Linear Assignment Model Research Articles

Spherical fuzzy analytic hierarchy process and linear assignment model based MCGDM method with its application in ranking of states for their business climate

Ranking of the states for business climate is often done by survey analysis and hence prejudiced by untrustworthy and instable responses of the participants. In the present study, we integrate spherical fuzzy set (SFS) and linear assignment model (LAM) with analytic hierarchy process (AHP) to develop a multi criteria group decision making (MCGDM) method to rank Indian states for their business climate and potential index. The proposed MCGDM method is developed using state investment potential index (SIPI) published by the National Council of Applied Economic Research (NCAER), New Delhi to analyse the 'ease of doing business' aspects of various states based on six parameters. We take these six parameters, sub parameters as criteria and sub criteria in proposed MCGDM method and find their global weight using AHP method. Advantages of the proposed method are that it uses SFSs which are more efficient than other extensions of fuzzy sets in handling non-determinacy, and applies LAM to avoid subjectivity in the preferences of decision makers. We also do the sensitivity analysis of the ranking by changing the weights of the criteria and sub criteria to confirm the robustness of the proposed MCGDM method.

Ranking Sub-Watersheds for Flood Hazard Mapping: A Multi-Criteria Decision-Making Approach

The aim of this paper is to assess the extent to which the Sad-Kalan watershed in Iran participates in floods and rank the Sad-Kalan sub-watersheds in terms of flooding potential by utilizing multi-criteria decision-making approaches. We employed the entropy of a drainage network, stream power index (SPI), slope, topographic control index (TCI), and compactness coefficient (Cc) in this investigation. After forming a decision matrix with 25 possibilities (sub-watersheds) and 5 evaluation indices, we used four MCDM approaches, including the analytic hierarchy process (AHP), best–worst method (BWM), interval rough numbers AHP (IRNAHP), picture fuzzy with AHP (PF-AHP), and picture fuzzy with linear assignment model (PF-LAM, hereafter PICALAM) algorithms, to rank the sub-watersheds. The study results demonstrated that PICALAM exhibited superior performance compared to the other methods due to its consideration of both local and global weights for each criterion. Additionally, among the methods used (AHP, BWM, and IRNAHP) that showed similar performances in ranking the sub-watersheds, the BWM method proved to be more time-efficient in the ranking process.

Topological structures on cubic bipolar fuzzy sets with linear assignment model and SIR method for healthcare

The idea of a cubic bipolar fuzzy set (CBFS) is a new hybrid extension of the cubic set (CS) and the bipolar fuzzy set (BFS). A CBFS is a strong model to deal with bipolarity and fuzziness in terms of positive membership grades (PMGs) and negative membership grades (NMGs). A positive interval and a positive numbers represent a PMG to express the degree of belongingness of a specific property, and a negative interval and a negative number represent a NMG which defines the degree of non-belongingness of the specific property (or satisfaction level of its counter property). The aim of this paper is to define the cubic bipolar fuzzy topology under P-order (CBFSP topology) as well as the cubic bipolar fuzzy topology under R-order (CBFSR topology). We investigate certain properties and results of CBFSP topology and CBFSR topology. Topological structures on CBFSs are helping in the development of new artificial intelligence (AI) techniques for healthcare domain strategies and investigating various critical diseases. Such techniques allow for the early detection and investigation of diseases, assisting clinicians in minimizing the possible risk factors. An extended linear assignment model (LAM) and superiority and inferiority ranking method (SIR method) are proposed for healthcare diagnosis based on newly developed structures. The proposed LAM and SIR method are successfully applied for investigation of critical diseases. Moreover, we discuss a comparison analysis of investigations made by suggested techniques with some existing approaches.

