Mean Value and Variance of Fuzzy Numbers with Non-continuous Membership Functions

2016 ◽  
pp. 1-8
Author(s):  
Luca Anzilli ◽  
Gisella Facchinetti
Keyword(s):  
Fuzzy Numbers ◽  
Mean Value ◽  
Membership Functions

The new weighted magnitude mean value and variance of fuzzy numbers

2014 ◽  
Vol 26 (5) ◽  
pp. 2303-2313
Author(s):  
Yanbing Gong
Keyword(s):  
Fuzzy Numbers ◽  
Mean Value

A MODIFICATION OF THE INDEX OF LIOU AND WANG FOR RANKING FUZZY NUMBER

2007 ◽  
Vol 15 (04) ◽  
pp. 411-424 ◽  
Author(s):  
M. SOCORRO GARCIA ◽  
M. TERESA LAMATA
Keyword(s):  
Satisfactory Result ◽  
Coefficient Of Variation ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Mean Value ◽  
Weighted Mean ◽  
Numerical Examples ◽  
Centroid Point ◽  
Ranking Fuzzy Number ◽  
Index Of Optimism

Different methods have been proposed for ranking fuzzy numbers. These include methods based on distances, centroid point, coefficient of variation, and weighted mean value. However, there is still no method that can always give a satisfactory result to every situation; some are counterintuitive and not discriminating. This paper presents an approach for ranking fuzzy numbers with integral value that is an extension of the index of Liou and Wang. This method, that is independent of the type of membership function used, can rank more than two fuzzy numbers simultaneously. This ranking method use an index of optimism to reflect the decision maker's optimistic attitude, but rather it also contains an index of modality that represents the neutrality of the decision maker. The approach is illustrated with numerical examples.

scholarly journals Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 569
Author(s):  
Wu
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Optimal Solutions ◽  
Membership Functions ◽  
Fuzzy Decision ◽  
Existence Of Optimal Solutions ◽  
Decision Variables ◽  
Linear Programming Problems

The numerical method for solving the fuzzy linear programming problems with fuzzydecision variables is proposed in this paper. The difficulty for solving this kind of problem is thatthe decision variables are assumed to be nonnegative fuzzy numbers instead of nonnegative realnumbers. In other words, the decision variables are assumed to be membership functions. One of thepurposes of this paper is to derive the analytic formula of error estimation regarding the approximateoptimal solution. On the other hand, the existence of optimal solutions is also studied in this paper.Finally we present two numerical examples to demonstrate the usefulness of the numerical method.

A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty

2006 ◽  
Vol 157 (19) ◽  
pp. 2614-2626 ◽  
Author(s):  
Yuji Yoshida ◽  
Masami Yasuda ◽  
Jun-ichi Nakagami ◽  
Masami Kurano
Keyword(s):  
Fuzzy Numbers ◽  
Mean Value ◽  
American Put Option ◽  
Put Option ◽  
American Put

scholarly journals On Fuzzy Critical Path Method Based On Ranking Of Various Type-2 Fuzzy Quantities Using Centroid Of Centroids

2019 ◽  
Vol 8 (6) ◽  
pp. 910-920
Keyword(s):  
Path Analysis ◽  
Explicit Form ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Simple Approach ◽  
Membership Functions ◽  
Project Network ◽  
Generalized Type ◽  
Activity Times

This paper proposes a simple approach to critical path analysis in a project network with activity times being intervals and which are converted into various Type-2 fuzzy quantities. The idea is based on generalized type-2 trapezoidal, hexagonal and octagonal fuzzy numbers and its ranking. The explicit form of membership functions of the type-2 fuzzy activity times is not required in the proposed approach. Moreover, the method is very simple and the numerical example is given for demonstrating and comparing the proposed approach with generalized type-2 trapezoidal, hexagonal and octagonal fuzzy numbers through proposed ranking function.

scholarly journals Fuzzy Number Addition with the Application of Horizontal Membership Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Andrzej Piegat ◽  
Marcin Pluciński
Keyword(s):  
Interval Arithmetic ◽  
Fuzzy Numbers ◽  
Order Relation ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Multidimensional Approach ◽  
Membership Functions ◽  
Multidimensional Information ◽  
Rdm Arithmetic ◽  
Horizontal Membership Functions

