement for many industries, including the medical, pharmaceutical, and chemical industries, among others. Access to purified water is the single most important factor determining a nation’s strength and prosperity. As a consequence, researchers all over the world are investigating a wide variety of potential strategies for improving and preserving the water supply. In this paper, we present the findings of our research into a possible water strategy for purifying water and improving accessibility to drinkable water in areas prone to drought. This article presents the concepts of the complex intuitionistic fuzzy Dombi weighted averaging (CIFDWA) operator, the complex intuitionistic fuzzy Dombi ordered weighted averaging (CIFDOWA) operator, the complex intuitionistic fuzzy Dombi weighted geometric (CIFDWG) operator, and the complex intuitionistic fuzzy Dombi ordered weighted geometric (CIFDOWG) operator in complex intuitionistic fuzzy (CIF) settings. In addition, we investigate several important key features of these operators. Moreover, we introduce an improved score function to overcome the deficiencies of the existing score function under CIF knowledge. Furthermore, we effectively apply the proposed score function and newly defined operators to select the best technique for purifying water at a commercial scale. Additionally, we establish a comparative analysis to show the validity and feasibility of the proposed techniques compared to existing methods.

Stock Reordering Decision Making under Interval Valued Picture Fuzzy Knowledge

Symmetrical and asymmetrical information plays a critical role in resolving many issues. The implications of symmetry and asymmetry in interval-valued picture fuzzy decision-making, lie in their ability to represent and manage complex data. Decision makers approach the problem of information asymmetry through various methods. Integrating symmetric and asymmetric data in the context of a specific physical phenomenon poses significant challenges. To address these challenges, interval-valued picture fuzzy (IVPF) sets have emerged as an effective tool for managing complex data. In decision-making processes, it is essential to consider the complementary and conflicting nature of the analyzed data. This article aims to refine the shortcomings of the existing score function for Multiple Criteria Decision-Making (MCDM) problems in an IVPF environment, and present an improved score function. The IVPF sets are leveraged to propose IVPF weighted arithmetic operators, IVPF ordered weighted arithmetic operators, IVPF weighted geometric operators, and IVPF ordered weighted geometric operators, which are analyzed in terms of their key features. To demonstrate the effectiveness of the proposed score function and newly defined operators, a case study involving the selection of the best food item for manufacturing, is conducted. Additionally, a comparative analysis is established to investigate the significance of the newly defined techniques in solving decision-making problems under IVPF knowledge.

Generalized q-rung orthopair fuzzy interactive Hamacher power average and Heronian means for MADM.

In this paper, we establish a novel q-rung orthopair fuzzy (q-ROF) multi-attribute decision making (MADM) model on the basis of the proposed q-ROF interactive Hamacher weighted adjustable power average (q-ROFIHWAPA) and q-ROF interactive Hamacher weighted coordinated Heronian means (HMs), which (1) can reflect the correlations among multiple attributes; (2) weakens the impacts of the extreme evaluation values more reasonably; (3) considers the interactions between the membership degree (MD) and non-membership degree (N-MD) of different q-ROF numbers (q-ROFNs); (4) has the characteristic of generality (It can generate different methods by different operations). Firstly, the q-ROF interactive Hamacher operations, improved score function and new q-ROF entropy (q-ROFE) formula, which are the necessary raw materials for the implementation of MADM, are presented. Secondly, we introduce the adjustable power average (APA) and its weight form (WAPA) to remedy the deficiencies of the classical power averages (PAs). Afterwards we extend the WAPA to q-ROF circumstance and propose the q-ROF interactive Hamacher WAPA (q-ROFIHWAPA), and its basic properties are analyzed. Further, the entropy weight fitting method is presented to determine the parameter carried by the q-ROFIHWAPA. Thirdly, inspired by the evolutionary process of Bonferroni means (BMs), we define the weighted coordinated HM (WCHM) and weighted geometric coordinated HM (WGCHM) based on the traditional HMs, respectively, which eliminate the redundancy of the dual generalized weighted BM (DGWBM) and dual generalized weighted Bonferroni geometric mean (DGWBGM), i.e., the case of Then we develop the q-ROF interactive Hamacher WCHM (q-ROFIHWCHM) and q-ROF interactive Hamacher WGCHM (q-ROFIHWGCHM) by combining them with the q-ROF interactive Hamacher operations, and the common properties and special cases are also investigated. Finally, we create a MADM algorithm relied on the q-ROFIHWAPA and q-ROFIHWCHM (resp. q-ROFIHWGCHM), and a practical example is introduced to illustrate the effectiveness and superiority of the proposed method.

