Interval Rough Numbers Research Articles

Integrated MADM of low-carbon structural design for high-end equipment based on attribute reduction considering incomplete interval uncertainties

With the increasingly severe energy supply and environmental pressures, high-end equipment is gradually adopted to reduce the carbon emissions of manufacturing industry which makes its low-carbon structural design a critical research hotspot. The best structural scheme can be got by multi-attribute decision-making (MADM) with design requirements. However, the decision-making attributes in the structural design of high-end equipment are too many at first and low-carbon attributes are seldom fully considered. Moreover, there are a large amount of related data with linguistic vagueness, interval uncertainty, and information incompleteness, which fail to be handled simultaneously. There, this paper proposes an integrated MADM method of low-carbon structural design for high-end equipment based on attribute reduction considering incomplete interval uncertainties. First, distribution reduction of low-carbon structural design is carried out to obtain the minimum attribute set and encompass low-carbon attributes comprehensively. Second, a collaborative filtering algorithm is utilized to complete the missing data in the subsequent design process. Third, interval rough numbers (IRNs) are integrated into DEMATEL-ANP (DANP) and multi-attribute border approximation area comparison (MABAC) to quickly rank the alternative schemes for high-end equipment and determine which is the best. The rationality and robustness of the proposed method are verified through the case study and comparative analysis of a hydraulic forming machine.

A Multi-attribute Decision-making Method for Interval Rough Number Information System Considering Distribution Types

This paper proposes a novel multi-attribute decision-making (MADM) method for interval rough numbers (IRNs) considering different distribution types, namely uniform, exponential, and normal distributions. Upper and lower approximate interval dominance degrees are defined and aggregated using dynamic weights to obtain pairwise comparisons of IRNs. The properties of dominance are verified, and an attribute weight determination method based on the dominance balance degree is introduced. The proposed MADM method is data-driven and does not rely on the subjective preferences of decision-makers. Case analysis demonstrates the effectiveness and rationality of the proposed method, revealing that the distribution type of IRNs significantly impacts decision results, potentially leading to reversed ranking outcomes. The proposed method offers a comprehensive framework for handling MADM problems with IRNs under different distributions.

Rough set model of incomplete interval rough number decision systems

The rough set model has been extended to interval rough number decision systems, but the existing studies do not consider interval rough number decision systems with missing values. To this end, a rough set model of incomplete interval rough number decision systems (IIRNDSs) is proposed, and its uncertainty measures are investigated. Firstly, the similarity of two incomplete interval rough numbers (IIRNs) are defined by calculating their optimistic and pessimistic distances of the lower and upper approximation intervals of IIRNs. Then, the rough sets in IIRNDSs are constructed by the induced similarity relation. Next, four uncertainty measures, including approximation accuracy, approximation roughness, conditional entropy, and decision rough entropy are given, which exhibit a monotonic variation with changes in the size of attribute sets, α, and θ. Finally, the experimental results demonstrate the proposed rough set model of IIRNDSs is feasible and effective.

Interval rough integrated SWARA-ELECTRE model: An application to machine tool remanufacturing

Rough set theory is an efficient and flexible tool for the removal of unnecessary or irrelevant attributes present in the evaluation process and interval rough numbers (IRNs) are designed to effectively treat the inherited uncertainty in human assessments in the multi-criteria decision making (MCDM) problems. In the ELECTRE (ELimination and Choice Expressing REality) family of MCDM techniques, the options that are outranked by others are eliminated in order to present the most accurate and feasible set of actions or solutions to the core problem. In order to deal with the subjectivity and unpredictability in judgements made by experts without much prior knowledge, membership functions, or other changes, this research study offers an innovative MCDM methodology that integrates interval rough numbers, Step-wise Weight Assessment Ratio Analysis (SWARA), and the ELECTRE I method (named as IRN SWARA ELECTRE I Model). To examine the uncertainty in linguistic terms, IRNs are employed, but intervals rather than single fixed values are used. Three kinds of interval rough concordance and discordance sets are defined to build the proposed strategy. The criteria weights are computed by employing effective and simplified technique of interval rough SWARA having the ability to deal with preference ratings in the form of IRNs. The applicability of the proposed methodology is demonstrated by solving a case study related to assessment of machine tool remanufacturing models. To elaborate the authenticity, rationality, out-performance, and efficacy of findings, a comprehensive comparative study as well as sensitivity analysis are conducted.

