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Similarity Measure Between Interval-valued Vague Sets Using Gravities, Spreads, Heights, and Similarities

Journal of Knowledge Information Technology and Systems
Abbr : JKITS
2012, 7(1), pp.93-100
Publisher : Korea Knowledge Information Technology Society
Research Area : Interdisciplinary Research

1초당대학교
2청운대학교
3청운대학교 • ABSTRACT

In this paper, we propose a similarity measure between interval-valued vague sets. The proposed method considers the similarity of the gravities between interval-value vague sets, the difference of the spreads, the heights, and the degree of similarities between interval-valued vague sets. In conventional researches on similarity measures, those have studied on the degree of match between the antecedents in rules and facts, similarity measure based on level average integration, similarity measure based on geometric concept, similarity measure based on geometric distance and COG points, similarity measure based on geometric distance, perimeters, similarity measure between the interval-valued trapezoidal fuzzy numbers, and heights, and similarity measure between interval-valued vague sets based on COG, spreads, and heights. The interval-valued vague sets are a kind of the fuzzy sets of which the upper bound and the lower bound are represented as the intervals of the interval-valued fuzzy sets respectively. We also prove three properties of the proposed similarity measure: 1) Two interval-value vague sets A and B are identical iif =1, 2) =, 3) If A and B are real numbers, then =. Let interval-valued vague sets A and B. It provides a useful way to deal with similarity measure between interval-valued vague sets in fuzzy systems, fuzzy decision making systems, fuzzy reliability analysis.
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