An intuitionistic fuzzy entropy-based gained and lost dominance score decision-making method to select and assess sustainable supplier selection

<abstract> <p>Sustainable supplier selection (SSS) is recognized as a prime aim in supply chain because of its impression on profitability, adorability, and agility of the organization. This work introduces a multi-phase intuitionistic fuzzy preference-based model with which decision experts are authorized to choose the suitable supplier using the sustainability "triple bottom line (TBL)" attributes. To solve this issue, an intuitionistic fuzzy gained and lost dominance score (IF-GLDS) approach is proposed using the developed IF-entropy. To make better use of experts' knowledge and fully represent the uncertain information, the evaluations of SSS are characterized in the form of intuitionistic fuzzy set (IFS). To better distinguish fuzziness of IFSs, new entropy for assessing criteria weights is proposed with the help of an improved score function. By considering the developed entropy and improved score function, a weight-determining process for considered criterion is presented. A case study concerning the iron and steel industry in India for assessing and ranking the SSS is taken to demonstrate the practicability of the developed model. The efficacy of the developed model is certified with the comparison by diverse extant models.</p> </abstract>

Contribution to decision-making in the big data industry based on the multiparametric similarity measure for Pythagorean fuzzy sets

Abstract Big Data allows analysing and assessing all human production types with its 5Vs, which are Volume, Velocity, Variety, Veracity and Value. Big Data is useful to improve decision-making to adjust it better to market demand, specifically selection of supplier that is an important link to optimize the logistic chain of enterprises. In this case, leadership or decider is ahead one serious complex problem, inexact and fuzzy. Pythagorean fuzzy set (PFS) is disposing the indeterminacy data by the membership and the nonmembership functions; it is a generalization of the intuitionist fuzzy set when the last set is limited. First, some results for PFSs are displaying in this study as particular cases and generalization of some binary operations. After, an improved score function of Pythagorean fuzzy number is proposed to avoid the comparison problem in practice. In addition, an existing approach exploring the combined alternatives weight to settle Pythagorean fuzzy issue by multi-parametric similarity measure is applied with the new proposed score function to selection of supplier issue with five serious criteria as a Big Data industry decision-making problem in economic environment. Finally, a comparison of the presented method with some existing approaches has been executed in the light of counterintuitive phenomena for validating its advantages.

Interval-valued Pythagorean fuzzy multi-criteria decision-making method based on the set pair analysis theory and Choquet integral

This paper proposes a novel fuzzy multi-criteria decision-making method based on an improved score function of connection numbers and Choquet integral under interval-valued Pythagorean fuzzy environment. To do so, we first introduce a method to convert interval-valued Pythagorean fuzzy numbers into connection numbers based on the set pair analysis theory. Then an improved score function of connection numbers is proposed to make the ranking order of connection numbers more in line with reality in multi-criteria decision-making process. In addition, some properties of the proposed score function of connection numbers and some examples have been given to illustrate the advantages of conversion method proposed in the paper. Then, considering interactions among different criteria, we propose a fuzzy multi-criteria decision-making approach based on set pair analysis and Choquet integral under interval-valued Pythagorean fuzzy environment. Finally, a case of online learning satisfaction survey and a brief comparative analysis with other existing approaches are studied to show that the proposed method is simple,convenient and easy to implement. Comparing with previous studies, the method in this paper, from a new perspective, effectively deals with multi-criteria decision-making problems that the alternatives cannot be reasonably ranked in the decision-making process under interval-valued Pythagorean fuzzy environment.

New complex proportional assessment approach using Einstein aggregation operators and improved score function for interval-valued Fermatean fuzzy sets

As a generalization of the Fermatean fuzzy set, the theory of interval-valued Fermatean fuzzy set (IVFFS) is a more robust and reliable tool to address the imprecise and incomplete information in the process of multi-criteria decision making (MCDM), thus can be employed on wider range of applications. The aim of this study is to purpose a novel decision-making approach by combining two well-recognized methods, named as the criteria interaction through inter-criteria correlation (CRITIC) and the complex proportional assessment (COPRAS) with IVFFSs. In this line, to compare the interval-valued Fermatean fuzzy numbers (IVFFNs), a new score function is proposed and its feasibility in comparison with existing interval-valued Fermatean fuzzy score and accuracy functions is discussed. To combine the various IVFFNs, some interval-valued Fermatean fuzzy Einstein aggregation operators are introduced. Further, the CRITIC is utilized to derive the objective weights of attributes within IVFFS context. To prioritize the alternatives, the IVFF-COPRAS method is presented on IVFFSs settings. Later, to assess the performance quality of the developed methodology, an illustrative case study is discussed to evaluate and rank the sustainable community-based tourism (CBT) location candidates. Moreover, the comparative study and sensitivity investigation are conducted to prove that the developed framework efficiently handles the problem of sustainable CBT locations evaluation and selection problem under IVFFSs environment. The findings of this study conclude that the developed method is a systematic, more comprehensive, accurate, and structured approach in the assessment of sustainable CBT locations under uncertain environment.