Ranking Sub-Watersheds for Flood Hazard Mapping: A Multi-Criteria Decision-Making Approach

The aim of this paper is to assess the extent to which the Sad-Kalan watershed in Iran participates in floods and rank the Sad-Kalan sub-watersheds in terms of flooding potential by utilizing multi-criteria decision-making approaches. We employed the entropy of a drainage network, stream power index (SPI), slope, topographic control index (TCI), and compactness coefficient (Cc) in this investigation. After forming a decision matrix with 25 possibilities (sub-watersheds) and 5 evaluation indices, we used four MCDM approaches, including the analytic hierarchy process (AHP), best–worst method (BWM), interval rough numbers AHP (IRNAHP), picture fuzzy with AHP (PF-AHP), and picture fuzzy with linear assignment model (PF-LAM, hereafter PICALAM) algorithms, to rank the sub-watersheds. The study results demonstrated that PICALAM exhibited superior performance compared to the other methods due to its consideration of both local and global weights for each criterion. Additionally, among the methods used (AHP, BWM, and IRNAHP) that showed similar performances in ranking the sub-watersheds, the BWM method proved to be more time-efficient in the ranking process.

Life cycle sustainability decision-support framework for CO2 chemical conversion technologies under uncertainties

With the emergence of numerous CO2 chemical conversion technologies to simultaneously reduce CO2 emissions and produce value-added products, it is of great importance to compare their difference and select the most sustainable routes for future development. This study quantitatively evaluated the sustainability performances of 21 alternative CO2 conversion technologies from economic, technical, and environmental perspectives and developed a novel Multi-criteria Decision-making (MCDM) model to prioritize the alternatives. To cope with the external and internal uncertainties during the decision-making, Interval-Rough Numbers (IRNs) were firstly used to deal with subjective vagueness and information incompleteness involved in the group judgements unavoidably. Secondly, DEMATEL-ANP was employed based on IRNs to specify the correlation type and degree among diverse criteria for determining the global weights accurately. Lastly, a Vector-based Algorithm method was applied to measure the alternatives’ overall performance and figure out the final ranking scores of sustainability. The results revealed that CO2 to methane, urea, methanol, dimethyl ether, and acetic acid were the top five promising conversion technologies with the highest R&D priority over the next decades from a sustainability perspective. Moreover, a detailed sensitivity analysis of criteria weights was conducted to scrutinize the effectiveness of the ranking results and to validate the reliability of the new proposed MCDM model. Furthermore, in consideration of the complexity of future technological advance, market transformation, economic and social trends, this life cycle sustainability decision-support framework for CO2 conversion technologies provides a well-informed benchmark to support the screening and selection of candidate technologies including both the existing and emerging processes, and strategically explore the development opportunities and limits under uncertainties.

Groundwater vulnerability to pollution assessment: an application of geospatial techniques and integrated IRN-DEMATEL-ANP decision model