Topological Data Analysis of m-Polar Spherical Fuzzy Information with LAM and SIR Models

The concept of m-polar spherical fuzzy sets (mPSFS) is a combination of m-polar fuzzy sets (mPFS) and spherical fuzzy sets (SFS). An mPSFS is an optimal strategy for addressing multipolarity and fuzziness in terms of ordered triples of positive membership grades (PMGs), negative membership grades (NMGs), and neutral grades (NGs). In this study, the innovative concept of m-polar spherical fuzzy topology (mPSF-topology) is proposed for data analysis and information aggregation. We look into the characteristics and results of mPSF-topology with the help of several examples. Topological structures on mPSFSs help with both the development of new artificial intelligence (AI) tools for different domain strategies and the study of different kinds of uncertainty in everyday life problems. These strategies make it possible to recognise and look into a situation early on, which helps professionals to reduce certain risks. In order to address various group decision-making issues in the m-polar spherical fuzzy domain, one suggestion has been to apply an extended linear assignment model (LAM) along with the SIR method known as superiority and inferiority ranking methodology in order to analyze road accident issues and dispute resolution. In addition, we examine the symmetry of optimal decision and perform a comparative study between the research carried out using the suggested methodology and several existing methods.

Prioritization of watersheds based on a picture fuzzy analytic hierarchy process and linear assignment model

Prioritization of watersheds based on a picture fuzzy analytic hierarchy process and linear assignment model

Ranking cities based on their smartness level using MADM methods

Urbanization and its consequent problems are urging cities to become smarter. Developing smart cities calls for a suitable while comprehensive assessment framework to assist city planners and decision-makers to suggest future directions for cities on how to become smarter by evaluating the smartness of cities. In this regard, this study follows two primary purposes. First, we investigate the concept of “smart city” and its pillars. Second, we develop a smartness assessment framework by considering both subjective and objective criteria and employing six effective multi-attribute decision making (MADM) methods. A linear assignment model is formulated to find an aggregated ranking vector using the ranking vectors obtained from these MADM methods. Then, as a case study, five out of the most important cities in Iran are compared and evaluated by adopting the proposed framework. Furthermore, different scenarios are introduced to investigate the sensitivity of results to the distribution of the importance weights amongst criteria. The results demonstrate the significance of the governmental, economic, and environmental indicators in evaluating the smartness of cities. Moreover, Tehran, the capital city of Iran, obtains the best ranking in all the methods and weighting scenarios, while Tabriz has the worst ranking among the cities under study.

A Novel Spherical Fuzzy Bi-Objective Linear Assignment Method and Its Application to Insurance Options Selection

Spherical fuzzy sets are the latest extension of the ordinary fuzzy sets. The main characteristic of the spherical fuzzy sets is satisfying the condition that the squared sum of the membership, nonmembership, and hesitancy degrees must be at least zero and at most one. In this research, by extending the classical linear assignment method to bi-objective linear assignment and integrating it with cosine similarity measure, we presented a novel beneficial method for solving multiple criteria group decision-making problems in the spherical fuzzy environment. A new concept for weighting the criteria, which is composed of positive and negative impacts (weights), is introduced. The proposed bi-objective model tries to maximize positive impacts and minimize the negative impacts simultaneously. In order to solve the bi-objective linear assignment model, [Formula: see text]-constraint method is applied. Therefore, a trade-off solution is formed between maximizing positive impacts and minimizing negative impacts. The applicability and validity of the proposed method are shown through an insurance options selection problem. To test the reliability and validity of the proposed method, comparative and sensitivity analysis are performed.

Evaluating public transport service quality using picture fuzzy analytic hierarchy process and linear assignment model

Group decision-making on a public service problem is often biased by untrustworthy responses of the participants, which affects negatively the outcome of the procedure. To eliminate this problem, the state-of-the-art methodologies apply fuzzy sets, generally within the frames of hybrid methodologies. The objective of the recent paper is to introduce a new hybrid model based on picture fuzzy sets and linear assignment and its first real-world application on a public transport development problem. The advantage of the proposed methodology is that it simultaneously considers the indeterminacy level of respondent evaluations on decision alternatives, and applies linear assignment to avoid subjectivity in responses. With the aim of testing the reliability of the new methodology, the results are compared with the generally applied intuitionistic fuzzy Technique of Order Preference Similarity to the Ideal Solution model. The comparative results have shown that the final outcomes of the proposed method are very similar to the well-proven reference technique, thus the hybrid picture fuzzy AHP-linear assignment model has been validated.

