Ranking Method For Fuzzy Numbers Research Articles

An extension of fuzzy TOPSIS approach using integral values for banking performance evaluation

Banks play a crucial role as financial intermediaries in advancing economies. Increasing market share is a top priority for all banks in today's fiercely competitive market. To achieve this, banks are expected to enhance their efficiency, which boosts their competitive capacity and helps decision-makers identify areas for development. This paper introduces an extended fuzzy TOPSIS approach that incorporates integral values to assess banking performance. Our method includes the averaging and normalization of decision-makers assigned ratings and weights, ensuring a standardized scale for comparison. Subsequently, we create membership functions for the ultimate fuzzy evaluation values of alternatives using interval arithmetic for fuzzy numbers. We employ a novel fuzzy number ranking method based on integral values to streamline the aggregation of fuzzy numbers to defuzzify the weighted ratings. Ultimately, we introduce a closeness coefficient for determining the ranking order of alternatives by computing their distances to both the positive and negative ideal solutions. To illustrate the effectiveness and applicability of our proposed method, we present an application example.

A new CoCoSo ranking-based QFD approach in Pythagorean fuzzy environment and its application on evaluating design attributes of mobile medical App

Quality function deployment (QFD) is a customer-driven product development technique that converts customer requirements (CRs) into design attributes (DAs) of a product and service. Nevertheless, in real situations, the traditional QFD method has been found that possesses some deficiencies, such as the accuracy assessment of relationships between CRs and DAs, and the inter-relationships among DAs. To fill in the above gaps, this study develops a new QFD approach by a CoCoSo-based ranking method under Pythagorean fuzzy environment. To begin with, an extended Pythagorean fuzzy decision-making trial and evaluation laboratory (DEMATEL) method is proposed to identify the relationships within DAs. Second, the aggregation method of the weighted average method and objective penalty function are propounded to construct the programming models for calculating the importance of DAs under Pythagorean fuzzy setting. Third, a new CoCoSo-based ranking method for Pythagorean triangular fuzzy numbers (PTrFNs) is proposed to obtain the ranking of DAs. Lastly, a case regarding “Ping An Health” mobile medical App is carried out to verify the effectiveness and superiority of the proposed QFD approach. The results show that the top DA is perceptibility. Therefore, perceptibility should be focus on firstly in the “Ping An Health” App design, such as system fluency, interface comfort and network stability. Additionally, the results show that the new QFD can express experts’ hesitant assessment information, deal with the interrelations among DAs, and yield more precise rankings of DAs in QFD.

Penerapan Metode Fuzzy Multi Criteria Decision Making Pada Interpretasi Hasil Penentuan Kemiskinan Provinsi Jawa Timur

Fuzzy Multi Criteria Decision Making (FMCDM) method is a method of making decisions based on certain criteria to determine the best alternative among several alternatives. The purpose of the FMCDM method is to obtain the best alternative that is accurate and optimal. Poverty is a condition in which economic needs are not met against the average standard of living in the region. Poverty is a very important issue for the government or related agencies. This problem can be solved by determining the district/city area which is included in the poor category. So a method is needed that can be used to determine the existence of poverty in an area. The solution to overcome this problem is to use the FMCDM method. The solution to overcome this problem is to use the FMCDM method. The FMCDM process begins by determining objectives, alternative decisions, and a collection of criteria that will be used to determine poor districts/cities in East Java Province. The alternative decisions consist of 38 regencies/cities of East Java Province, while the set of criteria consists of the Percentage of Poor People, Human Development Index, Poverty Depth Index, and Poverty Severity Index. The next step evaluates the fuzzy set by aggregating the weight of the criteria and the degree of fit of each alternative to its criteria. The aggregation result is called the fuzzy match index which consists of three values, namely, the value which represents the result of the lower limit aggregation, the value which represents the middle bound, and the value which represents the upper bound value. The three values are ranked using the ranking method for fuzzy numbers with degrees of optimasan. So that the total integral value for each alternative will be a decision from the highest priority to the lowest in determining the districts / cities included in the poor category and as an effort to reduce poverty in East Java Province.

