Article citation information:Sendek-Matysiak, E. Multi-criteria analysis and expert assessment of vehicles with different drive types regarding their functionality and environmental impact. Scientific Journal of Silesian University of Technology. Series Transport. 2019, 102, 185-195. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2019.102.15.Ewelina SENDEK-MATYSIAKMULTI-CRITERIA ANALYSIS AND EXPERT ASSESSMENT OF VEHICLES WITH DIFFERENT DRIVE TYPES REGARDING THEIR FUNCTIONALITY AND ENVIRONMENTAL IMPACTSummary. It is not easy to choose a car depending on the type of engine used in it. This is due to the diversity of properties characterising certain types of cars and doubts concerning the costs incurred during their operation (especially for new types as electric cars). Thus, this article presents a comparative analysis of cars provided with different energy sources. The analysis will allow finding the answer, which of the analysed car types best meet expectations, since both electric motor-driven vehicles and combustion engine-driven vehicles have a number of disadvantages and advantages. All compared vehicles are of the same model of a single make, with different drive sources and drive systems, classified in the same market segment. Therefore, the purpose of the article is to demonstrate, which vehicle type (that is, a car with spark-ignition engine, compression-ignition engine, electric motor, or Plug-In type hybrid drive) is currently the most optimal regarding technology, economy, and environment. For this purpose, the MAJA multi-criteria assessment method which has never before been used in comparisons of this sort was chosen.Keywords: criterion, the MAJA multi-criteria method, electric car, vehicle selection1. INTRODUCTIONIn decision-making challenges concerning the choice of a motor vehicle, for example, from the point of view of its environmental impact, the decision-makers very often consider not just one, but many criteria in order to arrive at their decision. The problems, which are subject to analysis and solving are most often complex, and require an exploration covering many areas and taking into account numerous points of view (assessment criteria), are called the multi-criteria problems. The domain that allows solving these complex decision-making problems, during analysis of which it is necessary to consider many, often opposite points of view [3, 11, 20], is a multi-criteria decision support, also called a multi-criteria analysis (French analyse multicritere), or multiple criteria decision making.According to B. Roy [7, 8], the multi-criteria decision support is the activity of an analyst, who helps the decision-maker in the decision-making process in order to find answers to questions connected with seeking the most desired solutions while taking into account the multitude of goals (criteria) set by the decision-maker. The multi-criteria analysis methodology is used to solve the multiple criteria decision-making problems, that is situations, in which, having at their disposal a defined set of actions (decisions, variants) and a coherent family of criteria, the decision makers seek to [11]: – specify the subset of actions (decisions, variants) deemed best from the point of view of the discussed criteria family (the problem of choice). – divide the set of actions (decisions, variants) into the subsets according to certain standards (the problem of classification or sorting).– rank the set of actions (decisions, variants) from the best to the worst (the problem of arranging or ranking). The basic attributes of the multiple criteria decision making problems are: the set of solutions (variants) A, and a coherent family of assessment criteria F. The set of solutions A is the set of objects, decisions, candidates, variants or actions, which are to be put to analysis and assessment during the decision-making procedure.The set of solutions may be defined directly [by listing all of its components (when the set is finite and sufficiently small)] or indirectly [by determining properties characteristic for the set components or limiting conditions (when the set is infinite or finite, but very large)]. Set A can be constant, that is defined in advance (a priori) and not liable to changes during the decision-making procedure, or evolving (variable), that is undergoing modifications during the decision-making procedure. The criteria family means a set of criteria, which should satisfy the following requirements: exhaustiveness of an assessment, which involves taking into account all possible aspects of the analysed problem. coherence of an assessment, based on proper forming of global decision-maker’s preferences by each criterion.non-redundancy of criteria – non-repeatability of criteria meaning range [5].Each criterion appearing in the set F is a function fj defined in set A, used to assess the set A and representing decision-maker’s preferences regarding certain aspect (dimension) of a decision-making problem. The multiple criteria decision.making