Spherical Fuzzy Linear Assignment Method for Multiple Criteria Group Decision-Making Problems

Spherical fuzzy sets theory is useful and advantageous for handling uncertainty and imprecision in multiple attribute decision-making problems by considering membership, non-membership, and indeterminacy degrees. In this paper, by extending the classical linear assignment method, we propose a novel method called the spherical fuzzy linear assignment method (SF-LAM) to solve multiple criteria group decision-making problems in the spherical fuzzy environment. A ranking procedure consisting of aggregation functions, score functions, accuracy functions, weighted rank frequency, and a binary mathematical model are presented to determine the criterion-wise preferences and various alternatives’ priority order. The proposed method’s applicability and validity are shown through the selection problem among wind power farm locations. The proposed method helps managers to find the best location to construct the wind power plant based on the determined criteria. Finally, a comparative analysis is performed between the proposed spherical fuzzy linear assignment (SF-LAM) model and the spherical fuzzy analytic hierarchy process (SF-AHP) and spherical fuzzy WASPAS methods.

SOLVING CONSTRUCTION PROJECT SELECTION PROBLEM BY A NEW UNCERTAIN WEIGHTING AND RANKING BASED ON COMPROMISE SOLUTION WITH LINEAR ASSIGNMENT APPROACH

Selecting a suitable construction project is a significant issue for contractors to decrease their costs. In real cases, the imprecise and uncertain information lead to decisions made based on vagueness. Fuzzy sets theory could help decision makers (DMs) to address incomplete information. However, this article develops a new integrated multi-criteria group decision-making model based on compromise solution and linear assignment approaches with interval-valued intuitionistic fuzzy sets (IVIFSs). IVIFSs by presenting a membership and non-membership degree for each candidate based on appraisement criteria could decrease the vagueness of selection decisions. The proposed algorithm involves a new decision process under uncertain conditions to determine the importance of criteria and DMs, separately. In this regard, no subjective or additional information is needed for this process; only the input information required is an alternative assessment matric. In this approach, weights of criteria and DMs are specified based on novel indexes to increase the reliability of obtained results. In this respect, the criteria’ weights are computed regarding entropy concepts. The basis for calculating the weight of each DM is the distance between each DM and an average of the DMs’ community. Furthermore, the linear assignment model is extended to rank the candidates. A case study about the construction project selection problem (CPSP) is illustrated to indicate the application of proposed model.

A Method for Multicriteria Group Decision Making with Different Evaluation Criterion Sets

Multicriteria group decision making (MCGDM) with different evaluation criterion sets is a special kind of MCGDM problem, where criterion sets considered by multiple experts may be different, while research concerning this issue is still relatively scarce. The objective of this paper is to develop a method for MCGDM with different evaluation criterion sets. In the method, according to different criterion sets, several criterion subsets are first constructed, where each criterion subset includes the criteria concerned by the same group of experts. Then, with respect to each criterion subset, a ranking of alternatives is determined by normalizing the decision matrix and calculating the ranking value of each alternative with respect to the criterion subset. Next, according to the ranking of alternatives with respect to each criterion subset, a ranking possibility matrix of alternatives with respect to the criterion subset is constructed. Further, the weight of each criterion subset is determined according to weights of the experts and weights of the criteria in the criterion subset. Moreover, an overall ranking possibility matrix is constructed by aggregating the ranking possibility matrices and weights concerning different criterion subsets, and the final ranking result of alternatives is determined by solving a linear assignment model, where the elements in the overall ranking possibility matrix are regarded as the benefits on assigning each alternative into different ranking positions. Finally, a numerical example is given to illustrate the use of the proposed method.

Graph edit distance as a quadratic assignment problem

The Graph Edit Distance (GED) is a flexible measure of dissimilarity between graphs which arises in error-correcting graph matching. It is defined from an optimal sequence of edit operations (edit path) transforming one graph into another. Unfortunately, the exact computation of this measure is NP-hard. In the last decade, several approaches were proposed to approximate the GED in polynomial time, mainly by solving linear programming problems. Among them, the bipartite GED received much attention. It is deduced from a linear sum assignment of the nodes of the two graphs, which can be efficiently computed by Hungarian-type algorithms. However, edit operations on nodes and edges are not handled simultaneously, which limits the accuracy of the approximation. To overcome this limitation, we propose to extend the linear assignment model to a quadratic one. This is achieved through the definition of a family of edit paths induced by assignments between nodes. We formally show that the GED, restricted to the paths in this family, is equivalent to a quadratic assignment problem. Since this problem is NP-hard, we propose to compute an approximate solution by adapting two algorithms: Integer Projected Fixed Point method and Graduated Non Convexity and Concavity Procedure. Experiments show that the proposed approach is generally able to reach a more accurate approximation of the exact GED than the bipartite GED, with a computational cost that is still affordable for graphs of non trivial sizes.

