TOWARDS RELIABLE DECISION-MAKING IN THE GREEN URBAN TRANSPORT DOMAIN

Operational research is a scientific discipline related to the decision theory that allows determining solutions for specific problems related to, for example, widely understood transport. Increasingly popular in this field are issues related to the domain of the green urban transport. In order to support the decision-making process in this area, methods of multi-criteria decision analysis (MCDA) are used more and more often. However, if we solve a specific problem using different MCDA methods, we get different rankings, as each method has a different methodological basis. Therefore, the challenge is how to make a reliable decision. This paper presents a numerical example from the green urban transport domain, which is solved by six different MCDA methods that return a complete ranking. We measure the similarity of these rankings using coefficients rw and WS, and then we propose a simple way of determining a compromise solution. The obtained compromise ranking is guaranteed to be the best match to the selected MCDA methods' rankings, which is proved in the paper. Finally, possible directions for further development work are identified

STUDY TOWARDS THE TIME-BASED MCDA RANKING ANALYSIS – A SUPPLIER SELECTION CASE STUDY

Decision-making processes increasingly use models based on various methods to ensure professional analysis and evaluation of the considered alternatives. However, the abundance of these methods makes it difficult to choose the proper method to solve a given problem. Also, it is worth noting whether different results can be obtained using different methods within a single decision problem. In this paper, we used three selected Multi-Criteria Decision Analysis (MCDA) methods called COMET, TOPSIS, and SPOTIS in order to examine how the obtained rankings vary. The selection of material suppliers was taken into consideration. The equal weights, entropy and standard deviation methods were used to determine the weights for criteria. Final preferences values were then compared with the WS similarity coefficient and weighted Spearman correlation coefficient to check the similarity of the received rankings. It was noticed that in the given problem, all of the methods provide highly correlated results, and the obtained positional rankings are not significantly different. However, practical conclusions indicate the need to look for improved solutions in the correct and accurate assessment of suppliers in a given period

Efficiency of Methods for Determining the Relevance of Criteria in Sustainable Transport Problems: A Comparative Case Study

Problems related to sustainable urban transport have gained in importance with the rapid growth of urban agglomerations. There is, therefore, a need to support decision-making processes in this area, a trend that is visible in the literature. Many methods have already been presented as a useful decision-making tool in this field. However, it is still a significant challenge to properly determine the relevance of the criteria because it is one of the most critical points of many presented techniques to solve decision problems. In this work, we propose two new approaches to determining the relevance of particular decision criteria effectively in sustainable transport problems. For this purpose, we examine a study case for the evaluation of electric bikes evaluated against eight criteria, which have been taken from earlier work. We calculate the relevance of each criterion using four different approaches and then evaluate their effectiveness using a reference ranking and popular multi-criteria decision analysis methods. The results are compared with each other by using similarity coefficients. Finally, we summarize the results obtained and set out further methods of development

Fuzzy Model Identification Using Monolithic and Structured Approaches in Decision Problems with Partially Incomplete Data

A significant challenge in the current trend in decision-making methods is the problem’s class in which the decision-maker makes decisions based on partially incomplete data. Classic methods of multicriteria decision analysis are used to analyze alternatives described by using numerical values. At the same time, fuzzy set modifications are usually used to include uncertain data in the decision-making process. However, data incompleteness is something else. In this paper, we show two approaches to identify fuzzy models with partially incomplete data. The monolithic approach assumes creating one model that requires many queries to the expert. In the structured approach, the problem is decomposed into several interrelated models. The main aim of the work is to compare their accuracy empirically and to determine the sensitivity of the obtained model to the used criteria. For this purpose, a study case will be presented. In order to compare the proposed approaches and analyze the significance of the decision criteria, we use two ranking similarity coefficients, i.e., symmetric rw and asymmetric WS. In this work, the limitations of each approach are presented, and the results show great similarity despite the use of two structurally different approaches. Finally, we show an example of calculations performed for alternatives with partially incomplete data

How to Make Decisions with Uncertainty Using Hesitant Fuzzy Sets?