Ranking Method of Intuitionistic Fuzzy Numbers and Multiple Attribute Decision Making Based on the Probabilistic Dominance Relationship

The uncertainty of intuitionistic fuzzy numbers (IFNs) is further enhanced by the existence of the degree of hesitation (DH). The shortcomings of existing researches are mainly reflected in the following situations: when comparing IFNs, the comparison rules of IFNs are difficult to apply to the comparison of any two IFNs, or the relevant methods do not fully consider the uncertainty expressed by DH. Thus, the rationality of the decision results needs to be improved. On the other hand, multi-attribute decision making (DADM) based on IFNs is often not objective due to the need to determine the attribute weight. Moreover, the strict condition of attribute aggregation of classical dominance relation makes it a method that fails considering the practical application. Aiming at the comparison problem of IFNs, this paper takes probability conversion as the starting point and proposes an IFN comparison method based on the area method, which can better deal with the comparison problem of “either superior or inferior” IFNs. In addition, aiming at the MADM problem of an intuitionistic fuzzy information system, we propose an intuitionistic fuzzy probabilistic dominance relation model and construct the MADM method under the probabilistic dominance relation. The series properties of IFNs and probabilistic dominance relation were summarized and proved, which theoretically ensured the scientificity and rigor of the method. The results show that the comparison and ranking method of IFNs proposed in this paper can be applied to the comparison of any two IFNs, and the dominance degree of IFNs is presented in the form of probability, which is more flexible and practical than the classical method. The probabilistic dominance relation method based on IFNs avoids the problem of determining attribute weights subjectively or objectively, and the decision maker can reflect decision preference by adjusting decision parameters to better match the actual problem. The application of this model to a campus express site evaluation further verifies the feasibility of the proposed method and the rationality of the results. In addition, various extension problems of the model and method proposed in this paper are discussed, which pave the way for future related research. This paper constructs a complete decision-making framework through theoretical analysis and application from practical problems, which provides a reference for enriching and improving uncertain decision-making theory and the MADM method.

A new ranking method for trapezoidal intuitionistic fuzzy numbers and its application to multi-criteria decision making

The ranking of intuitionistic fuzzy numbers is paramount in the decision making process in a fuzzy and uncertain environment. In this paper, a new ranking function is defined, which is based on Robust’s ranking index of the membership function and the non-membership function of trapezoidal intuitionistic fuzzy numbers. The mentioned function also incorporates a parameter for the attitude of the decision factors. The given method is illustrated through several numerical examples and is studied in comparison to other already-existent methods. Starting from the new classification method, an algorithm for solving fuzzy multi-criteria decision-making (MCDM) problems is proposed. The application of said algorithm implies accepting the subjectivity of the deciding factors, and offers a clear perspective on the way in which the subjective attitude influences the decision-making process. Finally, a MCDM problem is solved to outline the advantages of the algorithm proposed in this paper.

A unified ranking method of intuitionistic fuzzy numbers and Pythagorean fuzzy numbers based on geometric area characterization

A unified ranking method of intuitionistic fuzzy numbers and Pythagorean fuzzy numbers based on geometric area characterization

A user-configurable and explainable framework for ranking fuzzy numbers

Fuzzy number ranking is an important and fundamental subject matter within fuzzy set theory, just as the ranking of crisp values is important and fundamental to classical mathematics. For a user of fuzzy set theory, a fuzzy number ranking method that is user-configurable and user-explainable is highly desirable -- being user-configurable is important for ensuring the fitness of the fuzzy ranking method in relation with the assumptions of the application domain of interest, and being user-explainable is important for providing confidence to the user and the stakeholders of the appropriateness of the ranking outcomes in an expert system. In this article, a simple framework for ranking fuzzy numbers is proposed and developed. This simple framework consists of concrete constructs similar to the building blocks in a LEGO set, for the user to configure his/her own fuzzy ranking operator. The proposed framework is applied to examples taken from previous comparative studies from the fuzzy set theory literature, and to multiple-criteria-decision-making and other fuzzy ranking problems. First of all, these demonstrations will illustrate that fuzzy number ranking can indeed be done in a concrete, user-configurable, and user-explainable manner. Thus, the proposed framework represents a viable alternative for the fuzzy ranking literature, which currently consists of various ranking methods that are mathematically sophisticated yet oftentimes highly non-trivial for the user to interpret and to adapt/re-configure for his/her applications. Secondly, we note that the precursor of the proposed framework has been successfully employed to re-derive, instead of postulate, commonly used fuzzy set-theoretic operators, and to derive fuzzy arithmetic operators that do not produce anomalies plaguing other fuzzy arithmetic approaches. Thus, the applicability of such a framework to fuzzy ranking will further demonstrate its potential as a fundamental framework for tackling a wide range of issues in fuzzy set theory, rather than being an isolated approach limited to narrow aspects of fuzzy set theory.

