Fuzzy Positive Ideal Solution Research Articles

Multi-attribute approach for selection of polymeric materials for manufacturing gears: A case study in the automotive industry

Automotive industry is characterized by mass production, a large share in the gross national income and high employment of workers with different knowledge and skills. Improving the production process, as well as product quality, is one of the most important tasks of automotive enterprise as well as government management. This research promotes a new fuzzy hybrid model for determining the priority of polymeric materials for manufacturing gears in an exact manner, which leads to an incremental improvement in the quality of the considered product. The analysis of polymeric materials and their characteristic is based on data from the relevant literature and experiences of the best practice. The relative importance of material characteristics is stated as fuzzy group decision making problem. The weights vector is determined by using the fuzzy Analytic Hierarchical Process and fuzzy geometric mean. The rank of polymeric materials is obtained by employing the proposed Technique for Order Preference by Similarity to Ideal Solution with triangular fuzzy numbers. The fuzzy algebra rules have been used for determining: (i) distances from Fuzzy Positive Ideal Solutions and Fuzzy Negative Ideal Solutions and (ii) closeness coefficient values. The proposed fuzzy hybrid model testing and verification are performed on real data in an automotive enterprise.

An integrated QFD and fuzzy TOPSIS approach for supplier evaluation and selection

PurposeSupplier evaluation and selection is an essential (multi-criteria decision-making) MCDM process that considers qualitative and quantitative factors. This research work attempts to use a MCDM technique based on merging fuzzy Technique for Order Preference by Similarity to Ideal Solution (F-TOPSIS) and Quality Function Deployment (QFD) ideas. The study attempts to find the supplier's attributes (HOWs) to accomplish its goals after determining the product's characteristics to suit the company's needs (WHATs).Design/methodology/approachThe proposed research methodology comprises the following four steps: Step 1: Determine the product purchase requirements (“WHATs”) and those pertinent to supplier evaluation (“HOWs”). In Step 2, the relative importance of the “WHAT-HOW” correlation scores is determined and also the resulting weights of “HOWs”. In Step 3, linguistic evaluations of possible suppliers in comparison to subjective criteria are given to the decision-makers. Step 4 combines the QFD and F-TOPSIS techniques to select suppliers.FindingsA fuzzy MCDM method based on fusing and integrating fuzzy information and QFD is presented to solve the drawbacks of conventional decision-making strategies used in supplier selection. Using the F-TOPSIS method, fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS), the relative closeness coefficient values for all alternatives are computed. The suppliers are ranked by relating the closeness of coefficient values. This method permits the combination of ambiguous and subjective data expressed as fuzzy-defined integers or linguistic variables.Originality/valueQFD and TOPSIS, two widely used approaches, are combined in this article to rank and evaluate suppliers based on the traits that the suppliers choose to prioritize. This study demonstrates that the method employed could address multiple-criteria decision-making scenarios in a computationally efficient manner. The effectiveness and applicability of the method are illustrated using an example.

Fuzzy TOPSIS-based risk assessment model for effective nuclear decommissioning risk management

The dynamics of the nuclear decommissioning project warrant a critical study of the inherent risks and uncertainties. Previous works have identified several nuclear decommissioning risk factors. However, there is no detailed study that systematically ranks the risk factors to aid risk management decision-making. This work presents a fuzzy-based Technique for Order Preference by Similarities to Ideal Solution (Fuzzy TOPSIS) to evaluate the overall risk factors that may arise in a nuclear decommissioning project. The novel analytic tool presented in this work is used to rank eighteen nuclear decommissioning project risk factors according to their severity, for easy risk management. The evaluation and ranking metrics are the Fuzzy Positive Ideal Solution (FPIS), Fuzzy Negative Ideal Solution (FNIP), and Closeness Coefficient (CC). Feedback from nuclear decommissioning experts is processed in linguistic terms and converted into fuzzy values to perform the computation of the closeness coefficient rank for each of the risk factors. The ranking shows the effect of each risk factor on project safety, cost overrun, and time delay. The highest ranked risk factors are the structural condition of the facility before decommissioning, the radiological characteristics of the facility before decommissioning, and the established regulation for the disposal of radioactive material, with closeness coefficients of 0.54351, 0.53239, and 0.48637 respectively. The lowest ranked risk factors are the historical documentation, the availability and condition of waste management facility, and increasing public opposition, with closeness coefficients 0.33806, 0.33355, and 0.28917 respectively. The result shows the capability and the importance of the proposed approach for nuclear decommissioning risk assessment, risk management, and optimal decision-making.

