Fuzzy weighted average: A max-min paired elimination method

Guh, Yuh-Yuan; Hon, Cheng-Chung; Wang, Kuo-Ming; Lee, E.S.

doi:10.1016/0898-1221(96)00171-x

Cited by 80 publications

(45 citation statements)

References 2 publications

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“…For a better comprehensibility of the text, only the first situation where the fuzzy weights are noninteractive fuzzy numbers will be considered further in the paper. The calculation of the fuzzy extension of a w in such a case was studied e. g. in [1,5,11,12,14,15,20,21]. In the second situation, the assumption that the sum of w 1 , .…”

Section: Doi: 1014736/kyb-2017-1-0137mentioning

confidence: 99%

Fuzzy weighted average as a fuzzified aggregation operator and its properties

Pavlačka¹,

Pavlackova²,

Hetfleiš³

2017

Kybernetika

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Section: Doi: 1014736/kyb-2017-1-0137mentioning

confidence: 99%

Fuzzy weighted average as a fuzzified aggregation operator and its properties

Pavlačka¹,

Pavlackova²,

Hetfleiš³

2017

Kybernetika

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“…The example is also treated by Guh, Hon and Lee [4], by Guh, Hon, Wang and Lee [5] and by Liou and Wang [10]. There are 3 attributes and 3 weights; all of these are triangular fuzzy numbers.…”

Section: Examplementioning

confidence: 99%

Exact Membership Functions for the Fuzzy Weighted Average

Broek

Noppen

2011

Studies in Computational Intelligence

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Abstract. The problem of computing the fuzzy weighted average, where both attributes and weights are fuzzy numbers, is well studied in the literature. Generally, the approach is to apply Zadeh's extension principle to compute α-cuts of the fuzzy weighted average from the α-cuts of the attributes and weights for fixed values of α∈[0..1]; this means that all values of the membership functions of the fuzzy weighted average are computed separately. In this paper, we generalise this approach in such a way that α is considered to be a parameter; this enables us to compute exact analytical membership functions for the fuzzy weighted average in case the attributes and weights are triangular or trapeizoidal fuzzy numbers. To illustrate the power of our algorithms, they are applied to the examples from the literature, providing exact membership functions in each case.

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“…is locally monotonic with respect to each argument (according to Definition 3) and increasing with respect to the Polynomial algorithms have been later on developed for the real interval problem based on fractional linear programming [46], [47]. But a fuzzy configuration-based approach with linear complexity can be used to extend the interval-valued one of Lee and Park [23].…”

Section: B Handling the Kinksmentioning

confidence: 99%

Gradual Numbers and Their Application to Fuzzy Interval Analysis

Fortin

Dubois

Fargier

2008

IEEE Trans. Fuzzy Syst.

172

121

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Abstract-We introduce a new way of looking at fuzzy intervals. Instead of considering them as fuzzy sets, we see them as crisp sets of entities we call gradual (real) numbers. They are a gradual extension of real numbers, not of intervals. Such a concept is apparently missing in fuzzy set theory. Gradual numbers basically have the same algebraic properties as real numbers, but they are functions. A fuzzy interval is then viewed as a pair of fuzzy thresholds, which are monotonic gradual real numbers. This view enable interval analysis to be directly extended to fuzzy intervals, without resorting to ¢ -cuts, in agreement with Zadeh's extension principle. Several results show that interval analysis methods can be directly adapted to fuzzy interval computation where end points of intervals are changed into left and right fuzzy bounds. Our approach is illustrated on two known problems: computing fuzzy weighted averages, and determining fuzzy floats and latest starting times in activity network scheduling.

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Fuzzy weighted average: A max-min paired elimination method

Cited by 80 publications

References 2 publications

Fuzzy weighted average as a fuzzified aggregation operator and its properties

Fuzzy weighted average as a fuzzified aggregation operator and its properties

Exact Membership Functions for the Fuzzy Weighted Average

Gradual Numbers and Their Application to Fuzzy Interval Analysis

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