A deterministic and nature-inspired algorithm for the fuzzy multi-objective path optimization problem

Increasing evaluation indexes have been involved in the network modeling, and some parameters cannot be described precisely. Fuzzy set theory becomes a promising mathematical method to characterize such uncertain parameters. This study investigates the fuzzy multi-objective path optimization problem (FMOPOP), in which each arc has multiple crisp and fuzzy weights simultaneously. Fuzzy weights are characterized by triangular fuzzy numbers or trapezoidal fuzzy numbers. We adopt two fuzzy number ranking methods based on their fuzzy graded mean values and distances from the fuzzy minimum number. Motivated by the ripple spreading patterns on the natural water surface, we propose a novel ripple-spreading algorithm (RSA) to solve the FMOPOP. Theoretical analyses prove that the RSA can find all Pareto optimal paths from the source node to all other nodes within a single run. Numerical examples and comparative experiments demonstrate the efficiency and robustness of the newly proposed RSA. Moreover, in the first numerical example, the processes of the RSA are illustrated using metaphor-based language and ripple spreading phenomena to be more comprehensible. To the best of our knowledge, the RSA is the first algorithm for the FMOPOP that can adopt various fuzzy numbers and ranking methods while maintaining optimality.

Implementasi Fuzzy Multi Criteria Decision Making Pada Seleksi Beasiswa Bank Indonesia

The Bank Indonesia Scholarship is a scholarship provided by Bank Indonesia for students at various universities, one of which is UIN Maulana Malik Ibrahim Malang. In the scholarship selection process, there are several criteria that affect the graduation of prospective scholarship recipients. However, often the process is not transparently. So a calculation method is needed, one of which is using Fuzzy Multi Criteria Decision Making (FMCDM). With FMCDM it can help to get an accurate and optimal decision on scholarship recipients. The FMCDM process begins with collecting information related to scholarships, scholarship applicants, and a set of criteria that will be used for consideration of scholarship acceptance. The set of criteria consists of 11 criteria, namely, Academic Achievement Index (GPA), international level achievement, national level achievement, provincial level achievement, district/city level achievement, father's occupation, mother's income, number of family dependents, house area, land and building tax, as well as electricity bills. The next step is to evaluate the fuzzy set by aggregating the weight of the criteria and the degree of compatibility of each alternative with the criteria. The aggregation result is called the fuzzy fit index which consists of 3 values, namely, the y value which represents the lower limit of the aggregation result, the q value which represents the middle limit, and the z value which represents the upper limit value. The three values are ranked using a ranking method for fuzzy numbers with a degree of optimism. So that the total integral value for each alternative will be obtained, which will be the decision in accepting the scholarship. From the results of the FMCDM, there is a ranking of decision alternatives from the highest priority to the lowest in determining scholarship acceptance.

A New Ranking Method for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Multi-Criteria Decision-Making

Ranking of interval-valued intuitionistic fuzzy numbers (IVIFNs) is an important task for solving real-life Decision-Making problems. It is a potential area of research that has attracted the researchers working in fuzzy mathematics. Researchers worldwide are looking for a unique ranking principle that can be used to discriminate any two arbitrary IVIFNs. Various ranking functions on the set of IVIFNs have been proposed. However, every method has some drawbacks in ranking arbitrary IVIFNs due to the partial ordering. This paper introduces a new ranking principle for comparing two arbitrary IVIFNs by defining a new score function based on the non-membership value of IVIFNs. In this paper, firstly, the limitations of a few well-known and existing ranking methods for IVIFNs have been discussed. Secondly, a new non-membership score on the class of IVIFNs has been introduced. Thirdly, the superiority of the proposed score function in ranking arbitrary IVIFNs over the existing methods has been demonstrated. Finally, the proposed non-membership score function has been utilized in interval-valued intuitionistic fuzzy TOPSIS (IVIF-TOPSIS) using numerical examples.