A fuzzy TOPSIS model for selecting raw material suppliers in a manufacturing company

Multi-criteria decision model (MCDM) is used to describe a family of techniques which considers multiple criteria in order to make a choice (among several alternatives). Sometimes, both alternatives and criteria involve qualitative definitions which have to be accounted for. Accordingly, fuzzy TOPSIS is one of several MCDM methods and it serves as a scientific way to solve selection problems that involve uncertainty in criteria definition. This work considers a beverage manufacturing company where selection problem has caused a downturn in production. Inconsistency and unreliability of previous suppliers have caused the company to loose their competitive edge. Fuzzy TOPSIS is proposed to solve the challenge in selecting suppliers of a key raw material. Three decision makers evaluated three suppliers of sugar considering eight criteria for subjective weights based on a 5-point scale. Decision matrices were constructed and normalized for the three submissions. Result obtained showed that supplier 2 had the lowest fuzzy positive ideal solution and the highest fuzzy negative ideal solution. The same supplier had the highest closeness coefficient (0.782) which implies that supplier 2 is the best option.

ACHIEVING THE SELECTION OF OPTIMAL PRESS BRAKE DESIGN VIA A FUZZY TOPSIS APPROACH

Selecting optimal design concept from several design alternatives is still a major challenge for engineers in the field of engineering design and it is important to select the optimal design in order to avoid delay and unnecessary cost during project execution. This article presents the selection of optimal design of press brake considering several design requirements and features. The adoption of the fuzzy TOPSIS methodology considered various design features that are categorized into several sub-features and weighted considering the functional requirements from the optimal design. The cumulative Triangular Fuzzy Number (TFN) of the design alternatives from the sub-features of all the design features are harnessed to develop a decision matrix from which the fuzzy positive and negative ideal solutions are obtained. The distances of the design alternatives to the fuzzy positive and negative ideal solutions are determined in order to obtain a closeness coefficient that is used to rank the design alternatives. The proximity in the final values of the closeness coefficients of the design alternatives demonstrates that the fuzzy TOPSIS approach apportioned ratings to the design alternatives based on availability of sub-features in the design concepts and the relevance of the design features to the functional requirement of the optimal design.

Sustainable performance analysis and ranking of organizations through fuzzy multi-criteria group decision making - A case study

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.

INTERVAL-VALUED INTUITIONISTIC FUZZY TOPSIS-BASED MODEL FOR TROUBLESHOOTING MARINE DIESEL ENGINE AUXILIARY SYSTEM

In this paper, we present an interval-valued Intuitionistic Fuzzy TOPSIS model, which is based on an improved score function for detecting failure in a marine diesel engine auxiliary system, using groups of experts’ opinions to detect the root cause of failure in the engine system and the area most affected by failures in the diesel engine. The improved score function has been used for the computation of the separation measures from the intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) of alternatives while the criteria weight have been determined using an intuitionistic fuzzy entropy. The study is aimed at providing an alternative method for the identification and analysis of failure modes in engine systems. The results from the study show that although detection of failures in Engines is quite difficult to identify due to the dependency of the engine systems on each other, however using intuitionistic fuzzy multi-criteria decision-making method the faults/failure can easily be diagnosed.

Selection of resilient suppliers in manufacturing industries post-COVID-19: implications for economic and social sustainability in emerging economies

PurposeSelection of resilient suppliers has attracted the attention of researchers in the past one decade. The devastating effect of COVID-19 in emerging economies has provided great impetus to the selection of resilient suppliers. Under volatile and uncertain business scenarios, supplier selection is often done under imprecise and incomplete information, making the traditional decision-making methods ineffective. The purpose of this paper is to demonstrate the application of a fuzzy decision-making method for resilient supplier selection.Design/methodology/approachA group of three decision makers was considered for evaluating various alternatives (suppliers) based on their performance under different primary, sustainability and resilience criteria. Experts' opinion about each criterion and alternative was captured in linguistic terms and was modelled using fuzzy numbers. Then, an algorithm for solving resilient supplier selection problem based on the trapezoidal intuitionistic fuzzy technique for order preference by similarity to ideal solution (TrIFTOPSIS) was introduced and demonstrated through a case study.FindingsA closeness coefficient was used to rank the suppliers based on their distances from intuitionistic fuzzy positive-ideal solution and intuitionistic fuzzy negative-ideal solution. Finally, the proposed fuzzy decision making model was applied to a real problem of supplier selection in the clothing industry.Originality/valueThe presented TrIFTOPSIS model provides an effective route to prioritise and select resilient suppliers under imprecise and incomplete information. This is the first application of intuitionistic fuzzy multi-criteria decision-making for resilient supplier selection.