problems belong to the so-called mathematically ill-defined problems because while solving them, attempts are made to determine such solutions x, which maximize the multi-criteria objective function F(x). QUOTE QUOTE Fx=maxf1x,f2x,…,fjx (1)for limitations: QUOTE where:A – a set of acceptable solutions,fj(x) – individual partial criterial functions for j = 1, 2, …, J.In this case, the concept of a globally optimal solution is not justified, since in practice no solution exists, which would be best from the point of view of all assessment criteria. Instead of this, the term of a non-dominated or efficient solution is introduced (also called a Pareto-optimal solution) [1, 2]. Solution a is efficient when the set of acceptable solutions A contains no other solution b, which would dominate over a. The term of dominance relation is important here. Solution a dominates over b (aDb) when for each criterion j (j = 1, 2, ..., J) the ratings of solutions a and b - fj(a) and fj(b), respectively, maintain the relation fj(a)≥ fj(b) and at least one of the inequalities is sharp, that is for selected j fj(a)>fj(b). On the other hand, if none of the inequalities is sharp, then we speak of the so-called weak domination, and obtained solution a is weakly non-dominated. The set of non-dominated solutions obtained most often is quite numerous due to a considerable number of considered criteria. From this set of solutions, the decision-maker chooses the most satisfying solution, that is the compromise [2, 3, 10].2. IMPLEMENTATION OF THE MAJA MULTI-CRITERIA METHOD IN VEHICLE SELECTIONDiverse tools and methods are applied in order to solve the multiple criteria decision-making problems, which undoubtedly include car selection based on a certain criterion. The MAJA multi-criteria method was used in this study.This method involves using detailed ratings of vehicle selection variants and taking into account the ratios of the relative importance of partial criteria. In consequence, this allows choosing the best variant among the analysed vehicle types.Since variant ratings can be given in various units, they must be standardised in order to satisfy the requirement of value comparability in the entire evaluation system. As regards individual criteria, variant ratings can be standardised using different methods [4, 6]. As soon as the matrix of standardised ratings is obtained, the two matrices of compliance and incompliance are being developed. Components of the compliance matrix Z are obtained by comparing a pair of any two variants (v, v´), determining criteria QUOTE , QUOTE f∈F for which the design variant v receives better ratings than variant v´. As regards criteria satisfying the above condition, their weights are summed, and then divided by the sum of weights of all criteria. In this way, the compliance rate zvv´ is obtained, with values ranging within [0, 1]. QUOTE (2)where:(3)The highest value is reached when ratings for variant v for all criteria f are higher than ratings for variant v´. To sum up, the compliance matrix Z has the following form: QUOTE Z=zvv,N×M, zvv,∈0,1 QUOTE (4)Components of the incompliance matrix N are obtained by comparing, how far the rating of the design variant v is worse than the alternative variant v´. The value of the incompliance rate nvv´ is determined as the ratio of the maximum of the differences in ratings after standardisation, when the rating for variant v´ is higher than the rating for variant v, and the difference between the maximum and the minimum components of the matrix W: QUOTE QUOTE nvv,=1dmaxv,f:wv,f>wvfwv,f-wvf (5)where: d – the difference between components of the highest and the least value in matrix W of ratings after standardisation, given by the formula: QUOTE QUOTE d=maxv,f∈V×Fwvf-minv,f∈V×Fwvf (6)Much the same as the compliance rate, the incompliance rate has values ranging within [0,1]. Its value is highest in the case, when ratings for variant v´ for all criteria f are higher than ratings for variant v. It is the other way round when the incompliance rate is zero. Therefore, the incompliance matrix N has the following form: QUOTE (7)An important stage of the MAJA method is the determination of the compliance threshold pz and the incompliance threshold pn, needed to select the best variant from the set V. The compliance and the incompliance threshold values range within [0, 1] and are used to choose these vehicle selection variants v, which satisfy the criteria specified by both thresholds. Depending on the needs, the compliance and the incompliance threshold values can be reduced and/or increased, while the compliance threshold pz should range within [0.5; 1] and the incompliance threshold pn - within [0; 0.5].Comparison of the selection variants from the set of variants according to partial criteria and threshold values pz and pn indicates that the variant v is better than variant v´ only if pair (v, v´) meets the following condition: QUOTE ˄ QUOTE (8)This is the basis for developing the binary domination matrix D QUOTE