Preference implication-based approach to ranking fuzzy numbers

Dombi and Baczy'{n}ski presented a new approach to the problem of implication operation by introducing the preference implication, which has very advantageous properties. In this paper, it is presented how the preference implication is connected with soft inequalities and with sigmoid functions. Utilizing this connection the preference implication-based preference measure for two fuzzy numbers is introduced and its key properties, including the reciprocity, are described. Then, the exact expression for computing the new preference measure for trapezoidal fuzzy numbers is presented. Here, using the new preference measure, two crisp relations over trapezoidal fuzzy numbers are introduced. It is shown that one of them is a strict (but not a total) order relation, and the other one is an equivalence relation. The strict order relation can be used to rank comparable fuzzy numbers, while the equivalence relation, which we call the indifference relation, expresses that the order of some fuzzy numbers is indifferent. These two crisp relations can be used to rank a collection of trapezoidal fuzzy numbers. Lastly, the proposed ranking method is compared with some well-known existing fuzzy number ranking methods.

A Sophisticated Ranking Method of Fuzzy Numbers Based on the Concept of Exponential Area

Uncertainty is an unavoidable components of decision making process. The ranking of fuzzy numbers which deals with such uncertainties play again a significant role in the process. Fuzzy numbers must be ranked in order to take the appropriate action by a decision maker in any real life situation. A few numbers of ranking techniques have been encountered in last few decades. However, existing techniques are situation-dependent which have drawbacks/shortcomings. In this regard, this paper presents a sophisticated ranking method based on the concept of the exponential area of the fuzzy numbers. The outputs obtained from this approach are obtained to be more efficient in comparison to the other ranking methods and outperform in all situations. The novelty and validity have been established through comparison with existing works. Furthermore, the ranking approach has been applied in medical decision making problem and the results obtained by the approach absolutely conform with analytical results and human intuitions as well.

A complete ranking method for interval-valued intuitionistic fuzzy numbers and its applications to multicriteria decision making

In this study, a complete ranking method for interval-valued intuitionistic fuzzy numbers (IVIFNs) is introduced by using a score function and three types of entropy functions. This work is motivated by the work of Lakshmana Gomathi Nayagam et al. (Soft Comput 21, 7077–7082, 2017) in which a novel non-hesitant score function for the theory of interval-valued intuitionistic fuzzy sets was introduced. The authors claimed that the proposed non-hesitant score function could overcome the shortcomings of some familiar methods. By using some examples, they pointed out that the non-hesitant score function is better compared with Sahin’s and Zhang et al.’s approaches. It is pointed out that although in some specific cases, the cited method overcomes the shortcomings of several of the existing methods mentioned, it also created new defects that can be solved by other methods. The main aim of this study is to give a complete ranking method for IVIFNs which can rank any two arbitrary IVIFNs. At last, two examples to demonstrate the effectiveness of the proposed method are provided.

A novel FMEA model based on fuzzy multiple-criteria decision-making methods for risk assessment

PurposeRisk assessment is a very important step toward managing risks in various organizations and industries. One of the most extensively applied risk assessment techniques is failure mode and effects analysis (FMEA). In this paper, a novel fuzzy multiple-criteria decision-making (MCDM)-based FMEA model is proposed for assessing the risks of different failure modes more accurately.Design/methodology/approachIn this model, the weight of each failure mode is considered instead of risk priority number (RPN). Additionally, three criteria of time, cost and profit are added to the three previous risk factors of occurrence (O), severity (S) and detection (D). Furthermore, the weights of the mentioned criteria and the priority weights of the decision-makers calculated by modified fuzzy AHP and fuzzy weighted MULTIMOORA methods, respectively, are considered in the proposed model. A new ranking method of fuzzy numbers is also utilized in both proposed fuzzy MCDM methods.FindingsTo show the capability and usefulness of the suggested fuzzy MCDM-based FMEA model, Kerman Steel Industries Factory is considered as a case study. Moreover, a sensitivity analysis is conducted for validating the achieved results. Findings indicate that the proposed model is a beneficial and applicable tool for risk assessment.Originality/valueTo the best of authors’ knowledge, no research has considered the weights of failure modes, the weights of risk factors and the priority weights of decision-makers simultaneously in the FMEA method.

A New Ranking Approach for Solving Fully Fuzzy Transportation Problem in Intuitionistic Fuzzy Environment

Ranking of intuitionistic fuzzy numbers is an engrossing and very difficult task among the several researchers. The present studies introduce a new ranking method for intuitionistic fuzzy numbers (IFN) by using the concept of distance minimizer between two intuitionistic fuzzy numbers, with the help of their defined membership and non-membership functions. The proposed ranking method for intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied the developed ranking method to solve fully intuitionistic fuzzy transportation problems in which cost, supplies and requirements all are in term of intuitionistic fuzzy numbers. The developed method has been illustrated by an example, and the result obtained by the proposed method shows a superior performance compared with some existing methods available in the literature.

