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Fuzzy Comprehensive Evaluation of Mechanical Equipment Selection Plans Author: Guangdong Nengda Highway Maintenance Company, Zou Zhiyong, Chen Lianbing Abstract: This paper analyzes the various factors that need to be considered in the selection of mechanical equipment. On this basis, an evaluation index system for such selections is established, and a fuzzy comprehensive evaluation model for mechanical equipment selection plans is proposed. Finally, specific examples are provided to illustrate the evaluation process. Keywords: Equipment selection, Fuzzy comprehensive evaluation, AHP. In today’s highly developed market economy, with a large number of machinery manufacturers, complex product ranges, varying technical qualities and performance levels, as well as diverse operational requirements, it has become a new challenge for enterprise equipment managers to accurately and promptly select mechanical equipment that meets production requirements and boasts advanced technical specifications for use in construction projects. This is also a indicator of the level of construction companies. It is evident that proper selection and matching of mechanical equipment are important tasks in equipment management. The selection of equipment is a multi-objective decision-making problem, and the evaluation of alternatives involves numerous factors, including both quantitative factors (such as price) and qualitative factors (such as reliability in use). The diversity and uncertainty of factors make the selection of equipment complex and important. Traditional empirical selection methods lack thorough qualitative analysis as well as theories and methods for comparison; they are unable to take into account the preferences of multiple people. This inevitably leads to inadequate evaluation of options, and in some cases, the best option may even be discarded. Therefore, it is highly necessary to establish an effective comprehensive evaluation method for equipment selection, in order to achieve a transition from traditional experience-based selection to scientific selection. 1 Index system involved in the selection of mechanical equipment. To evaluate the quality of a chosen solution, it is first necessary to have a correct and comprehensive evaluation system along with appropriate evaluation indicators. When selecting mechanical equipment, various factors must be taken into full consideration. This article proposes to conduct a comprehensive evaluation from five aspects: economic indicators, technical performance, social aspects, the relationship between humans and machines, and compatibility, in order to carry out a thorough comparative analysis of different selection options and identify the best one. The evaluation index system is shown in Figure 1. 1.1 Factors affecting economic indicators: Pre-investment expenses: In addition to the costs associated with equipment installation and relocation, there are also early investments required for the operation of the equipment, such as hiring and training relevant personnel, as well as registering, calibrating, and certifying the equipment. Equipment shift cost: operating shift cost and downtime shift cost. Additional operating costs: During the normal operation of the equipment, the costs associated with that equipment that arise in addition to the hourly rate, such as maintenance and minor repair expenses. Installation and relocation costs: the total of the costs for bringing the equipment in and installing it, plus the costs for removing it and clearing the site. Price and payment terms: The price of the equipment and the payment terms are often key factors that small and medium-sized enterprises with limited financial resources need to consider, as they directly affect the continuity of the project. 1.2 Factors Affecting Technical Specifications – Reliability in use: This is one of the most important factors in evaluating the technical performance of equipment. At present, there are no unified requirements in our country regarding the reliability of use for road construction and maintenance machinery. Foreign construction machinery is generally required to be able to operate continuously for 1,500 to 2,000 hours after leaving the factory without experiencing mechanical failures. According to the reliability requirements for mechanical equipment set by most manufacturers, it is advisable that the continuous operating time of such machinery in China be guaranteed to be between 1,000 hours and 1,500 hours without failures. Due to the harsh operating conditions of road construction and maintenance machinery, its reliability in operation is more important than the technical sophistication of the machinery itself. Manufacturing process: The manufacturing process is an important prerequisite for ensuring the reliable operation of equipment; it reflects and measures the technical and managerial capabilities of the manufacturer. Productivity: Productivity fully reflects the capability of the equipment fleet to work together, as well as the performance of the equipment. Degree of automation: The level of automation is a fundamental indicator that reflects the technical capability of a device; it refers to the extent to which automated control techniques are utilized in operations and quality control tasks that cannot be carried out manually. The level of automatic