Grey Relational Analysis Method for Multiple Attribute Decision Making in Intuitionistic Fuzzy Setting

In this paper, the concept of multiple-attribute group decision-making (MAGDM) problems with interval-valued Pythagorean fuzzy information is developed, in which the attribute values are interval-valued Pythagorean fuzzy numbers and the information about the attribute weight is incomplete. Since the concept of interval-valued Pythagorean fuzzy sets is the generalization of interval-valued intuitionistic fuzzy set. Thus, due the this motivation in this paper, the concept of interval-valued Pythagorean fuzzy Choquet integral average (IVPFCIA) operator is introduced by generalizing the concept of interval-valued intuitionistic fuzzy Choquet integral average operator. To illustrate the developed operator, a numerical example is also investigated. Extended the concept of traditional GRA method, a new extension of GRA method based on interval-valued Pythagorean fuzzy information is introduced. First, utilize IVPFCIA operator to aggregate all the interval-valued Pythagorean fuzzy decision matrices. Then, an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method is established, to get the weight vector of the attributes. Based on the traditional GRA method, calculation steps for solving interval-valued Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. To determine the ranking order of all alternatives, a relative relational degree is defined by calculating the degree of grey relation to both the positive-ideal solution and negative ideal solution simultaneously. Finally, to illustrate the developed approach a numerical example is to demonstrate its practicality and effectiveness.

The aim of this paper is to investigate the multiple attribute decision making problems with interval-valued intuitionistic fuzzy information, in which the information about attribute weights is completely known, and the attribute values take the form of interval-valued intuitionistic fuzzy numbers. A modified grey relational analysis (GRA) method is proposed. Then, based on the traditional GRA method, calculation steps for solving interval-valued intuitionistic fuzzy multiple attribute decision-making problems with known weight information are given. The degree of grey relation between every alternative and positive ideal solution and negative ideal solution are calculated. Then, according to the concept of the GRA, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of grey relation to both the positive-ideal solution (PIS) and negative-ideal solution (NIS) simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

With the increasingly fierce competition in the market, the virtual enterprises are becoming a realistic choice of enterprises. As a new business mode, the virtual enterprises bring tremendous opportunities to improve the competitiveness of enterprises to a certain degree. However, without enough practical and proper theoretical experience, the failure probability of virtual enterprises is high. The virtual enterprises have certain advantages, but the complexity of their organization makes the uncertainties increasing, the risk analysis control is difficult and the risk management is complex. In order to achieve smooth operation and expected profits, the virtual enterprises must succeed to avoid the risks. Therefore, the risk management for virtual enterprises is significant in theoretical and practical research. In this paper, we investigate the 2-tuple linguistic multiple attribute group decision making problems with incomplete weight information, some basic concepts and operational laws of 2-tuple linguistic variables are introduced. A model based on the entropy weight method, by which the attribute weights can be determined, is established. According to the traditional ideas of grey relational analysis (GRA), the optimal alternative(s) is determined by calculating the linguistic degree of grey relation of every alternative and 2-tuple linguistic positive ideal solution and 2-tuple linguistic negative ideal solution. It is based on the concept that the optimal alternative should have the largest degree of grey relation from positive ideal solution and the smallest degree of grey relation from the negative ideal solution. Finally, an illustrative example for evaluating the virtual enterprise's risk is given to verify the developed approach and to demonstrate its practicality and effectiveness.

The software development life cycle (SDLC) encompasses diverse aspects, including design, requirements, methodologies, programming languages, tools, frameworks, and user interface design. Effective interoperability and integration among these components are crucial for streamlining workflows, mitigating compatibility issues, and delivering robust software solutions. This study employs the Grey Relational Analysis (GRA) method to evaluate the interoperability and relative importance of these SDLC elements in software development endeavors. The analysis reveals that fostering seamless collaboration among design, requirements, methodologies, languages, tools, and frameworks is essential for optimizing development processes and enhancing overall efficiency and effectiveness. The normalized data highlight the varying degrees of influence each component exerts across different SDLC phases, underscoring the need to recognize and leverage these interdependencies. The deviation sequence, obtained through the GRA method, unveils the relative importance or effectiveness of various elements, providing insights for informed decision-making and identifying areas for potential improvement or optimization. Furthermore, the Grey Relation Coefficient quantifies the correlations between different facets of software development, enabling stakeholders to prioritize areas for improvement and focus attention on elements with the most substantial influence. Notably, the final Grey Relational Grade (GRG) Rank reveals that testing frameworks secured the top rank, suggesting their significant impact on overall development quality, followed by programming languages and user interface design. These rankings offer valuable insights for prioritizing efforts and allocating resources, ultimately enhancing development processes and achieving better project outcomes. The study underscores the importance of a holistic and integrated approach to software development, recognizing the interdependencies among various components and leveraging the insights derived from the GRA method. By embracing this approach, software teams can make informed decisions, streamline workflows, and deliver high-quality, user-centric solutions that meet industry standards and drive success in an increasingly competitive digital landscape.