An Improved Fuzzy TOPSIS Method with a New Ranking Index

Owing to vague concepts frequently represented in decision data, the crisp values are inadequate to model real-life situations. In this paper, the rating of each alternative and the weight of each criterion is described by linguistic terms which can be expressed in triangular fuzzy numbers. Next, we focus on fuzzy TOPSIS (FTOPSIS) method. We show that, however, the conventional FTOPSIS is interesting, but it suffers from some flaws. The shortcomings of classical FTOPSIS are shown and some solutions are given. Further, a new similarity index is proposed and then is illustrated using numerical examples. By treating the separations of an alternative from the fuzzy positive ideal solution (FPIS) and the fuzzy negative ideal solution (FNIS) as “cost” criterion and “benefit” criterion, respectively, we reduce the original fuzzy multiple criteria decision making (FMCDM) problem to a new one with two criteria. Illustrative examples are given to show the advantages of the proposed approach.

Manager selection using Fuzzy TOPSIS method

Due to increasing competition in the global market, companies need employees especially managers who are knowledgeable and skilful to compete in the world market. Proper selection of managers can ensure the accomplishment of company goals. This study aims to propose Fuzzy Technique for order preference by similarity to ideal solution (TOPSIS) method in hiring new personnel for the middle level manager position in a company. The aim of the study is to assess the alternatives and criteria weights for selecting the middle level manager in a company by using Fuzzy TOPSIS method. A real-life data about the middle level manager selection problem in a company is implemented to demonstrate the application of Fuzzy TOPSIS method. There are three decision makers, three selected alternatives (A1, A2, A3) and twelve chosen criteria in the study. The best alternative is the alternative which is close to fuzzy positive ideal solution (FPIS) and far from fuzzy negative ideal solution (FNIS). Other than that, the sensitivity analysis is performed to validate the results of the study by shifting the weight of each criterion to zero to check whether there is any influence on the final ranking of the alternatives. The findings showed that the ranking order is A1 > A2 > A3. This shows that A1 is the most preferable candidate for the middle level manager position in the company.

A fuzzy rule-based Fuzzy Inferior Ratio method with reliability factor

Multi-criteria decision-making (MCDM) is a branch of decision-making method which able to deal with complex and conflicting decision problems. Besides, Fuzzy Multi-Criteria Decision-Making (FMCDM) method is later introduced to deal with vague and uncertain information in decision-making problems that imitates human perception in the evaluation process. Recently, Fuzzy Inferior Ratio (FIR) is developed as one of the effective FMCDM methods as it includes the compromise solution in which both distances to the Fuzzy Positive Ideal Solution (FPIS) and the Fuzzy Negative Ideal Solution (FNIS) are considered simultaneously. Nevertheless, in FIR, there is no consideration on the reliability of the information in the evaluation process. In this paper, an improvised FIR with reliability factor is introduced where the reliability factor is represented by Z-numbers. Furthermore, the lack of capability of providing systematic evaluation and consistent output raises a concern in most FMCDM methods including FIR. Hence, a decision-making procedure of Fuzzy Rule-Based FIR with reliability factor is also been proposed. A numerical example is given using the proposed procedure and a consistency analysis is carried out using the Spearman’s Rho Correlation to evaluate its effectiveness. It is found out that the proposed procedure gives a more comprehensive and systematic evaluation with the inclusion of reliability factor and the Fuzzy Rule-Based evaluation in FIR.

An extension of TOPSIS based on linguistic terms in triangular intuitionistic fuzzy structure

Chen [24] introduced the extension of TOPSIS in the fuzzy structure, while this article stretches the modern approach of TOPSIS to the intuitionistic fuzzy framework. Linguistic terms are used in this study to evaluate the weight of each criterion and the rating of alternatives in the context of a triangular intuitionistic fuzzy number. A new intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) are proposed in this model of extended TOPSIS. Euclidean distance is introduced between two triangular intuitionistic fuzzy numbers to calculate separation between each alternative to both (IFPIS) and (IFNIS). The proposed model’s mechanism is presented with the help of an algorithm, and then it is applied to the personal selection problem. Finally, a comparative study is given between this model and other TOPSIS techniques.

