The success of any activity and process depends fundamentally on the possibility of balancing (symmetry) needs and their satisfaction. That is, the ability to properly define a set of success indicators. The application of the developed new multi-criteria decision-making (MCDM) methods can be eliminated or decreased by decision-makers’ subjectivity, which leads to consistency or symmetry in the weight values of the criteria. In this Special Issue, 40 research papers and one review study co-authored by 137 researchers from 23 different countries explore aspects of multi-criteria modeling and optimization in crisp or uncertain environments. The papers proposing new approaches and elaborate case studies in the following areas of applications: MCDM optimization in sustainable engineering, environmental sustainability in engineering processes, sustainable multi-criteria production and logistics processes planning, integrated approach for modeling processes in engineering, new trends in the multi-criteria evaluation of sustainable processes, multi-criteria decision-making in strategic management based on sustainable criteria.

Received March 1, 2020 Revised May 10, 2020 Accepted May 25, 2020 In recent decades, due to the rapid consumption of natural resources and the need for environmental protection, sustainability in supply chain management has emerged as an increasingly important issue. Therefore, in this study, supplier selection has been performed in order to achieve sustainability, taking into account all aspects: economic, social and environmental criteria. For this purpose, combined FUCOM Rough SAW approach has been used. The evaluation of criteria grouped at two levels has been carried out by decision makers according to the needs of the company whose main activity is lime production. To obtain the criterion weight values, the FUCOM (FUll COnsistency Method) has been used.. In order to avoid uncertainty and imprecision in the supplier evaluation process, combination with the Rough SAW method, which is used for ranking and supplier selection, has been performed. In order to control the stability of the used model, a sensitivity analysis has been performed. The first phase involves changing the weights of the criteria, while the second phase involves a comparative analysis using other MCDM methods.

The decision-making trial and evaluation laboratory (DEMATEL) method is one of the most significant multi-criteria techniques for defining the relationships among criteria and for defining the weight coefficients of criteria. Since multi-criteria models are very often used in management and decision-making under conditions of uncertainty, the fuzzy DEMATEL model has been extended in this paper by D numbers (fuzzy DEMATEL-D). The aim of this research was to develop a multi-criteria methodology that enables the objective processing of fuzzy linguistic information in the pairwise comparison of criteria. This aim was achieved through the development of the fuzzy DEMATEL-D method. Combining D numbers with trapezoidal fuzzy linguistic variables (LVs) allows for the additional processing of uncertainties and ambiguities that exist in experts’ preferences when comparing criteria with each other. In addition, the fuzzy DEMATEL-D methodology has a unique reasoning algorithm that allows for the rational processing of uncertainties when using fuzzy linguistic expressions for pairwise comparisons of criteria. The fuzzy DEMATEL-D methodology provides an original uncertainty management framework that is rational and concise. In order to illustrate the effectiveness of the proposed methodology, a case study with the application of the proposed multi-criteria methodology is presented.

An arbitrary univariate polynomial of nth degree has n sequences. The sequences are systematized into classes. All the values of the first class sequence are obtained by Newton’s polynomial of nth degree. Furthermore, the values of all sequences for each class are calculated by Newton’s identities. In other words, the sequences are formed without calculation of polynomial roots. The New-nacci method is used for the calculation of the roots of an nth-degree univariate polynomial using radicals and limits of successive members of sequences. In such an approach as is presented in this paper, limit play a catalytic–theoretical role. Moreover, only four basic algebraic operations are sufficient to calculate real roots. Radicals are necessary for calculating conjugated complex roots. The partial limitations of the New-nacci method may appear from the decadal polynomial. In the case that an arbitrary univariate polynomial of nth degree (n ≥ 10) has five or more conjugated complex roots, the roots of the polynomial cannot be calculated due to Abel’s impossibility theorem. The second phase of the New-nacci method solves this problem as well. This paper is focused on solving the roots of the quintic equation. The method is verified by applying it to the quintic polynomial with all real roots and the Degen–Abel polynomial, dating from 1821.

