Abstract The use of multi-criteria decision-making (MCDM) methods to select the most appropriate one from a range of alternatives considering multiple criteria is a suitable methodology for making informed decisions. When constructing a decision or objective matrix (DOM) for MCDM procedure, either crisp numerical values or fuzzy linguistic terms can be used. A review of relevant literature indicates that decision experts often prefer to give linguistic terms (instead of crisp numerical values) based on their domain knowledge, to establish a fuzzy DOM. However, previous research articles have not adequately studied the selection between fuzzy and crisp DOM in MCDM, especially under the context of assessing the financial performance (FP) of listed firms – a notably complex decision-making problem. As such, the primary motivation of this study is to bridge this research gap through comparative analyses of fuzzy and crisp DOM in MCDM. Along this path, and in order to handle fuzzy DOM, this work also proposes two new fuzzy MCDM methods: fuzzy preference ranking on the basis of ideal-average distance (PROBID) and fuzzy sPROBID (simpler PROBID), extending the applicability of the original crisp PROBID and sPROBID methods. Moreover, for the first time in the literature, this work compares the FP rankings obtained using fuzzy MCDM methods with an objective benchmark we have identified, i.e., the real-life stock return (SR)-based ranking. The case study of ranking the FP of 32 listed firms demonstrates that the fuzzy MCDM methods produce higher correlation results with the SR-based ranking. The results also suggest that the proposed fuzzy sPROBID method with triangular fuzzy DOM performs the best for assessing the FP of firms in terms of Spearman’s rank correlation coefficient with the SR-based ranking. Overall, the contributions of this work are three-fold: first, it proposes two new fuzzy MCDM methods (i.e., fuzzy PROBID and fuzzy sPROBID); second, it advances the application of fuzzy MCDM methods in assessing and ranking the FP of listed firms to make rational investment decisions in the financial market; third, it studies the selection between fuzzy and crisp DOM through comparisons with an objective benchmark.

<abstract> <p>Newton's identities of an infinite polynomial with complex-conjugate roots <italic>n</italic>^{<italic>−(</italic>σ+<italic>it</italic>)} and <italic>n</italic>^{<italic>−(</italic>σ<italic>−it</italic>)} are multiple zeta functions for <italic>n</italic>∈[1, ∞), σ∈R and <italic>t</italic>∈R. All Newton's identities can be represented by Macdonald determinants. In a special case of the Riemann hypothesis, the multiple zeta function of the first order is equal to zero, ζ(σ+<italic>it</italic>)+ζ(σ−<italic>it</italic>) = 0. The special case includes all non-trivial zeros. The value of the last, infinite multiple zeta function, in the special case, changes the structure of the determinant that can be calculated. The result is the reciprocal of the factorial value (<italic>n</italic>!)⁻¹. The general value of the infinite multiple zeta function is calculated based on Vieta's rules and is equal to (<italic>n</italic>!)^−2σ. The identity based on the relation of the special case and the general case (<italic>n</italic>!)⁻¹ = (<italic>n</italic>!)^−2σ is reduced to the equation −1 = −2σ. The value of the critical line for all non-trivial zeros is singular, σ = ½.</p> </abstract>

Over 700 bike-sharing systems are currently in operation worldwide, and the number of systems has grown quickly in recent years. Rwanda's bike-sharing system has only recently begun operations and has encountered numerous challenges. The current study used an Ordinal Priority Approach (OPA) to examine these challenges and provide an acceptable strategy for overcoming them. Five strategies have been established. These strategies are prioritized using four criteria. The results indicate that “theft” and “damage of some bikes when being returned” are the most critical challenges while the first alternative “improving the current bike infrastructure to better serve the bike share system” is the appropriate strategy to overcome these challenges for a successful operation of the bike share system. Taking into account the findings, recommendations were provided to help local administrative bodies handle these challenges.