Application of linear programming and assignment model on optimizing the allocation of human resources in Emergency Department

Objective To explore the application of linear programming and assignment model on nursing shift mode, in order to reduce the nursing manpower allocation and reach nurse hierarchical use. Methods In 2014, linear programming was applied to calculate the number of the minimum number of daily work, and then we assigned job optimally according to the average operation time of each nurses. We analyzed comparisons retrospectively in the workload of nursing work in 2013, the number of personnel, skills assessment scores, self-assessment of the work load of nurses, and nursing quality control results. Results There were statistically significant in the differences of Emergency Room (ER) visits and times of 120 ambulance utilization in each month′s comparison (P 0.05); the comparisons in working hours, overtime hours, training time, nursing skills assessment had statistical significance (P<0.05), as well as the nurse′s skill assessment (P<0.05); all 9 nursing quality control indicators reached the requirements of the Nursing Department of our hospital. Conclusions It can optimize emergency nursing human resource allocation by using linear programming and assignment model. Key words: Nursing administration research; Allocation of human resources; Emergency Department; Assignment model; Linear program

Likelihood-based assignment methods for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets

The aim of this paper is to develop useful likelihood-based assignment methods for addressing multiple criteria decision-making problems within the environment of interval-valued intuitionistic fuzzy sets. Based on the likelihoods of interval-valued intuitionistic fuzzy preference relations, this paper determines the mean likelihoods of outranking relations and presents a mean likelihood determination method for generating a set of criterion-wise rankings of alternatives. By employing the concepts of rank frequency matrices and (ordinary) rank contribution matrices, this paper establishes a likelihood-based linear assignment model for multiple criteria decision analysis in the interval-valued intuitionistic fuzzy context. Additionally, this paper propounds two likelihood-based assignment models for handling incomplete and conflicting certain information of importance weights. These models can transform the criterion-wise ranks into the overall ranks for determining the optimal priority ranking of the alternatives. The feasibility and applicability of the proposed methods are illustrated with a practical problem of selecting a bridge construction method which involves various preference types. Finally, this paper conducts a comparative analysis with previous assignment-based methods in an interval-valued intuitionistic fuzzy setting to validate the effectiveness and advantages of the proposed methods.

Selection of Most Proper Blasting Pattern in Mines Using Linear Assignment Method: Sungun Copper Mine / Wybór Najodpowiedniejszego Schematu Prowadzenia Prac Strzałowych W Kopalni Miedzi Sungun Z Użyciem Metody Przyporządkowania Liniowego

Abstract One of the most important operations in mining is blasting. Improper design of blasting pattern will cause technical and safety problems. Considering impact of results of blasting on next steps of mining, correct pattern selection needs a great cautiousness. In selecting of blasting pattern, technical, economical and safety aspects should be considered. Thus, most appropriate pattern selection can be defined as a Multi Attribute Decision Making (MADM) problem. Linear assignment method is one of the very applicable methods in decision making problems. In this paper, this method was used for the first time to evaluate blasting patterns in mine. In this ranking, safety and technical parameters have been considered to evaluate blasting patterns. Finally, blasting pattern with burden of 3.5 m, spacing of 4.5 m, stemming of 3.8 m and hole length of 12.1 m has been presented as the most suitable pattern obtained from linear assignment model for Sungun Copper Mine.

