Positive Ideal Solution Research Articles

Integration of Fuzzy AHP-VIKOR Methods in Multi Criteria Decision Making: Literature Review

The rapid development of the times directly demands technology, culture and social development as well. The development of this era also gives us many problems that must be resolved. One of the problems that must be faced is the problem of making decisions. There are many methods for solving decision-making problems, one of which is Multiple-Criteria Decision Making (MCDM). MCDM is a decision-making method to determine the best alternative from a number of alternatives based on certain criteria. This journal will discuss one of the MCDM methods, namely Fuzzy AHP-TOPSIS. Basically, AHP breaks up a complex and unstructured situation into its component parts. Then arrange these parts or variables in a hierarchical arrangement and give numerical values to subjective considerations about the relative importance of each variable. The fuzzy set theory used to represent uncertainty, obscurity, inaccuracy, lack of information, and partial truth. In the VIKOR method, a ranking is performed on the weight that has been obtained in the FAHP method by comparing ratings from a series of alternatives. The VIKOR method calculate the ratio positive and negative ideal solution. The VIKOR method propose a compromise solution with profit rate. This method overcomes the drawbacks of other MCDM methods.

Selection of supplier for the evaluation of procurement of special chemical using entropy method and topsis in xyz company

In the process of procuring special materials, the company has more than one supplier for each item of goods, at XYZ companies selecting suppliers through process evaluation. In the evaluation process the supplier is chosen only based on the lowest price offered by the supplier, these criteria have not been able to ensure the selected supplier can meet other criteria such as quality, transportation system and so on. This study aims to determine whether the criteria that have the highest weight value in the selection of suppliers and to find out the best supplier in the purchase of special materials XYZ companies. In this study, the Entropy and TOPSIS methods are used to analyse the data.. Entropy method is used to calculate the weight of each criterion and alternatives, while the TOPSIS method is used to rank suppliers. The results showed that the criterion that had the highest weighting value in the selection of special material suppliers in the special material purchasing section of XYZ company was the criterion C3 and C12 with positive ideal solution value 0,0380 and 0,0389. Whereas the best supplier for PT XYZ’s special material purchasing department is supplier E with a preference value of 0.5517.

Analysis of Fuzzy AHP-TOPSIS Methods in Multi Criteria Decision Making: Literature Review

With the development of technology and times, we have faced various alternative problems. The problem of making decisions is one of the problems that is often encountered in everyday life. In the matter of decision-making, there are several methods that can be used, one of which is Multi-Criteria Decision Making (MCDM). MCDM is a method to make decision based on theory, process and analytical methods that involved uncertainty, dynamics and various aspects of criteria. This journal will discuss the use of one of the MCDM methods, namely Fuzzy AHP-TOPSIS. Basically, AHP breaks down unstructured situations into its components and organize these components or variables in a hierarchical order and assign a scientific value as a subjective assessment of the proportionate significance of each variable. Fuzzy theory is used to represent ambiguity, inaccuracies, lack of information, and partial truth. Then the TOPSIS method uses the principle that the preferred alternative must have the farthest from the negative ideal solution and the shortest interval from the positive ideal solution to find the optimal solution from the available alternatives.

A comparative study of two optimization approaches for solving bi-level multi-objective linear fractional programming problem

Despite the important role of bi-level multi-objective linear fractional programming (BL-MOLFP) problem for many hierarchical organizations, a very little success has been achieved to deal with this problem. This paper presents a comparative study between two computational approaches, namely fuzzy TOPSIS (technique for order preference by similarity to ideal solution) approach and Jaya (a Sanskrit word meaning victory) approach, for solving BL-MOLFP problem. The fuzzy TOPSIS (FTOPSIS) approach aims to obtain the satisfactory solution of BL-MOLFP problem by using linearization process as well as formulating the membership functions for the distances of positive ideal solution (PIS) and negative ideal solution (NIS) for each level, respectively. In this sense, the deadlock situations among levels are avoided by establishing the membership functions for the upper level decision variables vector with possible tolerances. On the other hand, Jaya algorithm is proposed for solving BL-MOLFP problem based on nested structure scheme to optimize both levels hierarchically. An illustrative example is presented to describe the proposed approaches. In addition, the performances among the proposed approaches are assessed based on ranking strategy of the alternatives to affirm the superior approach. Based on the examined simulation, Jaya algorithm is preferable than the FTOPSIS approach.