Road capacity utilization is causally connected with an appropriate level of efficiency and an optimal level of traffic safety. Therefore, in this paper, it is considered the issue of maximum utilization of road capacity through the maximization of the input parameter AADT (Annual Average Daily Traffic), and the minimization of output parameters related to the categories of traffic accidents. It was defined six main road sections, which were evaluated based on seven techno-operational criteria using an integrated Multi-criteria decision-making (MCDM) model. The data refer to buses as a vehicle category. The Improved Fuzzy Step-Wise Weight Assessment Ratio Analysis (IMF SWARA) method was chosen to determine the weights of criteria, while the road sections were ranked using the Evaluation based on distance from average solution (EDAS). In addition, in one of the stages of applying the model when it comes to AADT, the Bonferroni operator (BFO) is used. The results show that the highest level of safety refers to a main road section with the following characteristics: average AADT, minimal deviation from the speed limit, an ascent of 7% and the lowest number of traffic accidents by all categories. In the paper, it was performed a multi-phase sensitivity analysis in order to identify possible differences in results when determining new circumstances.

The impact of geometric characteristics on traffic risk is reflected through identifying conflict points on roads,traffic accidents, and any other unforeseen situation that is inherently hazardous for traffic participants. In order to identify the road sections with the highest risk, it is necessary to consider a number of criteria that affect risk, and conduct extensive empirical research, analysis and data synthesis. This paper evaluates 9 sections of two-lane roads in the territory of Bosnia and Herzegovina (the Republic of Srpska) using an integrated Multi-Criteria Decision-Making (MCDM) model.To determine the significance of 8 criteria for the evaluation of the sections, it was applied a subjective–objective model consisting of 3 methods: (1) CRiteria Importance Through Inter-criteria Correlation (CRITIC), (2) FUll COnsistency Method (FUCOM) and (3) fuzzy PIvot Pairwise RElative Criteria Importance Assessment (PIPRECIA). The aggregation of the criterion values obtained using the methods yielded the final criterion values. Measurement Alternatives and Ranking according to COmpromise Solution (MARCOS) method was used to evaluate the sections and determine their objective diversity. The obtained results identified one location as extremely hazardous by most of analysed input parameters. The section with the highest risk is the Rudanka – Doboj section (A4), which represents a section of the road infrastructure of the 105 road. The validation of the results obtained by applying the integrated MCDM model was performed through an extensive sensitivity analysis. The weights of criteria were observed through initially individual methods implemented in the MARCOS method. Then, a comparative analysis was performed with 6 other MCDM methods and Spearman’s Correlation Coefficient (SCC) was calculated as a statistical indicator of rank correlation in a sensitivity analysis. In addition,the Standard Deviation (STDEV) of the obtained results was determined.

Supplier selection is an important task in supply chain management, as suppliers have a vital role in the success of organisations in a supply chain. Sustainability has emerged as a solution to decreasing resources and increasing environmental and social problems in the past few decades. It has been applied to various industrial operations, one of them is supplier selection, to mitigate unwanted effects in the future. Sustainable supplier selection is a complicated multi-criteria decision making problem, including several criteria from economic, environmental, and social perspectives. To deal with subjective judgements of decision makers, fuzzy and grey methods are widely used in multi-criteria decision making, In the case of small, limited, and incomplete data, the grey theory provides satisfactory results, compared to fuzzy methods. Therefore, this study is an integrated method including grey Best-Worst Method (BWM) and grey Weighted Sum-Product (WISP) for choosing the most sustainable supplier for a textile manufacturer, which includes three main criteria and twelve sub-criteria. According to the result of the proposed model, the supplier with the best performance was determined to be the supplier with the SP2 coded. The results of the developed model were shown to the experts, and the accuracy of the results was confirmed. According to the experts, a higher amount of product can be purchased from the supplier with the SP2 code, and a tighter relationship can be worked with this supplier. The contributions of this study are: (1) Develop a new grey MCDM model called Grey WISP. (2) Create a new integrated MCDM model with grey theory, BWM, and WISP methods that can be applied to assess supplier sustainability using this hybrid model. The proposed model can be used not just for selecting sustainable suppliers, but also for any other decision problems that have multiple criteria and alternatives. The findings suggest that the Grey WISP method achieved accurate results.