INTERVAL-VALUED INTUITIONISTIC FUZZY TOPSIS-BASED MODEL FOR TROUBLESHOOTING MARINE DIESEL ENGINE AUXILIARY SYSTEM

In this paper, we present an interval-valued Intuitionistic Fuzzy TOPSIS model, which is based on an improved score function for detecting failure in a marine diesel engine auxiliary system, using groups of experts’ opinions to detect the root cause of failure in the engine system and the area most affected by failures in the diesel engine. The improved score function has been used for the computation of the separation measures from the intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) of alternatives while the criteria weight have been determined using an intuitionistic fuzzy entropy. The study is aimed at providing an alternative method for the identification and analysis of failure modes in engine systems. The results from the study show that although detection of failures in Engines is quite difficult to identify due to the dependency of the engine systems on each other, however using intuitionistic fuzzy multi-criteria decision-making method the faults/failure can easily be diagnosed.

Applying the Dijkstra Algorithm to Solve a Linear Diophantine Fuzzy Environment

Linear Diophantine fuzzy set (LDFS) theory expands Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PyFS) theories, widening the space of vague and uncertain information via reference parameters owing to its magnificent feature of a broad depiction area for permissible doublets. We codify the shortest path (SP) problem for linear Diophantine fuzzy graphs. Linear Diophantine fuzzy numbers (LDFNs) are used to represent the weights associated with arcs. The main goal of the presented work is to create a solution technique for directed network graphs by introducing linear Diophantine fuzzy (LDF) optimality constraints. The weights of distinct routes are calculated using an improved score function (SF) with the arc values represented by LDFNs. The conventional Dijkstra method is further modified to find the arc weights of the linear Diophantine fuzzy shortest path (LDFSP) and coterminal LDFSP based on these enhanced score functions and optimality requirements. A comparative analysis was carried out with the current approaches demonstrating the benefits of the new algorithm. Finally, to validate the possible use of the proposed technique, a small-sized telecommunication network is presented.

Learning from Docked Ligands: Ligand-Based Features Rescue Structure-Based Scoring Functions When Trained on Docked Poses.

Machine learning scoring functions for protein-ligand binding affinity have been found to consistently outperform classical scoring functions when trained and tested on crystal structures of bound protein-ligand complexes. However, it is less clear how these methods perform when applied to docked poses of complexes. We explore how the use of docked rather than crystallographic poses for both training and testing affects the performance of machine learning scoring functions. Using the PDBbind Core Sets as benchmarks, we show that the performance of a structure-based machine learning scoring function trained and tested on docked poses is lower than that of the same scoring function trained and tested on crystallographic poses. We construct a hybrid scoring function by combining both structure-based and ligand-based features, and show that its ability to predict binding affinity using docked poses is comparable to that of purely structure-based scoring functions trained and tested on crystal poses. We also present a new, freely available validation set─the Updated DUD-E Diverse Subset─for binding affinity prediction using data from DUD-E and ChEMBL. Despite strong performance on docked poses of the PDBbind Core Sets, we find that our hybrid scoring function sometimes generalizes poorly to a protein target not represented in the training set, demonstrating the need for improved scoring functions and additional validation benchmarks.

Pythagorean fuzzy weighted discrimination‐based approximation approach to the assessment of sustainable bioenergy technologies for agricultural residues

The inappropriate dumping of agricultural residues (ARs) can result in environmental pollution and the waste of valuable energy resources. The process of converting ARs to energy has been considered an important step for regional energy, agricultural development, and environmental sustainability and recently, many sustainable bioenergy technologies (BETs) have been developed for ARs. Since the assessment of ARs-to-energy conversion technologies contains several alternatives concerning multiple criteria with imprecise information, it is deliberated as an uncertain multicriteria decision-making (MCDM) problem. The Pythagorean fuzzy set (PFS) is an important and effective way to tackle the uncertainty present in real-life decision-making problems. To select a suitable conversion technology from a set of options and upgrade the ARs-to-energy industries, the present study develops a combined approach to PFSs based on weighted discrimination-based approximation (WDBA). This method extends the classical WDBA approach using an improved score function and discrimination measure within the PFS context, to evaluate MCDM problems with partial information on the criteria weights. To estimate the weights of the unknown attributes, a score function-based linear programming model is developed. A new ranking method is extended to grade the options using the proposed discrimination measure within the PFS environment. Further, a case study assessing ARs-to-energy conversion technologies is conducted to illustrate the practicality and feasibility of this method. A comparative analysis shows that the approach developed is more effective and proficient in facilitating decision experts' selection of desirable BETs for ARs.