The paper presents addition of fuzzy numbers realised with the application of the multidimensional RDM arithmetic and horizontal membership functions (MFs). Fuzzy arithmetic (FA) is a very difficult task because operations should be performed here on multidimensional information granules. Instead, a lot of FA methods useα-cuts in connection with 1-dimensional classical interval arithmetic that operates not on multidimensional granules but on 1-dimensional intervals. Such approach causes difficulties in calculations and is a reason for arithmetical paradoxes. The multidimensional approach allows for removing drawbacks and weaknesses of FA. It is possible thanks to the application of horizontal membership functions which considerably facilitate calculations because now uncertain values can be inserted directly into equations without using the extension principle. The paper shows how the addition operation can be realised on independent fuzzy numbers and on partly or fully dependent fuzzy numbers with taking into account the order relation and how to solve equations, which can be a difficult task for 1-dimensional FAs.

Fuzzy Number Approximation

1998 ◽  
Vol 06 (01) ◽  
pp. 69-78 ◽  
Author(s):  
Mariano Jiménez ◽  
Juan Antonio Rivas
Keyword(s):  
Initial Data ◽  
Economic Model ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Membership Functions ◽  
Simple Method ◽  
Non Linear

As the number of parameters involved in an economic model is often uncertain, we propose that it be estimated using fuzzy numbers. Since we move in an environment of uncertainty, it is logical to leave room for deviation in estimating membership functions. We should recall that when soft max-min operators are used, the resulting deviation is never greater than the variation introduced in estimating the initial data. Often, the result of our calculations is not a triangular fuzzy number. In this paper we study the value of approximating the resulting non-linear fuzzy number using a triangular fuzzy number having the same support and kernel. Finally, we present a simple method for weighing this approximation.

scholarly journals TRANSPORTATION MANAGEMENT IN A DISTRIBUTED LOGISTIC CONSUMPTION SYSTEM UNDER UNCERTAINTY CONDITIONS

2019 ◽  
Vol 4 ◽  
pp. 82-90
Author(s):  
Lev Raskin ◽  
Oksana Sira ◽  
Viacheslav Karpenko
Keyword(s):  
Mathematical Models ◽  
Programming Problem ◽  
Fuzzy Numbers ◽  
Statistical Processing ◽  
Linear Constraints ◽  
Mathematical Programming Problem ◽  
Membership Functions ◽  
Probability Representation ◽  
Source Data ◽  
Fuzzy Parameters

The problem of supply management in the supplier-to-consumer logistics transport system has been formed and solved. The novelty of the formulation of the problem consists in the integrated accounting of costs in the logistic system, which takes into account at the same time the cost of transporting products from suppliers to consumers, as well as the costs for each of the consumers to store the unsold product and losses due to possible shortages. The resulting optimization problem is no longer a standard linear programming problem. In addition, the work assumes that the solution of the problem should be sought taking into account the fact that the initial data of the problem are not deterministic. The analysis of traditional methods of describing the uncertainty of the source data. It is concluded that, given the rapidly changing conditions for the implementation of the delivery process in a distributed supplier-to-consumer system, it is advisable to move from a theoretical probability representation of the source data to their description in terms of fuzzy mathematics. At the same time, in particular, the fuzzy values of the demand for the delivered product for each consumer are determined by their membership functions. Distribution of supplies in the system is described by solving a mathematical programming problem with a nonlinear objective function and a set of linear constraints of the transport type. In forming the criterion, a technology is used to transform the membership functions of fuzzy parameters of the problem to its theoretical probabilistic counterparts – density distribution of demand values. The task is reduced to finding for each consumer the value of the ordered product, minimizing the average total cost of storing the unrealized product and losses from the deficit. The initial problem is reduced to solving a set of integral equations solved, in general, numerically. It is shown that in particular, important for practice, particular cases, this solution is achieved analytically. The paper states the insufficient adequacy of the traditionally used mathematical models for describing fuzzy parameters of the problem, in particular, the demand. Statistical processing of real data on demand shows that the parameters of the membership functions of the corresponding fuzzy numbers are themselves fuzzy numbers. Acceptable mathematical models of the corresponding fuzzy numbers are formulated in terms of bifuzzy mathematics. The relations describing the membership functions of the bifuzzy numbers are given. A formula is obtained for calculating the total losses to storage and from the deficit, taking into account the bifuzzy of demand. In this case, the initial task is reduced to finding the distribution of supplies, at which the maximum value of the total losses does not exceed the permissible value.

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