Solid-state data storage is becoming a widely accepted technology and is looking for new ways to provide cost-effective solutions across various information systems. Solid-state drives (SSDs), existing in different types and models, have several sustainable features: storage, dimensions, volume, etc. Due to the wide range of attributes, designing a robust method can easily select from the purchaser/retailer/wholesaler point of view. This work offers a joint multi-criteria decision-making (MCDM) to rank SSD alternatives, and a newly developed approach, namely Measurement Alternatives and Ranking according to the Compromise Solution (MARCOS) technique, is utilised, and a comparative investigation has also been achieved with other MCDM methods. Data of separate SSDs have been collected from the Indian market with twenty-six different models of eleven brands. The Bonferroni operator (BFO) allocates and compiles the objective weights using the Entropy weights technique (EWT), the Criteria Importance through Inter criteria Correlation (CRITIC) and the Method based on the Removal Effects of Criteria (MEREC). The sensitivity analysis using objective weights considering 18 scenarios was performed, and analysis with the Standard deviation shows that the joint MCDM possesses high accuracy and robustness. The results achieved have been tested with Spearman’s rank and Wojciech-Salabun (WS) coefficient, and the first rank goes to SSD-7. The presented results benefit the manufacturers to understand the market requirement better and for the consumer to make a wise decision while purchasing SSD. It also offers future scope for applying the proposed methodology in similar areas, social sciences and engineering, to make complex decisions.

Order-picking process management is one of the most demanding tasks within the operations of a warehouse system. It is especially evident in companies that have a high intensity of product flows, so the question of increasing the productivity of order picking arises. In this paper, a novel integrated fuzzy MCDM (Multicriteria Decision-Making) model was developed for the evaluation and selection of information technologies for order picking in a warehouse system, which is one of the most important novelties and contributions of the paper. Barcode, pick-to-light, pick-to-voice, and pick-to-vision technologies were evaluated based on IMF SWARA (improved fuzzy stepwise weight assessment ratio analysis) and fuzzy EDAS (evaluation based on distance from average solution) based on Z numbers. IMF SWARA-Z was applied to determine the importance of four criteria while the information technologies for order picking were evaluated with the fuzzy EDAS-Z method. The averaging of the estimates of the critera and alternatives was performed using the fuzzy Dombi aggregator. The results show that in this particular case under these research conditions, pick-to-vision is the best order-picking technology. Subsequently, validation tests were carried out, and they included the simulation of criteria weights and the impact of the reverse rank matrix.

Today’s economic systems are, on the one hand, exposed to various risks and uncertainties with their trends changing almost daily, while on the other hand, they represent an extremely complex system with a large number of sustainable influential parameters. The challenge is to model macroeconomic parameters and achieve sustainability, yet also satisfy conflict situations with an increased level of uncertainty. The aim of this paper is to create an appropriate functional model by examining the mutual influence of various macroeconomic factors. It assesses a total of four scenarios considering mutual influences of: FDI (foreign direct investments), GDP (gross domestic product), imports, exports, inflation rate, RER (real exchange rate) and employment rate as defined parameters. First, the DEA (Data envelopment analysis) model was applied to determine the initial efficiency of two countries, Bosnia and Herzegovina (BIH) and Serbia, for the period 2005–2020. Then, PCA (Principal Component Analysis) was applied in combination with DEA to obtain more precise values. In addition, IMF SWARA (Improved Fuzzy Stepwise Weight Assessment Ratio Analysis) was applied to define weight coefficients of macro-economic parameters. Finally, the CRADIS (compromise ranking of alternatives from distance to ideal solution) model was applied for the final ranking of part of decision-making units. This developed, integrated model can be classified as a mathematical method for economic analysis and gives extended opportunities for solving different problems. The results show that 2009, 2013 and 2016 were the most favorable years in terms of the conditions set when it comes to Bosnia and Herzegovina, and 2012, 2014 and 2016 when it comes to Serbia. These years have been singled out and can be a benchmark for further handling and modeling of macroeconomic elements. In addition, correlation was tested using statistical coefficients.

One of the most common tools for achieving optimization and adequate production process management is linear programming (LP) in various forms. However, there are specific cases of the application of linear programming when production optimization implies several potential solutions instead of one. Exactly such a problem is solved in this paper, which integrates linear programming and a Multi-Criteria Decision-Making (MCDM) model. First, linear programming was applied to optimize production and several potential solutions lying on the line segment AB were obtained. A list of criteria was created and evaluated using the Improved Fuzzy Stepwise Weight Assessment Ratio Analysis (IMF SWARA). To obtain the final solution, a novel Rough compromise ranking of alternatives from distance to ideal solution (R-CRADIS) method was developed and verified through comparative analysis. The results show that the integration of linear programming and a Fuzzy-Rough MCDM model can be an exceptional solution for solving specific optimization problems.