control in mechanical equipment is a direct reflection of the technological development level of an entire manufacturing enterprise. Maintainability: Here, maintainability refers to the accessibility for repairs and maintenance, the interchangeability of spare parts, as well as error-prevention designs for repairs. It is achieved through scientific and rational design along with excellent manufacturing processes. During the execution of a project, in order to improve the utilization rate of machinery, it is often necessary to be able to address mechanical failures on-site. This requires that the machinery be easy to disassemble and assemble, that spare parts be readily available and highly interchangeable, and that there be specialized tools designed for repairing specific parts. The ease of maintenance of a device directly reflects the design quality and manufacturing process capabilities of a manufacturing enterprise. 1.3 Factors related to social relationships: Source of goods and supply channels: In the case of leasing, this refers to the channels through which the equipment is leased; in the case of purchase, it refers to the equipment dealers or manufacturers. Differences in sources of supply and distribution channels directly affect the price (rental cost) of the equipment as well as after-sales service. Delivery or lead time: In principle, the shorter the period, the better. However, for equipment that is selected or ordered, it is necessary to ensure that the manufacturer has enough time for production, without compromising the overall project schedule, in order to avoid rushed work that could affect the quality of the equipment manufacturing. Transportation methods and requirements: Different transportation methods entail different costs as well as varying risks associated with shipping. The indicator of whether there are any special requirements for transportation also reflects the design level of manufacturing enterprises. After-sales service: The term after-sales service here is used in a general sense; it includes professional technical training, supply of spare parts, technical inspections, as well as equipment maintenance. Supply of repair parts: This item originally falls under after-sales service, but it is listed separately due to its importance. The supply of repair parts here refers not only to the provision of parts as part of after-sales service, but also to the ease with which repair parts can be obtained outside of after-sales service agencies. Degree of environmental pollution: The degree of environmental pollution mentioned here is also a general term, referring to the impact of equipment installation and operation on the surrounding environment. 1.4 Factors Related to the Human-Machine Relationship: Operational Safety: Operational safety refers to the degree of sophistication of the safety protection devices in the equipment. Operational comfort: Comfort refers to the operating conditions for the pilot. Good operating conditions mean that the machinery provides a comfortable seating environment, a wide field of vision, and air conditioning and ventilation systems. For road construction and maintenance machinery, due to its harsh operating conditions, high mobility, and frequent use, drivers tend to get fatigued, which can lead to operational errors and accidents. Therefore, good handling conditions should be considered an important factor in improving work efficiency and reducing accidents. Related supporting personnel: This indicator also reflects the operability and degree of automation of the equipment. 1.5 Factors Affecting Equipment Compatibility Project compatibility refers to the suitability of the equipment being introduced for this project. Fleet compatibility: refers to the degree of compatibility between the new equipment introduced and the existing equipment in a project, as well as the impact it has on that existing equipment. 2 Selection of evaluation methods As can be seen from the evaluation index system for machinery and equipment selection analyzed above, the evaluation of equipment selection options involves multiple indicators. It is necessary to take into account various factors such as technical performance, economic aspects, social considerations, the relationship between humans and machines, as well as compatibility, in order to conduct a comprehensive analysis and comparison and thus find the overall optimal solution. When evaluating solutions, the presence of multiple objectives leads to a large number of factors that need to be taken into consideration. Some of these factors are quantifiable, while others are not. Evaluating these non-quantifiable factors involves a degree of ambiguity, making it impossible to provide a qualitative assessment; this adds considerable difficulty to the evaluation process. Clearly, conventional evaluation methods, namely classical mathematical approaches, are inadequate for this task. For the above reasons, drawing on relevant literature and combining traditional experience-based selection methods with modern mathematical theories such as fuzzy mathematics, AHP (Analytic Hierarchy Process), and mathematical statistics, this paper adopts a multi-level, multi-factor fuzzy comprehensive evaluation method to conduct a comprehensive analysis, evaluation, and optimal selection of the available options. This method is based on Professor T.L. Sauty’s AHP approach, but uses an improved version of AHP to determine the degree of membership for various factors. It addresses the issue of many qualitative factors being unable to be quantified; different descriptions of those uncertain factors are provided by experts, who then conduct a comprehensive evaluation in order to avoid making absolute judgments. 