On Mean Value and Variance of Interval-Valued Fuzzy Numbers

2012 ◽  
pp. 19-28 ◽  
Author(s):  
Christer Carlsson ◽  
Robert Fullér ◽  
József Mezei
Keyword(s):  
Fuzzy Numbers ◽  
Mean Value ◽  
Interval Valued

Interval-valued intuitionistic fuzzy multiple attribute decision making and their applications

2021 ◽  
Vol 25 (2) ◽  
pp. 251-277
Author(s):  
Hong-Jun Wang
Keyword(s):  
Supplier Selection ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Green Supply Chain Management ◽  
Green Supply Chain ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operator Interval ◽  
Multiple Attribute ◽  
Interval Valued

In this paper, we expand the Muirhead mean (MM) operator and dual Muirhead mean (DMM) operator with interval-valued intuitionistic fuzzy numbers (IVIFNs) to propose the interval -valued intuitionistic fuzzy Muirhead mean (IVIFMM) operator, interval-valued intuitionistic fuzzy weighted Muirhead mean (IVIFWMM) operator, interval-valued intuitionistic fuzzy dual Muirhead mean (IVIFDMM) operator and interval-valued intuitionistic fuzzy weighted dual Muirhead mean (IVIFWDMM) operator. Then the MADM methods are proposed with these operators. In the end, we utilize an applicable example for green supplier selection in green supply chain management to prove the proposed methods.

scholarly journals Modified artificial bee colony algorithm for solving mixed interval-valued fuzzy shortest path problem

2021 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Mohammad Enayattabr ◽  
Homayun Motameni ◽  
Harish Garg
Keyword(s):  
Shortest Path ◽  
Artificial Bee Colony ◽  
Fuzzy Numbers ◽  
Pso Algorithm ◽  
Convergence Time ◽  
Bee Colony ◽  
Different Types ◽  
Implementation Time ◽  
Fuzzy Network ◽  
Interval Valued

AbstractIn recent years, numerous researchers examined and analyzed several different types of uncertainty in shortest path (SP) problems. However, those SP problems in which the costs of arcs are expressed in terms of mixed interval-valued fuzzy numbers are less addressed. Here, for solving such uncertain SP problems, first a new procedure is extended to approximate the summation of mixed interval-valued fuzzy numbers using alpha cuts. Then, an extended distance function is introduced for comparing the path weights. Finally, we intend to use a modified artificial bee colony (MABC) algorithm to find the interval-valued membership function of SP in such mixed interval-valued fuzzy network. The proposed algorithm is illustrated via two applications of SP problems in wireless sensor networks and then the results are compared with those derived from genetic and particle swarm optimization (PSO) algorithms, based on three indexes convergence iteration, convergence time and run time. The obtained results confirm that the MABC algorithm has less convergence iteration, convergence time and implementation time compared to GA and PSO algorithm.

scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

scholarly journals AN EXTENSION OF THE RATIO SYSTEM APPROACH OF MOORA METHOD FOR GROUP DECISION-MAKING BASED ON INTERVAL-VALUED TRIANGULAR FUZZY NUMBERS

2015 ◽  
Vol 22 (1) ◽  
pp. 122-141 ◽  
Author(s):  
Dragisa STANUJKIC
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
System Approach ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Weighted Averaging ◽  
Performance Ratings ◽  
Triangular Fuzzy Numbers ◽  
Moora Method ◽  
Interval Valued

Decision-making in fuzzy environment is often a very complex, especially when related to predictions and assessments. The Ratio system approach of the MOORA method and Intervalvalued fuzzy numbers have already proved themselves as the effective tools for solving complex decision-making problems. Therefore, in this paper an extension of the Ratio system approach of the MOORA method, which allows a group decision-making as well as the use of interval-valued triangular fuzzy numbers, is proposed. Interval-fuzzy numbers are rather complex, and therefore, they are not practical for direct assigning performance ratings. For this reason, in this paper it has also been suggested the approach which allows the expression of individual performance ratings using crisp, interval or fuzzy numbers, and their further transformation into the group performance ratings, expressed in the form of interval-valued triangular fuzzy numbers, which provide greater flexibility and reality compared to the use of linguistic variables. Finally, in this paper the weighted averaging operator was proposed for defuzzification of interval-valued triangular fuzzy numbers.

A method for solving linear programming with interval-valued trapezoidal fuzzy variables

2018 ◽  
Vol 52 (3) ◽  
pp. 955-979 ◽  
Author(s):  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Auxiliary Problem ◽  
Coefficient Matrix ◽  
Uncertain Parameters ◽  
Fuzzy Variables ◽  
Right Hand ◽  
Fuzzy Cost ◽  
The Right ◽  
Interval Valued

An efficient method to handle the uncertain parameters of a linear programming (LP) problem is to express the uncertain parameters by fuzzy numbers which are more realistic, and create a conceptual and theoretical framework for dealing with imprecision and vagueness. The fuzzy LP (FLP) models in the literature generally either incorporate the imprecisions related to the coefficients of the objective function, the values of the right-hand side, and/or the elements of the coefficient matrix. The aim of this article is to introduce a formulation of FLP problems involving interval-valued trapezoidal fuzzy numbers for the decision variables and the right-hand-side of the constraints. We propose a new method for solving this kind of FLP problems based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To do this, we first define an auxiliary problem, having only interval-valued trapezoidal fuzzy cost coefficients, and then study the relationships between these problems leading to a solution for the primary problem. It is demonstrated that study of LP problems with interval-valued trapezoidal fuzzy variables gives rise to the same expected results as those obtained for LP with trapezoidal fuzzy variables.

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.

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