This study evaluated the susceptibility to groundwater pollution using a modified DRASTIC model. A novel hybrid multi-criteria decision-making (MCDM) model integrating Interval Rough Numbers (IRN), Decision Making Trial and Evaluation Laboratory (DEMATEL), and Analytical Network Process (ANP) was used to investigate the interrelationships between critical hydrogeologic factors (and determine their relative weights) via a novel vulnerability index based on the DRASTIC model. The flexibility of GIS in handling spatial data was employed to delineate thematic map layers of the hydrogeologic factors and to improve the DRASTIC model. The hybrid MCDM model results show that net recharge (a key hydrogeologic factor) had the highest priority with a weight of 0.1986. In contrast, the topography factor had the least priority, with a weight of 0.0497. A case study validated the hybrid model using Anambra State, Nigeria. The resultant vulnerability map shows that 12.98% of the study area falls into a very high vulnerability class, 31.90% falls into a high vulnerability, 23.52% falls into the average vulnerability, 21.75% falls into a low vulnerability, and 9.85% falls into very low vulnerability classes, respectively. In addition, nitrate concentration was used to evaluate the degree of groundwater pollution. Based on observed nitrate concentration, the modified DRASTIC model was validated and compared to the traditional DRASTIC model; interestingly, the spatial model of the modified DRASTIC model performed better. This study is thus critical for environmental monitoring and implementing appropriate management interventions to protect groundwater resources against indiscriminate sources of pollution.

Assessment of alternative railway systems for sustainable transportation using an integrated IRN SWARA and IRN CoCoSo model

The long-term sustainability of the railway transportation system is determined by a set of criteria that must be considered. For this reason, multi-criteria decision-making (MCDM) techniques have been used because of their high possibility of providing complementary instruments with successful flexibility. Keeping this in mind, we developed a multi-criteria method to conduct an assessment of currently operational railway systems in West Africa for sustainable transportation based on the examination of key challenges affecting the railway system. This study presents the interval rough step-wise weight assessment ratio analysis-combined compromise solution (IR-SWARA-CoCoSo) model. We have adapted the model to group decision-making by incorporating a new technique for dealing with ambiguity and the utilization of interval rough numbers (IRNs). To evaluate the importance coefficients of criteria in the group decision-making procedure, a new interval rough SWARA method has been introduced as an improvement to handle the issues related to MCDM. For the evaluation of the railway transportation system for sustainable transportation, a novel interval rough CoCoSo method was used. According to the findings, information systems is the most critical challenge to the railway transportation system, while the railway system in Nigeria is the best among others. The results were validated in two stages of sensitivity analysis: a comparison with different interval rough approaches, and the calculation of Spearman's correlation coefficient and WS coefficient for all ranks in the comparative analysis.

A Novel Hybrid Interval Rough SWARA–Interval Rough ARAS Model for Evaluation Strategies of Cleaner Production

Cleaner production is certainly a challenge of our everyday life, and a lot of effort and energy is required to achieve it. This paper has created a model of five strategies for cleaner production in Libyan industry, which have been evaluated on the basis of eight criteria. In order to determine the significance of the criteria, a novel interval rough SWARA (step-wise weight assessment ratio analysis) method has been developed, which takes into account the preferences of decision-makers (DMs) by applying interval rough numbers. A novel interval rough ARAS (additive ratio assessment) method has been developed for the evaluation and selection of the most favorable strategy for cleaner production. The integration of the developed methods has yielded results showing that the first strategy, launching awareness-raising campaigns to publicize these policies, represents the most realistic and best current solution to achieve cleaner production in Libyan industry. A comparative analysis with some existing interval rough methodologies has been presented to verify the superiority of the proposed model. In addition, in a sensitivity analysis, the weight of the most significant criterion has been changed.

Decision-making model of machine tool remanufacturing alternatives based on dual interval rough number clouds

Remanufacturing of machine tools has become one of the crucial topical subjects as it can effectively reduce the manufacturing cost compared with traditional new product development. The assessment and selection of different remanufacturing alternatives are vital for successfully implementing the remanufacturing of machine tools. Although numerous fuzzy theory-based methods have been developed to evaluate and select the reasonable remanufacturing alternatives in the machine tool remanufacturing process, they still have some drawbacks, such as requiring extra assumptions, ignoring the impact of internal relationships among distinct criteria, and lacking the mechanism of manipulating diverse uncertain information. To cover such limitations, this study develops an applicable decision-making method to assist managers in extracting the essential remanufacturing alternatives for product improvement. First, a new concept named dual interval rough number clouds (DIRNCs) is developed by combining the merit of interval rough numbers (IRNs) and interval cloud model in handling uncertain information. Then, an applicable decision-making support model of remanufacturing alternatives is constructed based on DIRNCs, two non-linear weighting methods, and a technique for order performance by similarity to ideal solution (TOPSIS). Finally, an assessment of remanufacturing alternatives of machine tools is presented to illustrate the model, whose effectivity is demonstrated by comparing extant models. Results display that the developed DIRNC-based model is more advantageous than triangular fuzzy-based, cloud model-based, fuzzy rough-based, and IRN-based methods.