An Improved PL-VIKOR Model for Risk Evaluation of Technological Innovation Projects with Probabilistic Linguistic Term Sets

Risk evaluation is a primary but important task for technological innovation projects and this task is a multiple criteria group decision-making (MCGDM) process with probabilistic uncertainty and fuzzy uncertainty. Compromise programming decision-making methods with probabilistic linguistic term sets (PLTSs) are more appropriate for risk evaluation of technological innovation projects. This paper proposes a new approach named improved probabilistic linguistic-vise kriterijumska optimizacija kompromisno resenje (PL-VIKOR) method with probabilistic linguistic term sets for risk evaluation of technological innovation projects. Firstly, by fully considering both the relationship between each alternative and the positive ideal solution and the relationship between each alternative and negative ideal solution, the improved PL-VIKOR method for dealing with MCGDM problems is developed to make up the deficiency of the traditional PL-VIKOR method. Then, the improved PL-VIKOR method is applied to solve a practical MCGDM problem with probabilistic linguistic term sets involving the risk evaluation of technologically innovative projects for venture capital. Finally, we make some comparative analyses between the improved PL-VIKOR method and some existing methods to analyze the advantages and disadvantages of the proposed method. The results reflect that the improved PL-VIKOR method is more reasonable when calculating the distance measure between two PLTSs, and it can make the risk evaluation of technological innovation project MCGDM with PLTSs more objective.

Application of fuzzy TOPSIS method for risk evaluation in development and implementation of solar park in India

Renewable energy sector projects like development and implementation of solar power plants are given preference and boost in India to meet the target for generation of green and clean energy. Like other complex infrastructure projects, the solar power projects also face risks and uncertainties throughout all the phases. Although new techniques and methods are introduced, risk assessment for projects remains an unstructured problem that depends on human expertise. This paper aims at identifying the risks involved and associated with all the phases of the solar power project in India and develop a methodology of risk analysis through application of Fuzzy TOPSIS (Technique for Order Preference by Similarities to Ideal Solution) methodology. Risk severity has been computed through computation of Fuzzy Positive Ideal Solution (FPIS), Fuzzy Negative Ideal Solution (FNIS) and Closeness Coefficient (CC). It has been observed that the risk severity of phase 1 ranges between moderate to high. Phase 2 ranges between high to very high, phase 3 and 4 are very high and finally phase 5 varies between moderate to high. Thereby the project authorities cannot afford to ignore any of the phases. Furthermore, suitable corrective and preventive risk mitigation measures have been recommended.

EVALUATION OF FINANCIAL PERFORMANCES OF SME’S LISTED IN THE BIST SME INDUSTRIAL INDEX BY USING TOPSIS MULTICRITERIA DECISION MAKING METHOD

In this study, the financial performances of SMEs listed in the BIST SME Industrial Index are evaluated by using TOPSIS multicriteria decision-making method. The data of the study acquired from annual financial statements that reported between the 2016-2018 period. Financial performance ranks of SMEs are determined for each year and thus comparative financial performances of SMEs are detected.BIST SME Industrial Index is an index that includes stocks of industrial SMEs traded in BIST Stars, BIST Main, and BIST Emerging Companies markets. SMEs have great importance for the Turkish economy, with their dynamizing roles and with their crucial roles in regional development and job creation. According to the Turkey Statistical Institute data, Turkish SMEs constitute 99.8 % of all enterprises in Turkey. At the same time, Turkish SMEs provide 72.7% of total employment, 62% of total sales, and 58% of the total investments of the Turkish Economy.Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is one of the multicriteria decision-making methods that commonly used in the evaluation of financial performances of firms. The TOPSIS method is based on two main points: the positive ideal solution and the negative ideal solution. With the help of the TOPSIS method, the distances positive ideal solutions and negative ideal solutions of all options are calculated. Options are ranked according to their proximity to the positive ideal solution and their distance to the negative ideal solution.

