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This paper proposes the concept of a centroid for picture fuzzy numbers and particularly for triangular picture fuzzy numbers. The concept allows the implementation of a ranking function for the triangular picture fuzzy numbers, which has the advantage of reuniting the symmetry and asymmetry of the information. Then, empirical applications are considered for the picture fuzzy numbers. Specifically, multiple TPFNs are considered. The ranked, A comparison study is conducted for said ranked TPFNs relative to other methodologies in the specialized literature, illustrating that these methods exhibit limitations in specific scenarios. An additional compelling example is provided: before elections, opinion surveys are extensively utilised to assess voter intentions about candidates. The survey findings can be analysed through PFNs and the ranking mechanism proposed in this study. Another contribution of this paper is the development an algorithm meant to solve decision making problems in an uncertain environment. This is applied in the practical context of comparing the performance of several standards in two successive evaluations. [ABSTRACT FROM AUTHOR]

Calculus is a mathematics subject normally taught at the tertiary level. Many calculus textbooks with different approaches and styles have been published to cater to the needs of students. The selection of calculus textbooks is essential as it can help teachers and students to optimize their usage. Textbook selection problem is one type of multiple-criteria decisionmaking problem where the selection is based on several criteria. Thus, ranking fuzzy numbers based on the area dominance method ranks the calculus textbook.

The concept of alpha-order has been recently introduced as a binary relation that allows ranking fuzzy sets with bounded support and whose β -cuts are closed subsets with a finite number of connected components. This paper explores some key properties of such alpha-order. Specifically, we will focus on admissibility, a fundamental property for any ranking method defined for fuzzy numbers since it guarantees that such a ranking method is consistent with the usual order on the real line. [ABSTRACT FROM AUTHOR]

Supplier selection is a critical factor in the success of fertigation systems, which integrate irrigation and fertilization to enhance agricultural productivity. This process's inherent uncertainty and complexity necessitate decision-making methodologies considering human judgment and risk preference factors. This study proposes the fuzzy DEMATEL method with a ranking based on the degree of optimism to evaluate and prioritise supplier selection criteria in fertigation systems. Six experts were involved in evaluating the influence of criteria such as price, quality, delivery, public procurement policy, technical, and managerial. The proposed method consists of 11 steps, including developing a fuzzy direct-relation matrix, average matrix, normalised fuzzy direct-relation matrix, fuzzy total relation matrix, and ranking based on left and right integral value. The left integral value represents the decision maker's perspective that is more inclined towards pessimism, while the right integral value represents the perspective that is more inclined towards optimism. The proposed method is implemented in the selection of supplier criteria in the fertigation system at one branch of RISDA (Rubber Industry Smallholders Development Authority) on the East Coast of Malaysia. The findings reveal that technical and quality criteria are paramount, though their relative importance shifts depending on the decision-maker’s degree of optimism. Specifically, technical criteria are prioritised by neutral and optimistic decision-makers, while quality criteria are regarded as most important by pessimistic decision-makers. Furthermore, the study identifies public procurement policy and technical criteria as part of the causal group, significantly influencing other criteria such as price, delivery, and managerial factors. The results align with previous research, confirming the consistency aspect of the fuzzy DEMATEL method with a degree of optimism-based ranking. This approach provides a comprehensive decision for agricultural decision-makers, facilitating more greater knowledge and balanced supplier selection decisions.

This paper proposes the concept of a centroid for picture fuzzy numbers and particularly for triangular picture fuzzy numbers. The concept allows the implementation of a ranking function for the triangular picture fuzzy numbers, which has the advantage of reuniting the symmetry and asymmetry of the information. Then, empirical applications are considered for the picture fuzzy numbers. Specifically, multiple TPFNs are considered. The ranked, A comparison study is conducted for said ranked TPFNs relative to other methodologies in the specialized literature, illustrating that these methods exhibit limitations in specific scenarios. An additional compelling example is provided: before elections, opinion surveys are extensively utilised to assess voter intentions about candidates. The survey findings can be analysed through PFNs and the ranking mechanism proposed in this study. Another contribution of this paper is the development an algorithm meant to solve decision making problems in an uncertain environment. This is applied in the practical context of comparing the performance of several standards in two successive evaluations.