The analysis of operations of the passenger traffic operator in the Republic of Srpska (RS) showed that the volume of passenger transport has, for the last fifteen years, been in constant decline. It is of particular importance that the operator has, year after year, recorded a negative balance of business. The way out of the current unfavorable situation in the sector of passenger traffic is based on the application of Public Service Obligation (PSO) based on the Regulation 1370/2007. In order to solve the problems, seven realistically possible variants have been identified. This paper defines the criteria for selecting the best variant, as well as a new integrated fuzzy model for the selection of the best variant that will enable the operator to make a profit. To define the weights of criteria in this paper, we have used the fuzzy PIvot Pairwise RElative Criteria Importance Assessment (F-PIPRECIA) method, while for ranking and selection of the best variant, we have used the Fuzzy Evaluation based on Distance from Average Solution (F-EDAS) method. Results show that the seventh variant: “Increase in revenue from ticket sales and PSO services and reduction in costs“ is the best solution in current conditions. Validation tests are performed with different scenarios and approaches and show that the model is stable. A validity test was created consisting of variations in the significance of model input parameters, testing of reverse rank, applying the fuzzy Measurement Alternatives and Ranking according to the COmpromise Solution (F-MARCOS), fuzzy Simple Additive Weighing (F-SAW) method, and fuzzy Technique for Order of Preference by Similarity to Ideal Solution (F-TOPSIS). As a part of the validation tests, Spearman’s coefficient of correlation (SCC) in some scenarios is performed and weights of the criteria have been obtained using the Fuzzy Analytic Hierarchy Process (F-AHP) and Full Consistency Method (FUCOM).

The use of computers with outstanding performance has become a real necessity in order to achieve greater efficiency and sustainability for the accomplishment of various tasks. Therefore, with the development of information technology and increasing dynamism in the business environment, it is expected that these computers will be more intensively deployed. In this paper, research was conducted in Danube region countries: Austria, Bosnia and Herzegovina, Bulgaria, Croatia, Czech Republic, Germany, Hungary, Moldova, Montenegro, Romania, Serbia, Slovakia, Slovenia, and Ukraine. The aim of the research was to determine what criteria are most significant for the introduction of high-performance computing and the real situation in each of the countries. In addition, the aim was to establish the infrastructure needed to implement such a system. In order to determine the partial significance of each criterion and thus the possibility of implementing high-performance computing, a multi-criteria model in a fuzzy environment was applied. The weights of criteria and their rankings were performed using the Fuzzy PIvot Pairwise RElative Criteria Importance Assessment—fuzzy PIPRECIA method. The results indicate different values depend on decision-makers (DMs) in the countries. Spearman’s and Pearson’s correlation coefficients were calculated to verify the results obtained.

In this paper, a new fuzzy multi-criteria decision-making model for traffic risk assessment was developed. A part of a main road network of 7.4 km with a total of 38 Sections was analyzed with the aim of determining the degree of risk on them. For that purpose, a fuzzy Measurement Alternatives and Ranking according to the COmpromise Solution (fuzzy MARCOS) method was developed. In addition, a new fuzzy linguistic scale quantified into triangular fuzzy numbers (TFNs) was developed. The fuzzy PIvot Pairwise RElative Criteria Importance Assessment—fuzzy PIPRECIA method—was used to determine the criteria weights on the basis of which the road network sections were evaluated. The results clearly show that there is a dominant section with the highest risk for all road participants, which requires corrective actions. In order to validate the results, a comprehensive validity test was created consisting of variations in the significance of model input parameters, testing the influence of dynamic factors—of reverse rank, and applying the fuzzy Simple Additive Weighing (fuzzy SAW) method and the fuzzy Technique for Order of Preference by Similarity to Ideal Solution (fuzzy TOPSIS). The validation test show the stability of the results obtained and the justification for the development of the proposed model.

In this paper is presented a novel integrated fuzzy – rough Multi-Criteria Decision-Making (MCDM) model based on integration fuzzy and interval rough set theory. Model integrates Fuzzy PIvot Pairwise RElative Criteria Importance Assessment - fuzzy PIPRECIA and Interval rough Simple Additive Weighting (SAW) methods. An illustrative example for demonstration of the model is proposed that represents evaluation and supplier selection based on nine environmental criteria. Fuzzy PIPRECIA method is used for determining the significance of the following seven criteria: C1 - environmental image, C2 - recycling, C3 - pollution control, C4 - environmental management system, C5 – environmentally friendly products, C6 - resource consumption and C7 - green competencies. Iterval rough SAW method is applied for evaluation four alternatives. Results show that third criterion is most important while fourth alternative represents the best solution.