Eliciting Correlated Weights for Multi-Criteria Group Decision Making with Generalized Canonical Correlation Analysis

The proper solution of a multi-criteria group decision making (MCGDM) problem usually involves a series of critical issues that are to be dealt with, among which two are noteworthy, namely how to assign weights to the (possibly distinct) judgment criteria used by the different decision makers (DMs) and how to reach a satisfactory level of agreement between their individual decisions. Here we present a novel methodology to address these issues in an integrated and robust way, referred to as the canonical multi-criteria group decision making (CMCGDM) approach. CMCGDM is based on a generalized version of canonical correlation analysis (GCCA), which is employed for simultaneously computing the criteria weights that are associated with all DMs. Because the elicited weights maximize the linear correlation between all criteria at once, it is expected that the consensus measured between the DMs takes place in a more natural way, not necessitating the creation and combination of separate rankings for the different groups of criteria. CMCGDM also makes use of an extended version of TOPSIS, a multi-criteria technique that considers the symmetry of the distances to the positive and negative ideal solutions. The practical usefulness of the proposed approach is demonstrated through two revisited examples that were taken from the literature as well as other simulated cases. The achieved results reveal that CMCGDM is indeed a promising approach, being more robust to the problem of ranking irregularities than the extended version of TOPSIS when applied without GCCA.

Risk evaluation in failure modes and effects analysis: hybrid TOPSIS and ELECTRE I solutions with Pythagorean fuzzy information

This article proposes two novel modified techniques, namely Pythagorean fuzzy hybrid Order of Preference by Similarity to an Ideal Solution (PFH-TOPSIS) method and Pythagorean fuzzy hybrid ELimination and Choice Translating REality I (PFH-ELECTRE I) method, in order to measure risk rankings in failure modes and effects analysis (FMEA). These methods are designed to overcome the flaws and shortcomings of traditional crisp risk priority numbers and fuzzy FMEA techniques in risk rankings. The proposed methods consider subjective as well as objective weight values of all factors in risk rankings of identified failures. The FMEA experts team are allowed to submit their information by linguistic terms using Pythagorean fuzzy numbers. Both techniques use a Pythagorean fuzzy weighted averaging operator to aggregate their independent evaluations into group assessments. Subsequent steps are different. The PFH-TOPSIS approach computes the distances of failure modes from the Pythagorean fuzzy positive ideal solution and Pythagorean fuzzy negative ideal solution. To evaluate failure modes, the PFH-ELECTRE I approach produces Pythagorean fuzzy concordance and Pythagorean fuzzy discordance matrices. We illustrate the structure of both techniques with the help of flowcharts. The effectiveness of the methods that we develop is described by a numerical example, namely a case study of 1.8-in. color super-twisted nematic (CSTN). To validate their effectiveness and accuracy, we provide a comprehensive comparative analysis with existing techniques of risk evaluation, including intuitionistic fuzzy hybrid TOPSIS, intuitionistic fuzzy TOPSIS, IWF-TOPSIS, and fuzzy TOPSIS methods.

EDUCATIONAL PROGRAMS PERFORMANCE RANKING BY USE OF TOPSIS METHOD

Evaluation of an educational program is a complex task and its solution requires the analysis of data obtained on the basis of relevant to both quantitative and qualitative research. The collection of these data should be carried out using properly developed key performance indicators. The paper shows that such a task can be successfully solved using the TOPSIS method of multi-criteria decision analysis well known in information systems theory. The evaluation criteria can be positive or negative. The higher the rating value for a positive criterion, the better the alternative decision, while for the negative criterion the smaller the corresponding rating value, the better the alternative. The TOPSIS method is based on the concept that the best solution among the available alternatives is the one that has the minimum distance from the positive ideal solution and, at the same time, the maximum distance from the negative ideal solution. The paper presents both positive and negative criteria developed to evaluate the performance of educational programs. For the data relevant to the above criteria there are used the appropriate data of the four higher educational programs of Gori State Teaching University. Using the TOPSIS method the rating evaluation of the programs was carried out. The paper indicates that in the same way it is possible to assess the performance of one of the educational programs using data obtained at different intervals in relation to this program, and thereby determine the degree of success or failure of the program by comparing the results.