Offshore wind farm site selection using interval rough numbers based Best-Worst Method and MARCOS

Over the past 20 years, the development of offshore wind farms has become increasingly important across the world. One of the most crucial reasons for that is offshore wind turbines have higher average speeds than those onshore, producing more electricity. In this study, a new hybrid approach integrating Interval Rough Numbers (IRNs) into Best-Worst Method (BWM) and Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) is introduced for multi-criteria intelligent decision support to choose the best offshore wind farm site in a Turkey’s coastal area. Four alternatives in the Aegean Sea are considered based on a range of criteria. The results show the viability of the proposed approach which yields Bozcaada as the appropriate site, when compared to and validated using the other multi-criteria decision-making techniques from the literature, including IRN based MABAC, WASPAS, and MAIRCA.

A Novel Integrated Interval Rough MCDM Model for Ranking and Selection of Asphalt Production Plants

Asphalt production plants play an important role in the field of civil engineering, but also in the entire economic system since the construction of roads enables uninterrupted functioning within it. In this paper, the ranking of asphalt production plants on the territory of the Autonomous Province of Vojvodina has been performed. The modern economy needs contemporary models and methods to solve complicated MCDM problems and, for these purposes, it has been developed an original Interval Rough Number (IRN) Multi-criteria decision-making (MCDM) model that implies an extension of two methods belonging to the field with interval rough numbers. After forming a list of eight most significant criteria for assessing the efficiency of asphalt production plants, the Interval Rough Number PIvot Pairwise RElative Criteria Importance Assessment (IRN PIPRECIA) method was developed to determine the significance of the criteria. A total of 21 locations with asphalt mixture installation were considered. For that purpose, seven asphalt production plants were included, and for their ranking, the IRN EDAS (Evaluation based on Distance from Average Solution) method was created. The aim of this paper is to develop a novel interval rough model that can be useful for determining the efficiency of asphalt production plants. Averaging in group decision-making (GDM) for both methods was performed using an IRN Dombi weighted geometric averaging (IRNDWGA) aggregator. The obtained results show that (A15) Ruma (SP)–Mačvanska Mitrovica–Zasavica has the best characteristics out of the set of locations considered in this study. However, Alternatives A6 and A19 are also variants with remarkably good characteristics since there is very little difference in values compared to the first-ranked alternative. Also, the obtained results have shown that the developed model is applicable, which is proven through a comparative analysis.

An extension of the codas method based on Interval Rough Numbers for multi-criteria group decision making

This study aims to develop a new Interval Rough COmbinative Distance-based Assessment (IR CODAS) method for handling multiple criteria group decision making problems using linguistic terms. A single decision maker is unable to express his opinions or preferences on multiple criteria decisions, while a Multi-Criteria Group Decision Making MCGDM process ensures successful outcomes when handling greater imprecision and vagueness information. A real-life case study of risk assessment is investigated using our proposed IR-CODAS method to test and validate its application; a sensitivity analysis is also performed. Keywords: Interval Rough Numbers, group decision making, IR-CODAS method, risk assessment.