Real-world problems often deal with uncertainties related to imprecision and vagueness, for which fuzzy modeling has provided a successful approach. Ranking fuzzy numbers is a necessary and complex task in multiple processes, such as decision making. To facilitate the task of ranking fuzzy numbers, it has been introduced an approach to construct fuzzy distances from classical interval distances because their α-cuts are continuous intervals. Usually, extant interval distances use interval endpoints or midpoints, leading to results that might not reflect the correct distance because of information loss. This paper introduces a new fuzzy distance based on a novel interval distance that considers all points within the intervals by using the concept of integration to calculate the average distance between all points belonging to two intervals, respectively. Subsequently, a series of distances between fuzzy numbers based on the proposed interval distances are defined and proved. A new method for ranking fuzzy numbers using the new fuzzy distances is then presented. Finally, the validity and effectiveness of the proposed distances will be demonstrated by a comparative analysis of numerical examples. [ABSTRACT FROM AUTHOR]

In entrepreneurship management, the evaluation and selection of startups for acceleration programs, especially technology-based startups, are crucial. This process involves considering numerical and qualitative criteria such as sales, prior startup experience, demand validation, and product maturity. To effectively rank startups based on the varying importance of these criteria, a fuzzy multi-criteria decision-making (MCDM) approach is needed. Although MCDM methods have been successful in handling complex problems, their application in startup selection and evaluating criteria interrelationships from the accelerator perspective is underexplored. To address this gap, a hybrid DEMATEL-ANP-based fuzzy PROMETHEE II model is proposed in this study, facilitating startup ranking and examining interrelationships among factors. The resulting preference values are fuzzy numbers, necessitating a fuzzy ranking method for decision-making. An extension of ranking fuzzy numbers using a spread area-based relative maximizing and minimizing set is suggested to enhance the flexibility of existing ranking MCDM methods. Algorithms, formulas, and a comparative analysis validate the proposed method, while a numerical experiment verifies the viability of the hybrid model. The final ranking of four startup projects is A 4 < A 1 < A 3 < A 2 which indicates that startup project A2 has the highest comprehensive potential, followed by startup project A3. [ABSTRACT FROM AUTHOR]

Even though various ranking fuzzy numbers approaches have been presented so far, none of them can always provide satisfactory results in every situation. Some are counterintuitive, and some are inconsistent for the same circumstances. To overcome the issues mentioned above, we present a new technique for ranking fuzzy numbers using the mean value of the two points. The points are taken on the left and the right membership functions (reference functions) such that they divide the respective membership function in the same ratio m: n. The proposed technique determines the order of the fuzzy numbers significantly. To use this technique, the membership functions need not be normal and linear. [ABSTRACT FROM AUTHOR]

In entrepreneurship management, the evaluation and selection of startups for acceleration programs, especially technology-based startups, are crucial. This process involves considering numerical and qualitative criteria such as sales, prior startup experience, demand validation, and product maturity. To effectively rank startups based on the varying importance of these criteria, a fuzzy multi-criteria decision-making (MCDM) approach is needed. Although MCDM methods have been successful in handling complex problems, their application in startup selection and evaluating criteria interrelationships from the accelerator perspective is underexplored. To address this gap, a hybrid DEMATEL-ANP-based fuzzy PROMETHEE II model is proposed in this study, facilitating startup ranking and examining interrelationships among factors. The resulting preference values are fuzzy numbers, necessitating a fuzzy ranking method for decision-making. An extension of ranking fuzzy numbers using a spread area-based relative maximizing and minimizing set is suggested to enhance the flexibility of existing ranking MCDM methods. Algorithms, formulas, and a comparative analysis validate the proposed method, while a numerical experiment verifies the viability of the hybrid model. The final ranking of four startup projects is A4