More and more often, we have to deal with uncertain data while making decisions. One popular way to model uncertain data is to use one of the many generalizations of fuzzy sets. In this paper, we would like to draw attention for the use of Hesitant fuzzy sets (HFSs) in solving decision-making problems. The main challenge is the complex algorithms that can guarantee high accuracy and operate on HFSs. The HFS COMET approach is known in the literature but is rarely used due to its complexity. The main contribution of our work is the simplification of the HFS COMET algorithm to make it more applicable. For this purpose, we make comparisons of different score functions, which are used to infer based on a hybrid algorithm that combines the advantages of TOPSIS and COMET methods. Finally, we have shown the efficiency of the proposed approach by using reference rankings and similarity coefficients

A new distance between rankings

This paper analyzes the behavior of the well-known Spearman's footrule distance (F-distance) to measure the distance between two rankings over the same set of objects. We show that F-distance is not invariant to labeling, and therefore, it suffers from a serious drawback for its use in applications. To circumvent this problem, we propose a new distance between rankings which is invariant under indexing (i.e., labeling) and appears as a good alternative to the direct use of F-distance between rankings, and also the invariant-under-indexing Kemeny's distance as well. We also show how our new distance can work with importance weights. Some simple examples are given to show the interest of our method with respect to the classical one based on F-distance and Kemeny's distance

pymcdm—The universal library for solving multi-criteria decision-making problems

Multi-criteria decision-making/analysis is a vast field designed for solving decision-making problems. Due to the widespread use of many relevant MCDA/MCDM approaches and their frequent appearance in scientific papers, there is a particular gap regarding comprehensive software that should have relevant components. Therefore, this paper proposes a flexible library written in Python 3 for multi-criteria analysis/decision-making. It includes tools related to evaluating alternative options, determination of Pareto optimal solutions, determination of criteria relevance, comparative analysis, and visualization. The novelty that distinguishes the library from other software is the provision of a wide range of approaches, high performance, consistency of the software, and its small size. The research presented in this paper presents its high potential as a tool that decision-makers and domain experts can use in the decision-making process

Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model

A fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a significant problem in its uses, i.e., considerable data loss. The probabilistic hesitant fuzzy set (PHFS) has been proposed to improve the HFS. It provides probability values to the HFS and has the ability to retain more information than the HFS. Previously, fuzzy regression models such as the fuzzy linear regression model (FLRM) and hesitant fuzzy linear regression model were used for decision making; however, these models do not provide information about the distribution. To address this issue, we proposed a probabilistic hesitant fuzzy linear regression model (PHFLRM) that incorporates distribution information to account for multi-criteria decision-making (MCDM) problems. The PHFLRM observes the input–output (IPOP) variables as probabilistic hesitant fuzzy elements (PHFEs) and uses a linear programming model (LPM) to estimate the parameters. A case study is used to illustrate the proposed methodology. Additionally, an MCDM technique called the technique for order preference by similarity to ideal solution (TOPSIS) is employed to compare the PHFLRM findings with those obtained using TOPSIS. Lastly, Spearman’s rank correlation test assesses the statistical significance of two rankings sets

Similarity Analysis of Methods for Objective Determination of Weights in Multi-Criteria Decision Support Systems

Decision support systems (DSS) are currently developing rapidly and are increasingly used in various fields. More often, those systems are inseparable from information-based systems and computer systems. Therefore, from a methodical point of view, the algorithms implemented in the DSS play a critical role. In this aspect, multi-criteria decision support (MCDA) methods are widely used. As research progresses, many MCDA methods and algorithms for the objective identification of the significance of individual criteria of the MCDA models were developed. In this paper, an analysis of available objective methods for criteria weighting is presented. Additionally, the authors presented the implementation of the system that provides easy and accessible weight calculations for any decision matrix with the possibility of comparing results of different weighting methods. The results of weighting methods were compared using carefully selected similarity coefficients to emphasise the correlation of the resulting weights. The performed research shows that every method should provide distinctive weights considering input data, emphasising the importance of choosing the correct method for a given multi-criteria decision support model and DSS

Study of Transformed <i>η^ζ</i> Networks via Zagreb Connection Indices

A graph is a tool for designing a system’s required interconnection network. The topology of such networks determines their compatibility. For the first time, in this work we construct subdivided ηζ network S(ηζΓ) and discussed their topology. In graph theory, there are a variety of invariants to study the topology of a network, but topological indices are designed in such a way that these may transform the graph into a numeric value. In this work, we study S(ηζΓ) via Zagreb connection indices. Due to their predictive potential for enthalpy, entropy, and acentric factor, these indices gain value in the field of chemical graph theory in a very short time. ηζΓ formed by ζ time repeated process which consists ηζ copies of graph Γ along with η2|V(Γ)|ζηζ−1 edges which used to join these ηζ copies of Γ. The free hand to choose the initial graph Γ for desired network S(ηζΓ) and its relation with chemical networks along with the repute of Zagreb connection indices enhance the worth of this study. These computations are theoretically innovative and aid topological characterization of S(ηζΓ)