A New Similarity Measure Between Interval-Valued Trapezoidal Fuzzy Numbers Based on Geometric Distance and the Center-of-Gravity-Points
Published 1 January 2007
Shih-Hua Wei, Shyi‐Ming Chen
Citations3
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
A new similarity measure between interval-valued trapezoidal fuzzy numbers is proposed that combines the concepts of geometric distance, the perimeter, the height and the center-of-gravity-points of intervals-valued fuzzy numbers for calculation the degree of similarity.
Abstract
In this paper, a new similarity measure between interval-valued trapezoidal fuzzy numbers is proposed. It combines the concepts of geometric distance, the perimeter, the height and the center-of-gravity-points of interval-valued fuzzy numbers for calculation the degree of similarity between interval-valued trapezoidal fuzzy numbers. We also prove three properties of the proposed similarity measure. We use five sets of interval-valued trapezoidal fuzzy numbers to compare the calculating results of the proposed method with the existing methods. The proposed method can overcome the drawbacks of the existing methods. It provides a useful way to measure the degree of similarity between interval-valued trapezoidal fuzzy numbers.
Keywords
Computer ScienceDecision SciencesMathematics
Fuzzy Sets and SystemsAggregation of fuzzy opinions under group decision making
592 Citations1996Hsi-Mei Hsu, Chen‐Tung Arthur Chen
A method is proposed for aggregating individual fuzzy opinions into a group fuzzy consensus opinion using the index of consensus of each expert to the other experts using a similarity measure.
International Journal of Approximate ReasoningConstructing a fuzzy flow-shop sequencing model based on statistical data
116 Citations2002Jing-Shing Yao, Feng‐Tse Lin
A fuzzy flow-shop sequencing model is constructed based on statistical data, which uses level (1− α ,1− β ) interval-valued fuzzy numbers to represent the unknown job processing time and provides the same job sequence as that of the crisp problem.
An optimal aggregation method for fuzzy opinions of group decision
87 Citations2003Hsuan-Shih Lee
A similarity measure for trapezoidal fuzzy numbers and an iterative procedure for approximating the optimal consensus of expert opinions for aggregating individual fuzzy opinions into an optimal group consensus are proposed.
IEEE Transactions on Fuzzy SystemsFuzzy job-shop scheduling based on ranking level (λ, 1) interval-valued fuzzy numbers
47 Citations2002Feng‐Tse Lin
This paper considers a fuzzy job-shop scheduling problem with imprecise processing times, and uses fuzzy numbers and level (/spl lambda/, 1) interval-valued fuzzy numbers for the representation of vague processing times.
A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-mean Averaging Operator
31 Citations2006Shyi‐Ming Chen
A new similarity measure based on the geometric-mean averaging operator to handle the similarity measure problems of generalized fuzzy numbers is presented and results indicate that the proposed similarity measure is better than existing methods.
A New Method to Measure the Similarity Between Interval-Valued Fuzzy Numbers
16 Citations2007Jim-Ho Chen, Shyi‐Ming Chen
This paper proposes a new similarity measure between interval-valued fuzzy numbers that considers the similarity of the gravities on the X-axis between upper fuzzy numbers, the difference of the spreads between upper fuzzies, the heights of the upper fuzzyNumbers, the degree of similarity on theX-axis, and the gravITIES on the Y-axis.
A New Fuzzy Risk Assessment Method for the Network Security Based on Fuzzy Similarity Measure
11 Citations2006Yongtao Liao, Cunbao Ma +1 more
In the proposed method, a fuzzy weighted average method is presented to calculate the fuzzy risk value on the basis of the hierarchical security structures, and the ROG-based similarity measure of generalized fuzzy numbers is used to create a complete linguistic approximation model for the network security risks.
Journal of the Chinese Institute of EngineersHandling information filtering problems based on interval‐valued fuzzy numbers
11 Citations2006Shi‐Jay Chen, Shyi‐Ming Chen
The proposed prioritized information fusion algorithm can deal with information filtering problems in a more flexible manner due to the fact that it not only can deals with information filters problems based on interval‐valued fuzzy numbers, but also can dealWith multi‐level information filtering Problems.
Similarity and nearness of fuzzy sets
5 Citations2005Xiao-Jun Tong, She-Min Zhang +2 more
This work constructs some new similarity measure by the optimum factor of proportionality with l/sup 2/-norm, which is proposed by Kosko or Wang and is based on the mutual subsethood theorem.
The fuzzy similarity measures for content-based image retrieval
5 Citations2004Yun Li, Jai-Ming Liu +3 more
The principle of fuzzy similarity measure for CBIR is deeply inspected, the properties and the classes about fuzzy similarity measures are introduced and remarked, and a faster algorithm on similarity measure using center of gravity of fuzzy sets in CBIr is presented.
Mutuality measures corresponding to subjective judgment of similarity and matching
2 Citations1999Ayumi Yoshikawa
Results show that indices related to distance between two fuzzy sets along element axis correspond to subjective judgment of similarity, which confirms Yoshikawa-Nishimura's results (1996) and reveals two tendencies: 1) human can distinguish between two different concepts, similarity and matching; and 2) all the indices adopted are functional as matching measures rather as similarity measures.