Ranking generalized fuzzy numbers plays an important role in many applied models and, in particular, decision-making procedures. In ranking process of two generalized fuzzy numbers, it is natural to compare the sets of values in support of two generalised fuzzy numbers. Accordingly, the comparison of a real number and a generalised fuzzy number as well as two generalised fuzzy numbers have to be considered. On the other hand, it is seen that a definitive process of comparison of a real number and a generalised fuzzy number, as well as two generalised fuzzy numbers, is not possible. So in this study, a method for comparing a real number and a generalised fuzzy number with a degree of accuracy (between a zero and one) is defined and then the method is generalized to compare two generalised fuzzy numbers. In general, an index to rank a real number and generalised fuzzy number is constructed. Eventually, this index is extended to rank two generalised fuzzy numbers based on the concept of accuracy of comparison. The advantage of our method is that it can compare two generalised fuzzy numbers with an accuracy of comparison. Also, a definition is introduced to make a definitive comparison. Finally, the proposed method is illustrated by some numerical examples. [ABSTRACT FROM AUTHOR]

The use of fuzzy set theory in the analytic hierarchy process (AHP) has gained popularity in recent years as part of the multiple criteria decision‐making (MCDM) process to more realistically reflect human judgment. However, due to the nature of fuzzy calculations, this situation imposes more computational load. The aim of this study is to propose methods for obtaining accurate weights from fuzzy pairwise comparison matrices with the least amount of computational load possible. In this context, two different fuzzy AHP (FAHP) methods based on fuzzy numbers ranking methods have been proposed and these proposed methods are compared with commonly accepted FAHP methods. Magnitude‐ based fuzzy AHP (MFAHP), which is one of the proposed methods, has outperformed all other methods according to accurate weight and computational load. Although the other proposed method, called the total difference‐based fuzzy AHP (TDFAHP), gave better results than the frequently used Chang's fuzzy extent analysis method, it could not produce more accurate weight results than many other methods in general. But performance analysis shows that it is as good as the MFAHP in terms of computational load. The use of fuzzy set theory in the analytic hierarchy process (AHP) has gained popularity in recent years as part of the multiple criteria decision‐making (MCDM) process to more realistically reflect human judgment. However, due to the nature of fuzzy calculations, this situation imposes more computational load. The aim of this study is to propose methods for obtaining accurate weights from fuzzy pairwise comparison matrices with the least amount of computational load possible. In this context, two different fuzzy AHP (FAHP) methods based on fuzzy numbers ranking methods have been proposed and these proposed methods are compared with commonly accepted FAHP methods. Magnitude‐ based fuzzy AHP (MFAHP), which is one of the proposed methods, has outperformed all other methods according to accurate weight and computational load. Although the other proposed method, called the total difference‐based fuzzy AHP (TDFAHP), gave better results than the frequently used Chang's fuzzy extent analysis method, it could not produce more accurate weight results than many other methods in general. But performance analysis shows that it is as good as the MFAHP in terms of computational load. [ABSTRACT FROM AUTHOR]

Ranking the fuzzy numbers plays an important role in fuzzy decision-making, but it is challenging to rank multiple fuzzy numbers comprehensively and effectively. In previous studies, various properties and factors of fuzzy numbers are considered to construct the ranking scoring formula. Therefore, in theory, the uncertainty of fuzzy numbers can be better defuzzified, and the formula can measure the characteristics of fuzzy numbers. In application, it is meaningful and valuable to investigate the use of fuzzy number's ranking score in fuzzy portfolio to measure characteristics of the asset. Based on the classical mean-variance (M-V) model and four kinds of ranking score formulas, this paper constructs the score-variance (S-V) models. Finally, a numerical experiment is presented to illustrate the feasibility and validity of our proposed S-V model. Compared with the M-V model, on one hand the results of our proposed models are generally consistent with the classic M-V model; on the other hand, the return of our proposed model is slightly smaller in some part, but it performs better in skewness and Sharpe Ratio. [ABSTRACT FROM AUTHOR]

The numerous studies on comparing and ranking fuzzy numbers clear that this task is still young. However, the observation that many papers do not hesitate to use some incorrect ranking methods in risk analysis problems, encouraged the author to point out the shortcoming of some of these methods. In this note, we review briefly the methods for ranking fuzzy number in risk analysis.