New design concept evaluation method involving customer preferences based on rough distance to redefined ideal solution

Currently, to get more popular design solution, customers are allowed to provide their preferences for new design concepts to be evaluated. Existing customer-involved design concept evaluation (CDCE) methods based on multi-criteria decision-making (MCDM) models collect customer preferences for certain pre-determined criteria as the one kind of evaluation factor without further exploring these subjective data, and sort the alternatives according to their deviations to positive ideal solution (PIS) and negative ideal solution (NIS). The elements of PIS and NIS are defined only limited to considering the benefit-like or cost-like characteristics of criteria without considering the impacts of customer preferences. To make better use of the customer preferences in CDCE, we propose a new multi-criteria CDCE method which not only captures the customer-related weights and importance ratings of criteria from customer preferences, but also more importantly, redefines PIS and NIS by comprehensive considering the characteristics of criteria and their importance ratings. Rough distances between alternatives and redefined ideal solutions are calculated to obtain the preferred degrees of alternatives for priority ranking, so the proposed method is named as evaluation based on rough distance to redefined ideal solution (RD-RIS). With the help of new combined ideal solution definition strategy adopted in RD-RIS, the best design concept recommended by RD-RIS is favored by customers as well as satisfies the constraints of evaluation criteria. Besides theoretical research, a practical example is introduced to illustrate the process of RD-RIS, and the empirical comparisons between RD-RIS and other classical MCDM methods are carried out to validate the superiority of RD-RIS. Experimental results show that RD-RIS is a feasible CDCE method which can give more reliable and reasonable evaluation results based on different customer preference values.

Multiple criteria group decision analysis using a Pythagorean fuzzy programming model for multidimensional analysis of preference based on novel distance measures

The preference concerning criteria or alternatives from decision makers (DMs) is a critical element in multicriteria group decision making (MCGDM). The linear programming technique for the multidimensional analysis of preference (LINMAP) is the most influential technique in adjusting the error between the objective assessments on criteria and subjective preferences on alternatives via optimal programming for MCGDM problems. Considering the higher capacity for expressing the uncertainties of human inherent preferences of the Pythagorean fuzzy (PF) sets, this article explores the LINMAP technique for MCGDM problems under the PF scenario. First, we present a novel (squared) Euclidean distance measure for the PF sets since it possesses captivating characteristics of the PF sets and the distance measure. Second, we define the preference degrees over alternatives that are expressed as PF sets and calculate their magnitudes via relative distances, which are used to calculate the consistency and inconsistency indices. Third, the ordered weighted averaging (OWA) operator under the normal distribution is introduced to obtain the weights of DMs to reduce the influence of unfair arguments. Fourth, we construct the biobjective PF-LINMAP model for minimizing both the error extents and the overall distances to the PF positive ideal solution for the minimum error and global optimum. Then, we obtain the optimal criterion weights and ranks of the candidates via relative closeness indices. Finally, we perform our PF-LINMAP method to choose the optimal green supplier, and we implement the sensitivity analysis and comparative analysis with those of the available PF-LINMAP methods to verify the feasibility and superiority of our approach.

Adaptive Interval Trapezoid Fuzzy Number for Recommendation Systems E-Learning

This research aims to develop decision making models for Multi Criteria Decision Making (MCDM) with Adaptive Interval Fuzzy Analytic Hierarchy Process (AIVFAHP) and Adaptive Interval Fuzzy Technique for Order Preference of Similarity Ideal Solution (AIVFTOPSIS) integration methods by constructing a decision-making model using trapezoid fuzzy number. The strength of the AIVFAHP method is to consult the value of logical consistency in the assessment. This logical consistency is to calculate the assessor and determine the costs in multi-criteria decision making. AIVFTOPSIS is based on the principle that the chosen alternative should be close to a positive ideal solution and far from the ideal solution. Contribution of this research is to conduct a research of decision making with Adaptive Interval Value Fuzzy Multi Criteria Decision Making (AIVFMCDM) and to improve interval points by modifying the midpoint and degree on the trapezoid fuzzy number function. This modeling provides more accurate, more effective linguistic representation and flexible in determining the point of the interval for optimal results. The research produced a new decision-making model based on the Adaptive Interval Trapezoid Fuzzy Number (AIVTFN) and recommendations for improvement of e-learning indicators.