This paper develops a new Fuzzy Grey Multi-Criteria Group Decision Making (FG-MCGDM) model to solve evaluation and selection problems under uncertainty in real-life situations. The proposed model is based on a hybridization of fuzzy sets theory, Grey Relational Analysis (GRA) and compromise solution method. First, linguistic variables are employed to assess performance ratings of alternatives and weights of criteria represented in trapezoidal fuzzy numbers. Then, a new version of the GRA is introduced to solve group decision making problems with conventional fuzzy information, in which correlations are captured between the reference/aspiration-level criteria and alternatives. Consequently, a new ranking index is presented based on the concept of the compromise solution to obtain the ranking order of all alternatives. The solution is determined in terms of several conflicting criteria by considering the degree of grey relation to both the positive-ideal and negative-ideal solutions concurrently. Finally, an illustrative example is provided to verify the FG-MCGDM model and to demonstrate its suitability in manufacturing systems.

This paper describes the important significance of cutting-edge technology in the machining of polycrystalline diamond (PCD) cutting inserts by comparing the evaluation criteria. The LASER technology of cutting-edge machining is compared with grinding and electrical discharge machining (EDM) technologies. To evaluate the data from the experiments, the Grey Relational Analysis (GRA) method was used to optimize the input factors of turning to achieve the required output parameters, namely the deviation of roundness and chip cross-section. The input factors of cutting speed, feed rate, depth of cut and corner radius were applied in the experiment for three different levels (minimum, medium and maximum). The optimal input factors for turning of aluminum alloy (AW 5083) were determined for the factorial plan according to Grey Relational Grade based on the GRA method for the multi-criteria of the output parameters. The results were confirmed by a verification test according to the GRA method and optimal values of input factors were recommended for the machining of Al-alloy (AW 5083) products. This material is currently being developed by engineers for forming selected components for the automotive and railway industries, mainly to reduce weight and energy costs. The best values of the output parameters were obtained at a cutting speed of 870 m/min, feed rate of 0.1 mm/min, depth of cut of 0.5 mm and a corner radius of 1.2 mm.

Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making

In this paper, a decision support methodology for multiple attributes group decision making problem is developed. The proposed methodologies are based on Data Envelopment Analysis (DEA), Grey Relation analysis (GRA) and hybrid GRA-DEA methods. These methods are implemented for evaluation and ranking of organizations in sustainable perspective. In the proposed methods, the payoff values of alternatives are expressed in linguistic terms, given by the decision makers. Then, these linguistic terms are described by triangular fuzzy numbers. Charnes model of DEA is formulated in fuzzy environment to determine efficiencies of DMUs. Following the GRA method’s algorithm, a relative closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distances to the fuzzy positive-ideal solution (FPIS), as well as to the fuzzy negative-ideal solution (FNIS). Also, performance evaluation of these companies is made through hybrid GRA-DEA in fuzzy environment. The weights of the criteria are determined objectively during evaluation of these companies in the proposed GRA and DEA-GRA methods. Comparison of proposed approaches is made and final ranking of the organizations is sustainable perspective is arrived. The proposed methodologies are illustrated with a case study of five steel manufacturing companies in India.

In recent years, cultural and creative industry park is becoming a kind of hot industry to promote industrial restructuring and to improve the quality of urban space. For this reason, cultural and creative industrial parks are planning to build across the country. Currently, cultural and creative industrial parks that develop better than others thank to the government’s overall planning, construction, marketing, and management. At the same time, the new cultural and creative industry parks face enormous challenges, such as how to have together the cultural and creative industries and related groups or how to have area cultural creativity. And it is frequently regarded as a multiattribute group decision-making (MAGDM) process. Thus, a novel MAGDM process is needed to tackle it. Depending on the conventional grey relational analysis (GRA) method and intuitionistic fuzzy sets (IFSs), this paper designs a novel intuitive distance-based IF-GRA method for development potentiality evaluation of cultural and creative garden. First of all, some necessary theories related to IFSs are briefly reviewed. In addition, since subjective randomness frequently exists in determining criteria weights, the weights of criteria are decided objectively by utilizing the CRITIC method. Afterwards, relying on novel distance measures between IFSs, the GRA method is extended to the IFSs to calculate assessment score of each alternative. Eventually, an application about development potentiality evaluation of cultural and creative garden and some comparative analysis is given. The results think that the designed method is useful for development potentiality evaluation of cultural and creative garden.