It would be hard to deny the importance of fuzzy number ranking in fuzzy-based applications. The definition of fuzzy ranking, however, evades an easy description due to the overlapping of fuzzy sets. While many researchers have addressed this subject, close examination reveals that their results suffer from one or more shortcomings such as image-ranking problems or ranking two equally embedded fuzzy numbers with the same centroid and different spreads. This paper proposes a new fast and straightforward computational approach to ranking fuzzy numbers that aims to overcome such problems. The proposed approach considers several important factors such as spread, skewness and center, in addition to human intuition. Further, the proposed ranking approach involves a composition of these factors as demonstrated in the several examples provided and in comparison with other existing approaches. [ABSTRACT FROM AUTHOR]

Huynh et al. introduced a probability-based fuzzy relation for comparing fuzzy numbers (see V. Huynh, Y. Nakamori and J. Lawry (2008) [40]), but they did not detail how to compute it. Here, we will consider this fuzzy relation as a probability-based preference intensity index and present closed formulas for the integrals needed to compute this index for fuzzy sets that have trapezoidal membership functions. Also, we will propose an algorithm to compute this index and a numerical method to approximate it. The comparison of two fuzzy numbers should also be able to capture the situation where the order of the fuzzy numbers cannot be judged; and so, their order may be considered as being indifferent. Here, using the probability-based preference intensity index, we will introduce two crisp relations, which have a common parameter, over a collection of fuzzy sets that have trapezoidal membership functions. Next, we will show that - depending on the parameter value - one of them is a strict order relation and the other one may be interpreted as a relation that expresses the order indifference of fuzzy numbers. We will call this latter one the order indifference relation. Lastly, we will demonstrate how these two relations can be utilized to rank a collection of fuzzy sets that have trapezoidal membership functions. [ABSTRACT FROM AUTHOR]

Abstract The choice of suitable robots in manufacturing, to improve product quality and to increase productivity, is a complicated decision due to the increase in robot manufacturers and configurations. In this article, a novel approach is proposed to choose among alternatives, differently assessed by decision makers on different criteria, to make the final evaluation for decision-making. The approach is based on the ellipsoid algorithm for systems of linear inequalities. Most of the ranking methods depend on integration that becomes complicated for nonlinear membership functions, which is the case in robot selection. The method simply uses the membership function or its derivative. It takes the decision maker’s attitude in ranking. It effectively ranks fuzzy numbers and their images, preserving symmetry. It is a simple recursive algebraic formula that can be easily programmed. The performance of the algorithm is compared with the performance of some existing methods through several numerical examples to illustrate its advantages in ranking, and a robot selection problem is solved.

In the traditional transportation problem, it is assumed that decision makers are confident about the exact values of transportation costs, supply and demand of the product. When solving a transportation problem with inaccurately determined transportation costs, supply and demand quantities, a fuzzy approach is used. In this paper, a transportation problem based on statistical data is considered. The frequency distributions on the transportation costs and the supply and demand quantities in real-life transportation problems are used as the base for determining the parameters of exponential membership functions. An approach for solving fuzzy transportation problem using exponential fuzzy numbers is proposed. A numerical example is solved to illustrate the described approach [ABSTRACT FROM AUTHOR]

In this paper, we present the first moment have been defined based on the center of mass from the fuzzy number, then with calculating area between the center of mass, a new ranking method has been proposed. At last, we present some numerical examples to illustrate our proposed method, comparing with distance index ranking method. [ABSTRACT FROM AUTHOR]

Fuzzy numbers are used to represent numerical quantities in a vague environment since the measurements are imprecise in nature in this environment. Ranking fuzzy numbers is then an important issue for decision-making problems in a fuzzy environment. Most of the existing ranking methods transform a fuzzy number into a real number based on certain criteria. On the other hand, other methods define a ranking index between two fuzzy sets or between a fuzzy set and others. However, there is yet no method that can always give a satisfactory solution. In this paper, the authors propose a new algorithm for ranking of trapezoidal fuzzy numbers. This method is based on the principle that there are only four possible topological configurations when we compare two trapezoidal fuzzy numbers. Moreover, the proposed method is consistent with our intuition and, when it is necessary, takes into account the decision-maker’s risk-attitude. The paper also presents several comparative examples and an application demonstrating the usage, advantages (simplicity, flexibility, practicability, etc.) and applicability of the proposed ranking method. [ABSTRACT FROM AUTHOR]