The extended linear assignment method for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets

The theory of interval-valued intuitionistic fuzzy sets is useful and beneficial for handling uncertainty and imprecision in multiple criteria decision analysis. In addition, the theory allows for convenient quantification of the equivocal nature of human subjective assessments. In this paper, by extending the traditional linear assignment method, we propose a useful method for solving multiple criteria evaluation problems in the interval-valued intuitionistic fuzzy context. A ranking procedure consisting of score functions, accuracy functions, membership uncertainty indices, and hesitation uncertainty indices is presented to determine a criterion-wise preference of the alternatives. An extended linear assignment model is then constructed using a modified weighted-rank frequency matrix to determine the priority order of various alternatives. The feasibility and applicability of the proposed method are illustrated with a multiple criteria decision-making problem involving the selection of a bridge construction method. Additionally, a comparative analysis with other methods, including the approach with weighted aggregation operators, the closeness coefficient-based method, and the auxiliary nonlinear programming models, has been conducted for solving the investment company selection problem to validate the effectiveness of the extended linear assignment method.

An Improved Exact Algorithm for Least-Squares Unidimensional Scaling

Given n objects and an symmetric dissimilarity matrix D with zero main diagonal and nonnegative off-diagonal entries, the least-squares unidimensional scaling problem asks to find an arrangement of objects along a straight line such that the pairwise distances between them reflect dissimilarities represented by the matrix D. In this paper, we propose an improved branch-and-bound algorithm for solving this problem. The main ingredients of the algorithm include an innovative upper bounding technique relying on the linear assignment model and a dominance test which allows considerably reducing the redundancy in the enumeration process. An initial lower bound for the algorithm is provided by an iterated tabu search heuristic. To enhance the performance of this heuristic we develop an efficient method for exploring the pairwise interchange neighborhood of a solution in the search space. The basic principle and formulas of the method are also used in the implementation of the dominance test. We report computational results for both randomly generated and real-life based problem instances. In particular, we were able to solve to guaranteed optimality the problem defined by a Morse code dissimilarity matrix.

An assignment method for group decision making with uncertain preference ordinals

This paper presents an assignment method to solve the group decision making problem with uncertain preference information. The uncertain preference information is given as uncertain preference ordinals by decision makers. We first address the concept and calculation formulae of preference ordinal frequency, and then, uncertain preference ordinals are transformed into preference ordinal frequencies accordingly. Furthermore, a linear assignment model is built based on the derived preference ordinal frequencies, and the ranking of alternatives can be obtained by solving the model. Finally, a numerical example is used to illustrate the use of the proposed method.

A discrete particle swarm optimization approach for classification of Indian coal seams with respect to their spontaneous combustion susceptibility

Mine fires due to spontaneous combustion in coal mines is a global concern. This leads to serious environmental and safety hazards and considerable economic losses. Therefore it is essential to assess and classify the coal seams with respect to their proneness to spontaneous combustion to plan the production, storage and transportation capabilities in mines. This paper presents the formulation of clustering problem into a linear assignment model and the application of a discrete particle swarm optimization approach for the classification of coal seams based on their proneness to spontaneous combustion. In this research work, twenty nine coal samples of varying ranks belonging to both high and low susceptibilities to spontaneous combustion have been collected from all the major coalfields of India. Using moisture, volatile matter, and ash content and crossing point temperature of the coal samples as the parameters, the proposed algorithm has been applied to classify the coal seams into three different categories. This classification will be useful for the planners and field engineers for taking ameliorative measures in advance for preventing the occurrence of mine fires.

Optimizing the marriage market: An application of the linear assignment model

Abstract Research shows that the success of marriages and other intimate partnerships depends on objective attributes such as differences in age, cultural background, and educational level. This article proposes a mathematical approach to optimizing marriage by allocating spouses in such a way as to reduce the likelihood of divorce or separation. To produce our optimization model, we use the assumption of a central “agency” that would coordinate the matching of couples. Based on a representative and longitudinal sample of 1074 cohabiting and married couples living in Switzerland, we estimate various objective functions corresponding to age, education, ethnicity, and prior divorce concerning every possible combination of men and women. Our results show that the current state of marriages or partnerships is well below the social optimum. We reallocate approximately 68% of individuals (7 out of 10) to a new couple that we posit has a higher likelihood of survival. From this selection of new partners, we obtain our final “optimal” solutions, with a 21% reduction in the objective function.