An axiomatic design-based mathematical programming method for heterogeneous multi-criteria group decision making with linguistic fuzzy truth degrees

This paper aims to develop a new axiomatic design-based mathematical programming method for heterogeneous multi-criteria group decision making (HMCGDM) problems with linguistic fuzzy truth degrees (LFTDs). The main contributions of this paper are summarized in five aspects: (1) The information content definitions for six types of fuzzy numbers are initially provided according to axiomatic design . (2) Considering the authority of experts on different criteria and group consensus, a bi-objective programming model is constructed to derive experts’ weights by maximizing individual deviation and minimizing group discordance. (3) Each alternative is assessed on the basis of its information content to a fuzzy positive ideal solution. Information content is firstly used to define the linguistic fuzzy consistency and inconsistency indices. (4) A bi-objective linguistic fuzzy mathematic programming model is built to determine the criteria weights, which considers consistency and inconsistency indices simultaneously. This model can be dexterously transformed into a crisp linear programming model for resolution by the linguistic scale function. (5) The group information content of each alternative to fuzzy positive ideal solution is calculated to determine the ranking order of alternatives. Finally, an example of blockchain service provider selection is given to validate the proposed method.

TOPSIS Method for Teaching Effect Evaluation of College English with Interval-Valued Intuitionistic Fuzzy Information

Teaching effect evaluation of College English is frequently considered as a multiattribute group decision-making (MAGDM) issue. Thus, a novel MAGDM method is needed to tackle it. Depending on the classical TOPSIS method and interval-valued intuitionistic fuzzy sets (IVIFSs), this paper designs a novel intuitive distance-based IVIF-TOPSIS method for teaching effect evaluation of College English. First of all, a related literature review is conducted. Furthermore, some necessary theories related to IVIFSs are briefly reviewed. In addition, the weights of attribute are decided objectively by using the CRITIC method. Afterwards, relying on novel distance measures between IVIFSs, the conventional TOPSIS method is extended to the IVIFSs to calculate closeness degree of each alternative from the interval-valued intuitionistic fuzzy positive ideal solution (IVIF-PIS). Finally, an empirical example about teaching effect evaluation of College English and some comparative analyses have been given. The results show that the designed method is useful for teaching effect evaluation of College English.

Prioritization in Strategic Environmental Assessment Using Fuzzy TOPSIS Method with Random Generation for Absent Information in South Korea

This study evaluated a fuzzy technique for order performance by similarity to ideal solution (TOPSIS) as a multicriteria decision making system that compensates for missing information with undefined weight factor criteria. The suggested Fuzzy TOPSIS was applied to ten potential dam sites in three river basins (the Han River, the Geum River, and the Nakdong River basins) in South Korea. To assess potential dam sites, the strategic environment assessment (SEA) monitored four categories: national preservation, endangered species, water quality, and toxic environment. To consider missing information, this study applied the Monte Carlo Simulation method with uniform and normal distributions. The results show that effects of missing information generation with one fuzzy set in GB1 site of the Geum River basin are not great in fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS) estimations. However, the combination of two fuzzy sets considering missing information in Gohyun stream (NG) and Hoenggye stream (NH) sites of the Nakdong River basin has a great effect on estimating FPIS, FNIS, and priority ranking in Fuzzy TOPSIS applications. The sites with the highest priority ranking in the Han River, Geum River, and Nakdong River basins based on Fuzzy TOPSIS are the Dal stream 1 (HD1), Bocheong stream 2 (GB2) and NG sites. Among the sites in all river basins, the GB2 site had the highest priority ranking. Consequently, the results coincided with findings of previous studies based on multicriteria decision making with missing information and show the applicability of Fuzzy TOPSIS when evaluating priority rankings in cases with missing information.

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.

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.