This paper demonstrates and provides additional findings and instructions to produce new cold-recycled layers of pavement structures spatially and temporally sustainable. At the same time, recycled pavement structures have been enhanced with optimum amounts of new stone materials and binders made of cement and foamed bitumen. The subject of the research is based on the examination of recycled asphalt from surface and bituminous base courses of pavement structures for use on higher-type roads. The aim of the research is to model the process of producing recycled asphalt by cold recycling to optimize the process of influential parameters. In addition, one of the primary goals of the research is to demonstrate a sustainable way of producing new cold-recycled layers of pavement structures. The obtained results indicated the inevitability of the use of recycled material from pavement structures with the possibility of applying secondary and tertiary crushing of recycled mass, which depends on the type of layer for which the recycled material would be used. The research resulted in an optimum mixture variant of the stabilization layer of pavement structure that consists mainly of recycled material from a worn pavement structure improved with a relatively small amount of new aggregate with the addition of minimal stabilizers made of cement and foamed bitumen. The results showed that the optimum mixture variant of the stabilization layer is spatially and temporally stable. Additionally, the presented optimum variant of the stabilization layer enables sustainable development of road networks with minimum consumption of new natural resources.

The application of different evaluation approaches in logistics requires considering many factors with different significance for making the final decision. Multi-criteria decision-making (MCDM) methods are often applied in logistics to create different strategies and evaluations. In this paper, research has been carried out in a transport system of an international transport company. An MCDM model has been created for the purpose of human resource evaluation, on which the overall efficiency of the company depends. A total of 23 drivers were evaluated on the basis of five crucial criteria in order to increase employees’ motivation through their periodic remuneration. The Full Consistency Method (FUCOM) was applied to determine the significance of the criteria, while the evaluation of potential solutions was performed using Measurement Alternatives and Ranking according to COmpromise Solution (MARCOS). After the results had been obtained, the created model was validated throughout comparisons with seven other MCDM methods.

Achieving sustainability in constant development in every area in today’s modern business has become a challenge on the one hand, and an imperative on the other. If the aspect of business excellence achievement is also added to it, the complexity of the system increases significantly, and it is necessary to model a system considering several parameters and satisfying the multi-criteria function. This paper develops a novel integrated model that involves the application of a subjective-objective model in order to achieve business sustainability and excellence. The model consists of fuzzy PIPRECIA (fuzzy pivot pairwise relative criteria importance Assessment) as a subjective method, CRITIC (criteria importance through intercriteria correlation) and I-distance method as objective methods. The goal is to take the advantages of these approaches and allow for more accurate and balanced (symmetric) decision-making through their integration. The integrated subjective-objective model has been applied in a narrow geographical area to consider and evaluate banks as a significant factor in improving the social aspect of sustainability. An additional contribution of the paper is a critical overview of multi-criteria problems in which the levels of the hierarchical structure contain a different (asymmetric) number of elements. A specific example has also been used to prove that only a hierarchical structure with an equal number of lower-level elements provides precise weights of criteria in accordance with the preferences of decision-makers referring to subjective models. The results obtained are verified throughout the calculation of Spearman and Pearson correlation coefficients, and throughout a sensitivity analysis involving a dynamic reverse rank matrix.

Cost rationalization has become imperative in every economic system in order to create adequate foundations for its efficient and sustainable management. Competitiveness in the global market is extremely high and it is challenging to manage business and logistics systems, especially in regards to financial parameters. The presence of inventories is inevitability in every logistics system, and it tends to create adequate policies for their efficient and sustainable management. In order to be able to do this, it is necessary to determine which products represent the largest percentage share in the value of procurement, and which are the most represented quantitatively. In this paper, the warehouse of construction material that represents the wholesale system is considered. Taking into account that it is wholesale, it is necessary to determine what the procurement costs are and what the demand is for certain products. The grouping of products into three categories A, B and C was performed, after which it is necessary to identify appropriate suppliers for each category in order to rationalize procurement costs. Financial, logistical and quality parameters are taken into account. The FUCOM method has been used to determine the significance of these parameters and ARAS method is applied for supplier evaluation and selection.