3 Overview of the fuzzy comprehensive evaluation method: Based on the theories of fuzzy mathematics, the mathematical model for fuzzy comprehensive evaluation consists of three elements: the factor set U, the evaluation set V, and the evaluation matrix R. First, determine the factor set U = (u1, u2, …, ui, …, un), where ui represents the i-th factor that has an impact on the object under evaluation ； Next, determine the evaluation set V=(v1,v2,…,vk,…,vp), where vk represents the score for the kth level of evaluation for that factor. If the single-factor evaluation for the i-th factor is a fuzzy relation on U to V: R(ri1,ri2,…,rip), then the evaluation matrix for n factors is R=(rik)n×p. By determining the weights A = (a1, a2, …, ai, …, an), where ai is the weight corresponding to the i-th factor. Finally, the comprehensive evaluation result B = A·R = (b1, b2, …, bp) is obtained. Based on B and the evaluation set V, scores are calculated for each option, and the option with the highest score is identified as the optimal one. 3.1 Determination of the factor set, criterion set, and object set of evaluation. The factor set U = (u1, u2, …, ui, …, un), where ui represents the i-th factor that has an impact on the object under evaluation; ui can be further divided into multiple factors uij, and so on, thereby enabling the creation of a multi-level, multi-factor set. The set of ratings V = (v1, v2, …, vk, …, vp), where vk represents the k-th level of evaluation for a factor. Both U and V are given finite domains. 3.2 Construction of comparison matrices among factors According to the principles of the Analytic Hierarchy Process (AHP), it is necessary to compare each pair of factors at various levels in order to determine their relative importance. Each expert must conduct pairwise comparisons of the relative importance of the relevant factors, starting from the top level down to the bottom level; the factors compared must be from the same level and must belong to the same indicator at the higher level. This process yields a series of comparison matrices. The relative importance of various factors can be quantified using scaling methods; referring to the literature, this paper adopts the exponential scaling method shown in Table 1. Let the expert group be S = (s1, s2, …, ss) (s ≥ 1). Each expert Sk in group S compares the factors ui and uj, quantifies them according to Table 1, to obtain a comparison matrix; here, i, j = 1, 2, …, n. Clearly, A(k) is an involution matrix, and therefore an antisymmetric matrix. According to the literature, when the overall standard deviation of expert evaluations is less than 1, it can be assumed that the opinions of the experts are relatively consistent; in such cases, the arithmetic average of the individual experts’ judgments can be used as the result of the group judgment. However, this result may not necessarily be consistent, and therefore a group judgment matrix can be constructed. It is known from the literature that matrix A* is a quasi-optimal transfer matrix of A (the arithmetic mean matrix of Ak), and it is consistent. When such differences exist, it indicates that there is significant disagreement among the experts; in such cases, it is not possible to simply use the mathematical average of the individual experts’ judgments to construct a group judgment matrix. According to literature, the optimal transfer matrix method can be used for this purpose, that is, finding the optimal transfer matrix that minimizes a certain value. Here, α represents the objective importance ratio between two adjacent levels of evaluation, and values of 1.3161 or 1.7321 can be used for this purpose. Matrix A* is then the desired group comparison judgment matrix, and it is consistent. Based on the obtained group judgment matrix, we can use the square root method to determine the weights of each indicator. After normalization, the standard weights of these indicators relative to the higher-level goal layer can be obtained; subsequently, the overall hierarchical sorting allows us to determine the standard weight of the lowest level with respect to the overall goal layer. 3.3 Comprehensive Evaluation: Create an evaluation form, organize a \"expert group\" to conduct investigations, and perform an independent assessment of the existing equipment selection options; then fill in the evaluation results in the form. The format of the evaluation table is shown in Table 2: Based on the survey form, an evaluation matrix for the secondary factor set with respect to the primary factors can be obtained, where i=1,2,∧,n, j=1,2,∧,m, k=1,2,∧,p; rijk represents the degree of membership of factor Uij with respect to the k-th evaluation level in the aforementioned evaluation set V. Thus, there is a comprehensive evaluation matrix R for the set of primary factors with respect to the overall goal (the equipment selection plan): finally, the comprehensive evaluation result B is obtained as B = A·R = (b1, b2, …, bp). On a percentage scale, let the evaluation set V = {Good, Fair, Average, Poor} = {100–85, 85–75, 75–60,