Search

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]

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]

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]

Abstract: In this work, a new concept of upper dense sequence in interval is introduced. There are infinitely many upper dense sequences in interval . Using any upper dense sequence, a new decomposition theorem for fuzzy sets is established and proved. Then, using a chosen upper dense sequence as one of the necessary reference systems, infinitely many total orderings on the set of all fuzzy numbers can be well defined. Among them, a common upper dense sequence based on the binary numbers is suggested as a natural default option. Another upper dense sequence based on the rational numbers is also suggested. Regarding real numbers as special fuzzy numbers, all of these total orderings defined by using the suggested upper dense sequences are consistent with the natural ordering of real numbers. Building total ordering on the set of all fuzzy numbers in such a way is significant for fuzzy data analysis and, therefore, may be used in decision making with fuzzy information. [Copyright &y& Elsevier]

Abstract: Designing a logistic network is a strategic and critical problem that provides an optimal platform for the effective and efficient supply chain management. In this research, we address the application of fuzzy sets to design a multi-product, multi-period, closed-loop supply chain network. The presented supply chain includes three objective functions: maximization of profit, minimization of delivery time, and maximization of quality. In the context of fuzzy mathematical programming, the paper jointly considers fuzzy/flexible constraints for fuzziness, fuzzy coefficients for lack of knowledge, and fuzzy goal of decision maker(s). According to fuzzy components considered, a fuzzy optimization approach is adopted to convert the proposed fuzzy multi-objective mixed-integer linear program into an equivalent auxiliary crisp model to obtain the relevant solutions. Finally, the numerical experiments are given to demonstrate the significance of the proposed model as well as the solution approach. [Copyright &y& Elsevier]

Highlights: [•] Shortcomings of Liou and Wang's (1992) fuzzy number ranking method are discussed. [•] An improved method that can overcome these shortcomings is proposed. [•] Validity and advantages are illustrated through several comparative examples. [Copyright &y& Elsevier]

Highlights: [•] An epsilon-deviation degree approach based on deviation degree is proposed. [•] Overcome the shortcomings of the left and right deviation degree becoming worthless. [•] Tackle the conflict between ranking order of fuzzy numbers and that of their images. [•] An optimism index is employed for ranking symmetric fuzzy numbers effectively. [ABSTRACT FROM AUTHOR]

Abstract: Ranking fuzzy numbers is important in decision-making, data analysis, artificial intelligence, economic systems and operations research. In this paper, to overcome the limitations of the existing studies and simplify the computational procedures an approach to ranking fuzzy numbers based on -cuts is proposed. The approach is illustrated by numerical examples, showing that it overcomes several shortcomings such as the indiscriminative and counterintuitive behavior of existing fuzzy ranking approaches. [Copyright &y& Elsevier]

Abstract: Parting curve selection and evaluation plays an important role in mold design. Multiple criteria decision-making (MCDM) is an effective tool for evaluating and ranking problems involving multiple criteria. In order to select suitable parting curve, several criteria need to be taken into account. Therefore, this paper proposes an extension of fuzzy MCDM approach to solve parting curve selection problem. In the proposed model, the ratings of alternatives and importance weights of criteria for parting curve selection are expressed in linguistic terms. The membership functions of the final fuzzy evaluation value in the proposed model are developed based on the linguistic expressions. To make the procedure easier and more practical, the normalized weighted ratings are defuzzified into crisp values by using a new maximizing set and minimizing set ranking approach to determine the ranking order of alternatives. An example of parting curve evaluation and selection is given. The results show that the proposed approach is very effective in selecting the optimal parting curve for the molded part. Finally, this paper compares the proposed approach with another fuzzy MCDM approach to demonstrate its advantages and applicability. [Copyright &y& Elsevier]

Abstract: Ranking fuzzy numbers plays an important role in decision making under uncertain environment. Recently, [Chen, S. M. & Sanguansat, K. (2011). Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers. Expert Systems with Applications, 38(3), (pp. 2163–2171)] proposed a method for ranking generalized fuzzy numbers. It considers the areas on the positive side, the areas on the negative side and the heights of the generalized fuzzy numbers to evaluate ranking scores of the generalized fuzzy numbers. can overcome the drawbacks of some existing methods for ranking generalized fuzzy numbers. However, in the situation when the score is zero, the results of the ranking method are unreasonable. The aim of this short note is to give a modification on to make the method more reasonable. [Copyright &y& Elsevier]

Abstract: In this paper, a novel method, based on the areas on the left and the right sides of fuzzy numbers is proposed for ranking fuzzy numbers. The merits of the results given here is to overcome certain shortcomings in the recent literature that mostly does not end in the right ordering of fuzzy numbers. The method also has very easy and simple calculations compared to other methods. Moreover, numerical examples are given to compare the proposed method with other existing ones. [ABSTRACT FROM AUTHOR]