Analyzing fuzzy risk based on similarity measures between interval-valued fuzzy numbers

2011 ◽  
Vol 38 (7) ◽  
pp. 8612-8621 ◽  
Author(s):  
Shyi-Ming Chen ◽  
Kata Sanguansat
Keyword(s):  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Interval Valued

scholarly journals Ranking and Similarity Measures of Interval-Valued Pentagonal Fuzzy Numbers

2019 ◽  
Vol 8 (4) ◽  
pp. 9314-9320
Keyword(s):  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Flow Chart ◽  
Geometric Distance ◽  
Signed Distance ◽  
Mathematical Formulas ◽  
Interval Valued

We define generalized interval-valued pentagonal fuzzy numbers. Based on the height of the lower and upper pentagonal fuzzy numbers we propose to categorize interval-valued pentagonal fuzzy numbers into three different categories. Using signed distance concept de-fuzzification of interval-valued pentagonal fuzzy numbers is proposed and mathematical formulas are derived using   cut representations. We also introduce two similarity measures for interval-valued pentagonal fuzzy numbers based on geometric distance, area and height of pentagonal fuzzy numbers and geometric distance, perimeter and height of pentagonal fuzzy numbers respectively. Algorithms for finding de-fuzzification value and similarity measures are proposed with flow-chart illustration.

scholarly journals A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 441 ◽  
Author(s):  
Minxia Luo ◽  
Jingjing Liang
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.

Interval-Valued $$E_N$$ -functions and Similarity Measures

2019 ◽  
pp. 140-150
Author(s):  
Zdenko Takáč ◽  
Humberto Bustince ◽  
Javier Fernandez ◽  
Graçaliz Dimuro ◽  
Tiago Asmus ◽  
...  
Keyword(s):  
Similarity Measures ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document