Sustainable feedstocks selection and renewable products allocation: A new hybrid adaptive utility-based consensus model

Nowadays, preferred compromise response of renewable energies' demands regarding the candidate sustainable feedstocks is a crucial issue for market change management. Thus, selecting the most suitable sustainable feedstock is a key factor for optimum renewable products allocation problem. To address the issue, this study proposes a hybrid adaptive framework based on consensus evaluation approach, weighting and ranking procedure, and preferred demand assignment under dynamic hesitant fuzzy sets. In this respect, the consensus evaluation approach is tailored regarding the direct and indirect feedback mechanisms to enhance the quality evaluation of candidate sustainable feedstocks under assessment criteria. Thereby, the weight of each criterion is determined based on the developed dynamic hesitant fuzzy entropy method and the candidate sustainable feedstocks are ranked with respect to developed dynamic hesitant fuzzy positive and negative ideal solutions. Then, a revised multi-choice goal programming model is extended regarding the dynamic hesitant fuzzy closeness indexes to attend to preferred compromise response of demand centers by optimum renewable products allocation. Meanwhile, the presented hybrid adaptive framework is implemented to a real case study to represent the applicability and efficiency of the proposed approach. Furthermore, a comparative analysis is provided by defining eight comparison indexes to compare the obtained results with two recent studies in relevant literature for representing the validation and verification of the proposed approach. The comparative analysis shows that the proposed approach versus the two other approaches has merits such as modeling of uncertainty, experts' weights, adaptive structure, unanimous agreement-based approach, and last aggregation framework. Finally, a sensitivity analysis is represented to show the sensitiveness and robustness of the obtained results from changing the criteria weights, goals values, and consensus elimination. Thereby, the sensitivity analysis indicates that the obtained ranking results are sensitive to sustainability criteria unlike the technical criterion.

Optimisation of performance parameters of stationary VCR diesel engine using hybrid FTOPSIS-FAHP approach

ABSTRACT This paper deals with the hybrid FTOPSIS-FAHP approach to optimise the performance parameters of the stationary VCR diesel engine fuelled with jatropha biodiesel. Three performance parameters known as performance defining attributes (PDAs), i.e. brake thermal efficiency, smoke and NOx, have been used for the performance prediction. Experiments on the engine have been performed at a constant speed of 1500 rpm with variation of load (12–24 Nm), compression ratio (16.5–19.5), injection timing (19–25 CA btdc) and injection pressure (180–220 bar). In total, 16 cases are designed to obtain the results. The weight of different PDAs, BTE (0.130, 0.219, 0.351), smoke (0.097, 0.151, 0.280) and NOx (0.403, 0.630, 0.957), respectively, has been evaluated with the help of FAHP. The test number (alternative) of 08 with a load of 16 Nm, compression ratio of 19.5, injection timing of 21 CA btdc and injection pressure of 210 bar exhibit the optimal formulation. Abbreviations: BSFC: Brake specific fuel consumption; BTE: Brake thermal efficiency; CA: Crank angle; CO: Carbon monoxides; CR: Compression ratio; FAHP: Fuzzy analytical hierarchy process; : Fuzzy positive ideal solution; : Fuzzy negative ideal solution; FTOPSIS: Fuzzy technique for order preference by similarity of an ideal solution; HC: Hydrocarbons; IP: Injection pressure; IT: Injection timings; MCDM: Multi criteria decision making; PDA: Performance defining attributes; PM: Particulate matter; VCR: Variable compression ratio

An interval type-2 fuzzy TOPSIS using the extended vertex method for MAGDM

In this article, the technique of order preference by similarity to an ideal solution (TOPSIS) is modified to handle interval type-2 fuzzy sets (IT2FSs) using the extended vertex method for distance measure. While the existing TOPSIS techniques for IT2FSs depend on the defuzzification of the average decision matrix or the average weighted decision matrix from the very beginning, the proposed method maintains fuzziness in the preference technique up to the hilt to avoid any information distortion which might lead to false ranking. First, the vertex method for distance measure is extended to encompass IT2FSs. The extended vertex method is an efficient simple formula that requires few computations in contrast to other distance measures based on embedding type 1 fuzzy sets or α-cuts that need special algorithms and can be restrictive in applications that require high computations. Second, the fuzzy positive and negative ideal solutions are defined. Then, the relative degree of closeness to the ideal solutions is computed for each alternative using the extended vertex method. As the relative degree of closeness of an alternative increases, its preference increases. Therefore, the preference technique avoids the flaws of the existing techniques and the computations are reduced. Two illustrative examples are given and the results are compared with the results of the existing TOPSIS methods. In light of the results and comparisons, the role of the defined ideal solutions in ranking is clarified.