Hot water storage in the insulated tank is an effective method of energy storage and also fills the permanent and intermittent domestic need for hot water. In this study, an insulated water tank with 29 litres capacity is developed, and its energy storage performance is analysed through numerical simulation method. Silica gel and Polyurethane are the insulation materials attached to the concrete tank. This water tank is optimised for minimum cost and temperature loss using grey relation analysis (GRA) and response surface method (RSM). The thickness of concrete, polyurethane and silica gel layer are the considered control parameters. The best value obtained from the two optimisation methods are compared, and from GRA method, thickness of concrete, polyurethane and silica gel are identified as 7.5cm, 0.25cm and 0.25cm, respectively. Finally, from the confirmation test, the temperature loss in 24 hours is predicted as 6.29°C with a minimum material cost for the tank as 5914 INR.

The selection of the most appropriated external technological acquisition mode for a specific technological innovation is one of the important strategic decision-makings. To solve the complicated decision making problem, this study aims (i) to identify the multi-attribute criteria which influenced the selection of the external technological innovation acquisition mode and (ii) to illustrate the comprehensive proposed model by applying Multi-Criteria Decision Making (MCDM) approach, which was combined of Analytic hierarchy process (AHP) and Grey Relational Analysis (GRA) methods. The result can provide the prioritization of the relative important weight of criteria and the final ranking of alternative. This study is expected to effectively assist the managements or the decision-makers to choose the best appropriated alternatives which matched with their business objectives. A study case for the Thai technology-based firm was also applied in this article. KeywordsAnalytic hierarchy process, External technological innovation acquisition mode, Grey relational analysis, Multi-criteria decision-making method.

Multi-objective optimisation of ionic liquid parameters for hydrogen compressors by Taguchi and grey relational analysis methods

Decision making remains a prominent issue in all the problem domains. To make better decisions, multiple factors of the given problem need to be considered and evaluated. Multi-criteria decision-making methods have been used popularly for solving decision-making problems characterized by multiple factors. When multiple factors are considered, it is recommended to categorize the factors into the main criteria and sub-criteria. In this paper, GRAP-an integrated ranking algorithm has been developed by combining Grey Relational Analysis, Rank Sum, and Preference Ranking Organization Method Enrichment Evaluation methods (PROMETHEE) to solve decision-making problems. The weights of the sub-criteria are calculated using the Rank Sum method. Grey Relational Analysis method is used to convert the sub-criteria values into main criteria values in the form of evaluation scores of alternatives. The final ranking scores of the alternatives are obtained using the PROMETHEE method. A decision model is developed using the proposed GRAP algorithm and applied to the Job Profile selection case study. The developed decision model showed much better results compared to other MCDM approaches namely the Simple Additive Weight method, TOPSIS, VIKOR, and Complex Proportional Assessment (COPRAS). Further, a sanity check has been carried out by comparing the results of the decision model with experts’ opinions.

Security evaluation has become a hot topic in the research field of water resource management. In this paper, we established a novel water resource security indicator system based on the Pressure-Status-Response (PSR) framework using gray relation analysis (GRA) and technique for order preference by similarity to ideal solution (TOPSIS). A case study of Beijing from 1996 to 2007 was conducted to verify the evaluation system. Results showed that the gray relative closeness degrees of water resource security to the positive ideal solution were low, with the least one of 0.360 in 1999 and the largest one of 0.527 in 2007, implying that Beijing was facing severer challenges with water resources during the concerned time. Also, the analysis of water resource security indicated that the pressure of water resource was constantly increasing. Finally, factor analysis was employed to calculate the gray relation degrees of evaluating indices with the ideal solutions so as to reveal the relativity of water resource security of Beijing, which may contribute to a better understanding of the urban water resource management and regulation.

Radial distribution system is an important link connecting power supply and users, and its power supply reliability is directly related to users. Radial distribution network reconfiguration can transform the network structure by changing the switching state of the distribution network lines, and achieve the goals of reducing network operational losses, improving power quality, and power supply reliability while meeting various constraints such as radial operation, power supply and demand balance, capacity, and voltage. Radial distribution systems have the characteristics of multiple components and complex structures. How to quickly and accurately evaluate the health performance of radial distribution systems and find an optimal solution for network reconfiguration are important issues in distribution network analysis. The network health performance evaluation of radial distribution system is classical multiple attributes group decision making (MAGDM). The probabilistic hesitancy fuzzy sets (PHFSs) are used as a tool for characterizing uncertain information during the network health performance evaluation of radial distribution system. In this paper, we extend the classical grey relational analysis (GRA) method to the probabilistic hesitancy fuzzy MAGDM with unknown weight information. Firstly, the basic concept, comparative formula and Hamming distance of PHFSs are briefly introduced. Then, the definition of the score values is employed to compute the attribute weights based on the information entropy method. Then, probabilistic hesitancy fuzzy GRA (PHF-GRA) method is built for MAGDM under PHFSs. Finally, a practical case study for network health performance evaluation of radial distribution system is designed to validate the proposed method and some comparative studies are also designed to verify the applicability.