In this paper, a new geometric method for ordering generalized trapezoidal fuzzy numbers with different left and right heights, based on the Gergonne point of a triangle is presented. The suggested method can order not only generalized trapezoidal fuzzy numbers but also crisp numbers and generalized triangular fuzzy numbers with the same centroid point. We also give an application of the proposed ordering method to the fuzzy matrix games, whose payoffs are represented by generalized trapezoidal fuzzy numbers with different left and right heights. [ABSTRACT FROM AUTHOR]

The incentre and circumcentre are two important concepts in geometric quality of triangle. Rouhparvar [Appl. Soft Comput. 30(2015) 577-584] presented the incentre point computational formula for defuzzification of generalized fuzzy numbers. On this basis, we will further consider the circumcenter point computational formula of generalized fuzzy numbers. This paper presents a new method for ranking fuzzy numbers with convex combination coordinate points of incentre and circumcentre that is an extension of Rouhparvar’s method. This extension method can effectively rank various fuzzy numbers and their images. Some numerical examples are illustrated to show the utility of proposed method. [ABSTRACT FROM AUTHOR]

Fuzzy risk analysis, as a powerful tool to address uncertain information, can provide an appropriate method for risk analysis. However, the previous fuzzy risk analysis methods still have some weaknesses. To overcome the weaknesses of existing fuzzy risk analysis methods, a novel method for ranking generalized fuzzy numbers is proposed for addressing fuzzy risk analysis problems. In the proposed method, a new value of ranking score is obtained based on ordered weighted averaging (OWA) operator. The proposed method takes into consideration of the different importance of the three scoring factors defuzzified value, height and spread. Comparing to some existing methods, the new method can get more reasonable results in some situations. [ABSTRACT FROM AUTHOR]

The choice of suitable robots in manufacturing, to improve product quality and to increase productivity, is a complicated decision due to the increase in robot manufacturers and configurations. In this article, a novel approach is proposed to choose among alternatives, differently assessed by decision makers on different criteria, to make the final evaluation for decision-making. The approach is based on the ellipsoid algorithm for systems of linear inequalities. Most of the ranking methods depend on integration that becomes complicated for nonlinear membership functions, which is the case in robot selection. The method simply uses the membership function or its derivative. It takes the decision maker’s attitude in ranking. It effectively ranks fuzzy numbers and their images, preserving symmetry. It is a simple recursive algebraic formula that can be easily programmed. The performance of the algorithm is compared with the performance of some existing methods through several numerical examples to illustrate its advantages in ranking, and a robot selection problem is solved. [ABSTRACT FROM AUTHOR]

Failure mode and effects analysis (FMEA) is one of the most important risk assessment tools which has been extensively used in different industries and organizations. In the conventional FMEA, sometimes the difference between some failure modes cannot be distinguished. In order to evaluate various failure modes more precisely, a novel fuzzy hybrid model for FMEA is proposed in this paper. In this method, fuzzy weighted risk priority number (FWRPN) is considered instead of RPN for each failure. The weights of the three factors and the weights of failure modes are computed by extended fuzzy AHP and fuzzy MULTIMOORA methods, respectively. The proposed fuzzy MULTIMOORA method calculates the weight of each failure based on three criteria of time, cost, and profit through fuzzy linguistic terms. After calculating FWRPN for each failure, corrective actions are performed for eliminating the identified failures or decreasing the effects of them. Then, corrected fuzzy weighted risk priority number (CFWRPN) is computed for each failure. Finally, the average of FWRPNs (AFWRPNs) with the average of CFWRPNs (ACFWRPNs) are compared to evaluate the effectiveness of corrective actions by a novel ranking fuzzy numbers method. In addition, the proposed ranking fuzzy number method is also used in both previously mentioned fuzzy multi-criteria decision making (MCDM) methods. Eventually, Kerman Steel Industries Factory is considered as a case study to demonstrate the applicability and benefits of the proposed fuzzy hybrid method. A sensitivity analysis is performed to validate the obtained results. Findings show that AFWRPNs decreased by 56% compared to ACFWRPNs. [ABSTRACT FROM AUTHOR]