A noval ranking approach based on incircle of triangular intuitionistic fuzzy numbers

Since proposed by Zadeh in 1965, ordinary fuzzy sets help us to model uncertainty and developed many types such as type 2 fuzzy, intuitionistic fuzzy, hesitant fuzzy etc. Intuitionistic fuzzy sets include both membership and non-membership functions for their each element. Ranking of a number is to identify a relationship of scalar quantity between these numbers. Ranking of fuzzy numbers play an important role in modeling problems such as fuzzy decision making, fuzzy linear programming problems. In this study, a new ranking method for triangular intuitionistic fuzzy numbers is proposed. The method based on the incircle of the membership function and non-membership function of TIFN uses lexicographical order to rank intuitionistic fuzzy numbers. Two examples are provided to illustrate the applicability of the method. Also, a comparative study is performed to demonstrate the validity of the proposed method. The results indicate that proposed method is consistent with other methods in the literature. Also, the method overcomes the problems such as numbers being very small or close to each other.

A ranking method based on interval type-2 fuzzy sets for multiple attribute group decision making

Ranking of fuzzy numbers has become an important research direction for decision-making problems due to its role to find the best objects under uncertainty. In this paper, we propose a new approach to perform multiple attribute group decision-making (MAGDM) problems using the ranking of interval type-2 fuzzy sets. Initially, a new ranking method for interval type-2 fuzzy numbers based on centroid and rank index has been proposed. Next, we present a comparative study to analyze the ranking values of the proposed method with the existing approaches, where we explore the necessity of the proposed ranking method. After that, a new MAGDM approach has been developed using the proposed ranking procedure to solve uncertain MAGDM problems. Finally, the applicability of the proposed approach has been illustrated using two numerical examples and a case study related to car-sharing problems. The proposed study exhibits a useful way to solve fuzzy MAGDM problems with much efficient manner since it applies interval type-2 fuzzy sets compared to type-1 fuzzy sets to signify the evaluating values and weights of the attributes.

Trapezoidal Linguistic Cubic Fuzzy TOPSIS Method and Application in a Group Decision Making Program

Abstract The aim of this paper is to define some new operation laws for the trapezoidal linguistic cubic fuzzy number and Hamming distance. Furthermore, we define and use the trapezoidal linguistic cubic fuzzy TOPSIS method to solve the multi criteria decision making (MCDM) method. The new ranking method for trapezoidal linguistic cubic fuzzy numbers (TrLCFNs) are used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method.

A novel parametric ranking method for intuitionistic fuzzy numbers

Since the inception of intuitionistic fuzzy sets in 1986, many authors have proposed different methods for ranking intuitionistic fuzzy numbers (IFNs). How ever, due to the complexity of the problem, a method which gives a satisfactory result to all situations is a challenging task. Most of them contained some shortcomings, such as requirement of complicated calculations, inconsistency with human intuition and indiscrimination and some produce different rankings for the same situation and some methods cannot rank crisp numbers. For overcoming the above problems, in this paper, a new parametric ranking method for IFNs is proposed. It is developed based on the concept α-cuts and β-cuts and area on left side of IFNs. The proposed ranking method is applied to solve partner selection problem in which the rating of partner on attributes are expressed by using triangular IFNs. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method.

A Novel Ranking Approach to Solving Fully LR-Intuitionistic Fuzzy Transportation Problems

To the extent of our knowledge, there is no method in fuzzy environment to solving the fully LR-intuitionistic fuzzy transportation problems (LR-IFTPs) in which all the parameters are represented by LR-intuitionistic fuzzy numbers (LR-IFNs). In this paper, a novel ranking function is proposed to finding an optimal solution of fully LR-intuitionistic fuzzy transportation problem by using the distance minimizer of two LR-IFNs. It is shown that the proposed ranking method for LR-intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied ranking approach to solve an LR-intuitionistic fuzzy transportation problem in which all the parameters (supply, cost and demand) are transformed into LR-intuitionistic fuzzy numbers. The proposed method is illustrated with a numerical example to show the solution procedure and to demonstrate the efficiency of the proposed method by comparison with some existing ranking methods available in the literature.