A New Bell Shape Fuzzy Number (original) (raw)
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Journal of Fuzzy Set Valued Analysis, 2014
This study presents an approximate approach for ranking fuzzy numbers based on the centroid point of a fuzzy number and its area. The total approximate is determined by convex combining of fuzzy number's relative and its area that based on decision maker's optimistic perspectives. The proposed approach is simple in terms of computational efforts and is efficient in ranking a large quantity of fuzzy numbers. By a group of examples in [3] demonstrate the accuracy and applicability of the proposed approach. Finally by this approach, a new distance is introduced between two fuzzy numbers.
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Communication in Mathematical Modeling and Applications, 2018
With no doubt, ranking the fuzzy numbers are extremely effective and useful in different scientific fields such as Artificial Intelligence, Economics, Engineering and decision-making units and etc. The fuzzy quantities must be ranked before their engagement in the cycle of the applied functionalities. In this article, We offer a valid and advanced method for ranking the fuzzy numbers based on the Distance Measure Meter. In addition to the Distance Measure, we define a particular condition of the generalized fuzzy numbers. Having discussed some examples in this regard, we touch upon the advantages of this new method.
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Abstract: Ranking fuzzy numbers plays an important role in a fuzzy decision making process. However, fuzzy numbers may not be easily ordered into one sequence due to the overlap between fuzzy numbers. A new approach is introduced to detect the overlapped fuzzy numbers based on the concept of similarity measure incorporating the preference of the decision maker into the fuzzy ranking process. Numerical examples and comparisons with other method are straight forward and are practically capable of comparing similar fuzzy numbers. The proposed method is an absolute Ranking and no pair wise comparison of fuzzy numbers is necessary. Furthermore, through some examples discussed in this work, it is proved that the proposed method possesses several good characteristics as compared to the other comparable methods examined in this work.
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Mathematical Problems in Engineering, 2013
This study presents an approximate approach for ranking fuzzy numbers based on the centroid point of a fuzzy number and its area. The total approximate is determined by convex combining of fuzzy number's relative and its area that is based on decision maker's optimistic perspectives. The proposed approach is simple in terms of computational efforts and is efficient in ranking a large quantity of fuzzy numbers. A group of examples by demonstrate the accuracy and applicability of the proposed approach. Finally by this approach, a new measure is introduced between two fuzzy numbers.
Springer eBooks, 2019
In this chapter, preliminaries related to fuzzy numbers have been discussed. Fuzzy numbers and fuzzy arithmetic may be considered as an extension of classical real numbers and its arithmetic. As such, we may understand fuzzy arithmetic as basics for handling fuzzy eigenvalue problems, nonlinear equations, system of nonlinear equations (Abbasbandy and Asady 2004), differential equations (Chakraverty et al. 2016), etc. There exist different types of fuzzy numbers as discussed in Hanss (2005), but for the sake of completeness of the chapter, triangular, trapezoidal, and Gaussian fuzzy numbers based on the membership functions have only been included here. Further, the conversions of these fuzzy numbers to fuzzy intervals with respect to the concept of intervals (Chap. 1) are incorporated. In this regard, the interval arithmetic mentioned in Chap. 1 has been further extended to fuzzy intervals in Sect. 3.4. 3.1 Preliminaries of Fuzzy Numbers A convex fuzzy setà is a fuzzy set having membership function μÃ(x), satisfying μÃ(λx 1 + (1 − λ)x 2) ≥ min(μÃ(x 1), μÃ(x 2)), (3.1) where x 1 , x 2 ∈ X and λ ∈ [0, 1]. Figure 3.1 depicts convex and non-convex fuzzy sets. Convex fuzzy sets defined with respect to universal set (set of all real numbers) may be interpreted as fuzzy numbers. In this respect, the classical definition of fuzzy number is given below. Fuzzy number: A fuzzy setà is referred as a fuzzy numberã if the following properties are satisfied:
Ranking Fuzzy Numbers by Sign Length
Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques has been shown to produce non-intuitive results in certain cases. In this paper,we introduce an approximate method for ranking of fuzzy numbers based on the centroid point of the surface bounded above by the graph of the membership function of fuzzy number below by X-axis. The calculation of proposed method is far simple than the other approaches.
A Revision on Area Ranking and Deviation Degree Methods of Ranking Fuzzy Numbers
2015
Recently two important methods ([1],[2]) [Wang. Zh.X, Liu. Y.J, and Feng. B, “Ranking L–R fuzzy number based on deviation degree”. information science(2009). pp 2070-2077.],and [Wang.Y.M, and Luo. Y, “Area ranking of fuzzy numbers based on positive and negative ideal points.’’ Computers and Mathematics with Applications(2009). pp 1769-1779.] proposed for ranking fuzzy numbers. But we found that they both have a same basic disadvantage. In this paper after a short review on different proposed fuzzy number ranking methods, we explain the drawback on deviation degree and the area ranking methods and provide an improvement method to overcome this shortage. Our approach is based on the maximization set and minimization set methods concepts. The results show the superiority of the proposed method in comparison with other ranking methods, especially when the ranking of the inverse and the symmetry of the fuzzy numbers is of interest.
Ranking Generalized Fuzzy Numbers using Area, Mode, Spreads and Weights
2012
This paper describes a ranking method for ordering fuzzy numbers based on area, mode, spreads and weights of generalized fuzzy numbers. The area used in this method is obtained from the generalized trapezoidal fuzzy number, first by splitting the generalized trapezoidal fuzzy numbers into three plane figures and then calculating the centroids of each plane figure followed by the centroid of these centroids and then finding the area of this centroid from origin which is a process of defuzzification proposed in this paper. This method is simple in evaluation and can rank various types of fuzzy numbers and also crisp numbers which are considered to be a special case of fuzzy numbers.
Generalized Trapezoidal Fuzzy Numbers
2013
In this paper, we want proposed a new method for ranking in areas of two generalized trapezoidal fuzzy numbers. A simpler and easier approach is proposed for the ranking of generalized trapezoidal fuzzy numbers. For the confirmation this results, we compared with different existing approaches. 2010 AMS CLASSIFICATION: 47S20, 03E72.