Selection of Karanja Biodiesel Blend for Engine Performance by using TOPSIS and VIKOR Method

Demand for energy is increasing due to the development of industries, expanding urbanization, and population growth which further increases the use of fossil fuel in large amount. This also affects an environmental pollution and engine sector too. In internal combustion (IC) engines, alternative fuel blends has one of the most important decision for balancing a number of opinions and criteria for making different strategic decision by an engine expert. Choice of alternative sources of suitable blending of biodiesel and biodiesel plays an important role in engine sector. In this paper, discuss the Multi Criteria Decision Making (MCDM) techniques is used for selecting the best alternative blend of Karanja methyl ester biodiesel to fulfil the demand in IC engine sector. Optimization was done by using of VIKOR (Visekriterijimsko Kompromisno Rangiranje) and TOPSIS (technique for order performance by similarity to ideal solution) techniques. The parameter considered for optimization includes brake thermal energy, brake specific fuel consumption at different load at different compression ratio as input. Emission parameters as carbon mono oxide un burnt hydrocarbon, carbon di-oxide, oxygen and oxides of nitrogen was also determined. A productive examination of the procedure and positioning of choices can be accomplished for enhancement blends choice through TOPSIS and VIKOR techniques. Starting with normalized and weighted normalized decision matrix, positive and negative ideal solution, the distance of alternative from positive and negative ideal solution was calculated and closeness coefficient of alternative in the form of ranking of alternative was done. It was found that a mix B75 was the most appropriate blend for Karanja biodiesel for best use in CI engine without influencing the emission and performance parameters.

Three-way decision models based on multigranulation support intuitionistic fuzzy rough sets

To capture the influence of various uncertain factors during delayed decision-making, support intuitionistic fuzzy sets (SIFSs) are introduced for three-way decisions (TWDs) to study this topic from the perspective of multigranulation. First, the concepts of support intuitionistic fuzzy rough sets are defined, and their related properties are discussed. Then, we combine support intuitionistic fuzzy rough sets with multigranulation rough sets (MRSs), present optimistic/pessimistic multigranulation support intuitionistic fuzzy rough set models, and discuss their corresponding properties. Second, a parameter α is introduced to constrain the disjunction and conjunction of multiple support intuitionistic fuzzy relations, and variable optimistic and pessimistic multigranulation support intuitionistic fuzzy rough set models are constructed. Third, we define the similarity measure, positive ideal solution, negative ideal solution, and conditional probability based on multigranulation support intuitionistic fuzzy rough sets. Four kinds of TWD models based on four proposed multigranulation support intuitionistic fuzzy rough set models are established. Finally, decision rules can be obtained from a new score function and accuracy function, and the decision rule extraction algorithm based on multigranulation support intuitionistic fuzzy rough sets is designed. Experimental results on a series of examples demonstrate the effectiveness of our proposed TWD models.

Group decision-making framework using complex Pythagorean fuzzy information

This paper contributes to the expanding literature on VIKOR, a well-known multi-criteria decision-making technique. It is abundantly used to find the compromise solution regarding some significant criteria under different models. The general VIKOR methodology implements the principle that a recommended response must be a feasible solution which is nearest to positive ideal solution having maximum group utility and minimum individual regret. In this article, we propose a new strategy to address multi-criteria group decision-making problems named complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method. It is designed to handle a great deal of vagueness and hesitation which are often present in human decisions. The CPF-VIKOR method allows the linguistic terms to express individual opinions of experts about the performance of alternatives and the weights of the criteria. We combine the individual judgments of experts with the help of complex Pythagorean fuzzy weighted averaging operator. Further, we compute the ranking measure with the help of group utility and regret measures by adjusting the weight of strategy of maximum group utility within the unit interval. We sort the alternatives in an ascending order relative to group utility measure and individual regret measure. Moreover, we demonstrate our proposed method with the help of a flow chart and two numerical examples: one for the selection of the most beneficial renewable energy project in Spain and another for the selection of the most suitable logistic village location in Turkey. Finally, we present the comparative analysis of our proposed method with the CPF-TOPSIS method to prove its validity.