A HYBRID LBWA - IR-MAIRCA MULTI-CRITERIA DECISION-MAKING MODEL FOR DETERMINATION OF CONSTRUCTIVE ELEMENTS OF WEAPONS

The paper demonstrates a model whose goal is to define the construction elements of weapons necessary to meet minimum requirements of users. The complexity of the problem, conditioned by different construction elements of weapons and specific situations of their use, is the reason for using methods of multi-criteria decision-making. In the paper we used the hybrid LBWA – IR-MAIRCA model. With this model, one can conduct an analysis of characteristics of the existing weapons, based on which we define the construction elements for modifying the existing and manufacturing new weapons. Regarding a large number of different types of weapons, the paper is limited to the analysis of close-quarters combat weapons. The LBWA method was used to calculate weight coefficients of the criteria. The MAIRCA method, which was modified by interval rough numbers, was used to select the best close-quarters combat weapon that has the best characteristics in accordance with the requests of the users. Based on the analysis, the users have the option to clearly and precisely define requests for improvement of the existing, and manufacturing new weapons.

The Application of the Hybrid Interval Rough Weighted Power-Heronian Operator in Multi-Criteria Decision-Making

In this paper, a new multi-criteria model which enables the processing of uncertainty and inaccuracy data through the application of interval rough numbers (IRN) is presented. The multi-criteria model represents the integration of the Power Aggregator (PA) and the Weighted Heronian Mean (WHM) operators. The goal of the forming of a hybrid Weighted Power Heronian Mean (WPHM) is to integrate the advantages of both operators into a single multi-criteria model, which has the following advantages: 1) it eliminates the influence of unreasonable arguments; 2) it takes into account the degree of support between input arguments and 3) it takes into account the interconnectedness of input arguments. Based on the mathematical concept of the IRN, the hybrid WPHM operator was extended and the IRNWPHM multi-criteria model was created. The IRNWPHA multi-criteria model enables objective decision-making in the case of imprecise input parameters in the initial decision matrix. Also, the IRNWPHA model allows flexible decision-making and the verification of the robustness of results through a variation of the p and q parameters. The IRNWPHM model was tested on a real-world multi-criteria example. The results showed that the IRNWPHM operator enabled a successful transformation of the uncertainties and inaccuracies that exist in group decision-making.

Group Decision-Making Based on Set Theory and Weighted Geometric Operator with Interval Rough Multiplicative Reciprocal Matrix

Interval rough numbers play an important role in dealing with complex fuzzy relationships. In this paper, a group decision-making (GDM) model based on interval rough multiplicative reciprocal (IRMR) matrix is proposed. Firstly, the inconsistency, satisfactory consistency and complete consistency of the IRMR matrix are defined from the perspective of set theory. Secondly, an improved method for the inconsistent IRMR matrix is introduced to address the inconsistent preference matrix in GDM. We define the uniform approximation matrix of the IRMR matrix, prove its existence, and provide a new calculation method for the sorting vector of IRMR matrix. Finally, the multiplicative reciprocal matrix obtained with a weighted geometric operator assembly is still the IRMR matrix. A GDM algorithm of the IRMR matrix is presented. The proposed algorithm is demonstrated using an illustrative example, and its feasibility and effectiveness are verified through comparison with other existing methods.

A rough based multi-criteria evaluation method for healthcare waste disposal location decisions

Healthcare waste disposal management is one of the biggest day-to-day challenges faced by healthcare providers and urban municipalities. Poor management of healthcare waste can cause serious problems for healthcare workers, patients, and the general public. Healthcare providers and urban planners usually struggle with the action of locating an appropriate waste disposal center in a municipal area. Healthcare waste disposal location planning is a difficult task due to complexities inherent in the evaluation of alternative locations according to multiple and often competing criteria. We propose a new best-worst method with interval rough numbers (IRN) for healthcare waste disposal location decisions. A new IRN Dombi-Bonferroni (IRNDBM) means the operator is also introduced to process the rough data because of the unavailability of precise information. A case study at a private hospital in Madrid is presented to demonstrate the applicability and exhibit the efficacy of the proposed multi-criteria evaluation method.

