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.

DECISION MAKING BASED ON STATISTICAL DATA, SIGNED DISTANCE AND COMPOSITIONAL RULE OF INFERENCE

2004 ◽  
Vol 12 (02) ◽  
pp. 161-190 ◽  
Author(s):  
JING-SHING YAO ◽  
MING-MIIN YU
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Statistical Data ◽  
Fuzzy Decision Making ◽  
Seamless Integration ◽  
Transit System ◽  
Signed Distance ◽  
Decision Making Problem ◽  
Interval Valued

An assessment of a set of alternatives under certain evaluation criteria has difficulty in dealing with the priority of these alternatives, especially with a lack of precise information in an uncertain environment. Fuzzy numbers are usually applied to represent the imprecise numerical measurements of different alternatives. In this study statistical data are used to derive level (1-α,1-β) interval-valued fuzzy numbers to represent unknown alternative effectiveness scores, after which, by using the compositional rule of inference and signed distance to transform the fuzzy decision making problem into crisp one, one can conveniently obtain the order of these different alternatives and subsequently obtain the best alternative. The approach presented is computationally efficiency, and its underlying concepts are simple and comprehensible. By using this extended generalized method, two cases of an organizational type of rapid-transit-system selection problem are presented as examples to illustrate the applicability of the interval-valued fuzzy numbers and ranking system for decision making. The key contribution of the method is the seamless integration of the statistical data, interval-valued fuzzy number and signed distance to analyze multicriteria decision making problem. The innovation introduced in the model concerns interval-valued fuzzy number which is recognized as a determinant of the effectiveness score in fuzzy relation matrix.

Signed-Distance Measures Oriented to Rank Interval-Valued Fuzzy Numbers

2018 ◽  
Vol 26 (6) ◽  
pp. 3506-3513 ◽  
Author(s):  
Mohammad Ghasem Akbari ◽  
Gholamreza Hesamian
Keyword(s):  
Fuzzy Numbers ◽  
Distance Measures ◽  
Signed Distance ◽  
Interval Valued

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
Sign in / Sign up

Export Citation Format

Share Document