TOPSIS Evaluation System of Logistics Transportation Based on an Ordered Representation of the Polygonal Fuzzy Set

The polygonal fuzzy set is an effective tool to approximate the general fuzzy set by means of a finite number of ordered real numbers. It not only overcomes the shortcomings (which does not satisfy the closeness) of arithmetic operations of fuzzy sets based on Zadeh extension principle, but also realizes the non-linear operation of general fuzzy sets by an ordered representation of the polygonal fuzzy set. In this paper, the definition, geometric interpretation, ordered representation and arithmetic operations of the polygonal fuzzy sets are introduced for the first time, and the method of solving polygonal fuzzy sets and their ordered representation based on convex fuzzy sets are given by an example. Second, a new Euclidean metric of polygonal fuzzy sets is proposed, and the approximation accuracy of polygonal fuzzy sets to convex fuzzy sets is discussed. In addition, the linear function describing transportation cost index information of logistics companies is obtained through the ordered representation of Gauss membership function, and according to the ordered representation a new normalization method for the polygonal decision matrix is given. Finally, the method of solving the positive (negative) ideal solution and degree of relative closeness of the polygonal decision matrix is suggested by the weighted Euclidean distance. Then a new TOPSIS evaluation system is established, and the effectiveness of the proposed method is illustrated by an example of logistics transportation.

Decision Support System Employee Performance Appraisal Method Using TOPSIS

Employee performance is the level of achievement of an employee of a particular task that is influenced by internal and external factors of the company where the employee works. Employee performance is influenced by many factors including competency, attendance, loyalty and length of work. The purpose of this study is to create and design a Decision Support System (SPK) for evaluating employee performance using the TOPSIS method and applying the method to employee performance evaluation SPK. TOPSIS is a decision-making method that has multiple criteria or criteria. This type of research is a quantitative descriptive method that presents methods and research objects based on numbers. The study population was 42 employees at PT Catur Karya Sentosa and used as many as 4 employees as research samples and data were collected by interview method. The results showed that the calculation of employee performance using the TOPSIS algorithm runs well and efficiently and can be done every month so as to minimize or even eliminate the employee performance appraisal method subjectively. Ranking taken from the results of this method is the final result after the calculation of positive and negative ideal solutions as consideration of the final decision making by the board of directors.

Node importance evaluation based on neighborhood structure hole and improved TOPSIS

It is of great significance to identify the important nodes accurately and rapidly for preventing accidents in the network. This paper improves the traditional neighborhood structure hole indicators from the perspective of the topology and network characteristics between a node and its neighbors, and the improved indicators are applied to the importance evaluation of the network node. In order to avoid the subjectivity of artificially determining the indicator weights, we use Gini coefficient and Kendall coefficient to calculate the objective weight of evaluation indicators by combining the difference among the indicator values and the conflict among the indicators. Correspondingly, this paper proposes the information efficiency of the evaluation indicators to measure the contribution of traditional indicators and improved indicators. At the same time, the prospect theory is adopted to solve the problem of the traditional node evaluation methods that the influence of decision-makers' experience and knowledge on evaluation results is easily neglected. For the shortages of the traditional TOPSIS method, the relative entropy is utilized to solve the problem that the vertical line nodes in the positive and negative ideal solutions cannot be distinguished effectively in the traditional TOPSIS, and the gray correlation is introduced to measure the curve edge coupling degree to enhance the accuracy of the evaluation result. The evaluation and comparison results of the ARPA network and the standard IEEE 39-bus system validate the effectiveness and superiority of the improved indicators and evaluation methods.

An Interactive Decision-Making Method for Third-Party Logistics Provider Selection under Hybrid Multi-Criteria

Due to the complexity and uncertainty of third-party logistics (3PL) provider selection circumstances, the research on the hybrid multi-criteria decision-making (HMCDM) method with fuzzy hesitation information is becoming more and more important. Based on symmetry principles, both the objectivity of the decision information and the subjectivity of decision makers’ (DMs) preferences should be considered in the HMCDM method. In this paper, a novel interactive decision-making method to deal with the 3PL provider selection problem of hesitant fuzzy sets, intuitionistic fuzzy sets and real numbers is developed. We first investigate the positive and negative ideal solutions of the alternative and the satisfaction degree of the DMs under hybrid multi-criteria circumstances. Then, the interactive HMCDM models based on satisfaction degrees are established, which can use objective decision information to rank alternatives and, symmetrically, the preference information of the DMs is also taken into account. DMs can modify their preference information using the models and thus make the most reasonable selection of 3PL provider. Finally, the case analysis and sensitivity analysis show that the change of parameter and the setting of the satisfaction lower limit will not affect the optimal rank of alternatives, and the feasibility of the proposed method is confirmed.