Comparing fuzzy numbers has become one of the key challenging issues in fuzzy sets. Many researchers have proposed different procedures to rank fuzzy numbers, but the results frequently contradict each other. This work addresses the key weakness of several fuzzy ranking methods which have been introduced in recent articles. In this paper, we reveal that in nearly all ranking methods that the ranking procedure depends on the height of fuzzy numbers the result is unreliable. However, the final aim of this study is to propose some suggestions for a meaningful comparison in new methods. We demonstrate our reasoning with several numerical cases taken from literature. [ABSTRACT FROM PUBLISHER]

In this paper, a modified epsilon-deviation degree method of ranking fuzzy numbers is proposed. The epsilon-deviation degree method and other ranking methods are available in the literature and applied in the field of decision-making. Despite of the merits, some limitations and shortcomings are observed in these methods. Namely, (1) these methods cannot distinguish fuzzy numbers sharing the same support and different cores, (2) these methods cannot distinguish crisp-valued fuzzy numbers with different heights, (3) these methods also cannot make a preference between a crisp-valued fuzzy number and an arbitrary fuzzy number, (4) if the expectation values of the centroid points are the same for the fuzzy numbers to be compared, then these methods give an incorrect ranking, (5) if fuzzy numbers depict compensation of areas, then these methods fail to give a proper ranking, and (6) further inconsistency in ranking the fuzzy numbers and their images is also observed. Hence, a modified epsilon-deviation degree method is developed, based on the concept of the ill-defined magnitude ‘value’ and the angle of the fuzzy set. The proposed method bears all the properties of epsilon-deviation degree method and overcome all the limitations and shortcomings of this method and other existing methods. Various sets of fuzzy numbers are considered for comparative study between the existing ranking methods and the proposed method for validation. Further, the proposed method seems to outperform in all situations. Risk analysis problem under uncertain environment are often studied under fuzzy domain. Hence, a study is done by applying the proposed method to risk analysis in poultry farming. [ABSTRACT FROM AUTHOR]

Uncertainty is one of the main difficulties that increases the complexity of multi-criteria decision analysis (MCDA) problems, and often uncertainty cannot be managed by probabilistic models. In such cases, the use of fuzzy methods has been successfully applied to multi-criteria decision methods in which the ranking of fuzzy quantities is crucial for the decision analysis. This paper aims to introduce a new approach to MCDA problems defined under fuzzy contexts that implements the concept of acceptability analysis, Fuzzy Multi-Criteria Acceptability Analysis (FMAA), based on the Fuzzy Rank Acceptability Analysis (FRAA), that provides a ranking and a confidence degree about the ranking of fuzzy quantities. Based on the fuzzy extension of MAVT method, the FMAA is implemented and then applied to a case study, and its results are compared with other well-known MCDA methods in order to show its validity, interpretability and consistency. [ABSTRACT FROM AUTHOR]

Integrated supply chain includes different components of order, production and distribution and it plays an important role on reducing the cost of manufacturing system. In this paper, an integrated supply chain in a form of multi-objective decision-making problem is presented. The proposed model of this paper considers different parameters with uncertainty using trapezoid numbers. We first implement a ranking method to covert the fuzzy model into a crisp one and using multi-objective particle swarm optimization, we solve the resulted model. The results are compared with the performance of NSGA-II for some randomly generated problems and the preliminary results indicate that the proposed model of the paper performs better than the alternative method.