Rough set models of interval rough number information system

Classical rough set theory (RST) is based on equivalence relations, and does not have an effective mechanism when the attribute value of the objects is uncertain information. However, the information in actual problems is often uncertain, and an accurate or too vague description of the information can no longer fully meet the actual needs. Interval rough number (IRN) can reflect a certain degree of certainty in the uncertainty of the data when describing the uncertainty of the data, and can enable decision makers to make decisions more in line with actual needs according to their risk preferences. However, the current research on rough set models (RSMs) whose attribute values are interval rough numbers is still very scarce, and they cannot analyze the interval rough number information system (IRNIS) from the perspective of similar relation. therefore, three new interval rough number rough set models (IRNRSMs) based on similar relation are proposed in this paper. Firstly, aiming at the limitations of the existing interval similarity degree (ISD), new interval similarity degree and interval rough number similarity degree (IRNSD) are proposed, and their properties are discussed. Secondly, in the IRNIS, based on the newly proposed IRNSD, three IRNRSMs based on similar class, β-maximal consistent class and β-equivalent class are proposed, and their properties are discussed. And then, the relationships between these three IRNRSMs and those between their corresponding approximation accuracies are researched. Finally, it can be found that the IRNRSM based on the β-equivalent classes has the highest approximation accuracy. Proposing new IRNRSMs based on similar relation is a meaningful contribution to extending the application range of RST.

A Novel Multi-Criteria Decision-Making Model: Interval Rough SAW Method for Sustainable Supplier Selection

Sustainability in a supply chain is a demand on the one hand and a challenge on the other. It is necessary to balance between these dimensions in order to fulfill the purpose of the supply chain. Therefore, in the first phase—i.e., in procurement—it is necessary to take into account its sustainability. In this paper, a sustainable supplier was selected respecting all three aspects of sustainability. The evaluation was carried out on the basis of a total of 21 criteria arranged into two levels and three groups. A new Interval Rough SAW (simple additive weighting) method, which represents a contribution to the treatment of problems belonging to the multi-criteria decision-making (MCDM), was developed. The integration of interval rough numbers with the SAW method was completed. In addition, the full consistency method (FUCOM) was applied to determine the weights of the criteria. The integrated FUCOM-Interval Rough SAW model enables treatment of multi-criteria problems while reducing subjectivity to the lowest possible level and eliminating uncertainties and ambiguities. The results obtained were determined throughout a sensitivity analysis consisting of a change in the weight of the criteria and the influence of dynamic matrices on the change in ranks. In addition, Spearman’s rank correlation coefficient (SCC) was calculated to confirm the stability of the previously obtained results.

A Hybrid GIS Multi-Criteria Decision-Making Method for Flood Susceptibility Mapping at Shangyou, China

Floods are considered one of the most disastrous hazards all over the world and cause serious casualties and property damage. Therefore, the assessment and regionalization of flood disasters are becoming increasingly important and urgent. To predict the probability of a flood, an essential step is to map flood susceptibility. The main objective of this work is to investigate the use a novel hybrid technique by integrating multi-criteria decision analysis and geographic information system to evaluate flood susceptibility mapping (FSM), which is constructed by ensemble of decision making trial and evaluation laboratory (DEMATEL), analytic network process, weighted linear combinations (WLC) and interval rough numbers (IRN) techniques in the case study at Shangyou County, China. Specifically, we improve the DEMATEL method by applying IRN to determine connections in the network structure based on criteria and to accept imprecisions during collective decision making. The application of IRN can eliminate the necessity of additional information to define uncertain number intervals. Therefore, the quality of the existing data during collective decision making and experts’ perceptions that are expressed through an aggregation matrix can be retained. In this work, eleven conditioning factors associated with flooding were considered and historical flood locations were randomly divided into the training (70% of the total) and validation (30%) sets. The flood susceptibility map validates a satisfactory consistency between the flood-susceptible areas and the spatial distribution of the previous flood events. The accuracy of the map was evaluated by using objective measures of receiver operating characteristic (ROC) curve and area under the curve (AUC). The AUC values of the proposed method coupling with the WLC fuzzy technique for aggregation and flood susceptibility index are 0.988 and 0.964, respectively, which proves that the WLC fuzzy method is more effective for FSM in the study area. The proposed method can be helpful in predicting accurate flood occurrence locations with similar geographic environments and can be effectively used for flood management and prevention.