In this paper we present some models to analyze the efficiency of a set of Decision Making Units, DMUs, and the ordination of them taking into account their level of efficiency. Typically, the data that are managed for the analysis are often affected of uncertainty that hardly support a random treatment. In this context models using fuzzy efficiency analysis, in particular Fuzzy Data Envelopment Analysis Models, are very useful. To illustrate, the proposed models are applied to the evaluation and classification of a group of textile companies in the areas of Alcoy, Cocentaina and Muro in Alicante.

Ranking fuzzy numbers plays a very important role in linguistic decision making and other fuzzy application systems. In spite of many ranking methods, no one can rank fuzzy numbers with human intuition consistently in all cases. Shortcoming are found in some of the convenient methods for ranking triangular fuzzy numbers such as the coefficient of variation (CV index), distance between fuzzy sets, centroid point and original point, and also weighted mean value. In this paper, we introduce a new method for ranking triangular fuzzy number to overcome the shortcomings of the previous techniques. Finally, we compare our method with some convenient methods for ranking fuzzy numbers to illustrate the advantage our method.

Fuzzy measures are suitable in analyzing human subjective evaluation processes. Several different strategies have been proposed for distance of fuzzy numbers. The distances introduced for fuzzy numbers can be categorized in two groups: 1. The crisp distances which explain crisp values for the distance between two fuzzy numbers. 2. The fuzzy distance which introduce a fuzzy distance for normal fuzzy numbers. It was introduced by Voxman [29] for the first time through using a -cu t. However, both mentioned concepts can lead to unsatisfactory results from the applications point of view, bu t there is no method, which gives a satisfactory result to all situations. In this paper, a new attitude coupled with fuzzy thinking to the fuzzy distance function on the set of fuzzy numbers is proposed. In this new fuzzy distance, we considered both mentioned attitudes, then we introduced new fuzzy distance based on a combination (hybrid) of those two. Some properties of the proposed fuzzy distance have been discussed. Finally, several examples have been provided to explain the application of the proposed method and compare this methods with others. [ABSTRACT FROM AUTHOR]

Ranking fuzzy numbers is generalization of the concepts of order, and class, and so have fundamental applications. Moreover, deriving the final effciency and powerful ranking are helpful to decision makers when solving fuzzy problems. Selecting a good ranking method can apply to choosing a desired criterion in a fuzzy environment. There are numerous methods proposed for the ranking of fuzzy numbers, some of them seem to be good in a particular context but not in general. In this paper, a new attitude coupled with the basic thinking of ordering for ranking of fuzzy numbers is proposed. The properties of the proposed method are discussed in detail. The ranking results show that the proposed method can overcome certain shortcomings that exist in the previous ranking methods. The method also has very easy and simple calculations compared to other methods. Finally, numerical examples are presented to illustrate the advantage of our proposed method, and compare them with other common ranking methods. The future prospect of this paper is a new attitude to fuzzy distance, which will be referred to in the end. [ABSTRACT FROM AUTHOR]

Methods for ordering fuzzy numbers play an important role as decision criteria, with applications in areas such as optimization and data mining, among others. Although there are several proposals for ordering methods in the fuzzy literature, many of them are difficult to apply and present some problems with ranking computation. For that reason, this work proposes an ordering method for fuzzy numbers based on a simple application of a polynomial function. We study some properties of our new method, comparing our results with those generated by other methods previously discussed in literature. [ABSTRACT FROM AUTHOR]

In this study, a new method for ranking trapezial fuzzy numbers, generalized trapezoidal fuzzy numbers with different left and right heights, is presented. It considers triangles of a trapezium, a quadrilateral with no parallel sides, and uses the centers' of the nine-point circles and the areas of these triangles' to calculate the ranking score of the trapezial fuzzy number. The score of the trapezial fuzzy number is also expressed in terms of vertices of the trapezium. The method is simple and efficient, making the application of this method to real life problems more effective. The advantages of the proposed method are given with examples. Certain applications of the proposed ranking method to the fuzzy risk analysis problem, based on trapezial fuzzy numbers, are also presented. The proposed method ranks not only standardized, but also arbitrary trapezial fuzzy numbers. As a result, it is unnecessary to normalize to fuzzy numbers to apply the fuzzy risk algorithm. [ABSTRACT FROM AUTHOR]