Comparison of fuzzy numbers using a fuzzy distance measure

Tran, Liem; Duckstein, Lucien

doi:10.1016/s0165-0114(01)00195-6

Cited by 339 publications

(151 citation statements)

References 18 publications

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“…For this aim, a comparison method which was proposed by Tran and Duckstein (2002) is used. The method is based on the comparison of distances from fuzzy numbers (FNs) to some predetermined targets: the crisp maximum (Max) and the crisp minimum (Min).…”

Section: Fig 5 the Membership Functions Of Intelligent Building Altmentioning

confidence: 99%

A Fuzzy Multiple Attribute Utility Model for Intelligent Building Assessment

Kahraman

Kaya

2012

Journal of Civil Engineering and Management

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Abstract. Multi-Attribute Utility Theory (MAUT) is an evaluation scheme which is very popular by decision makers for evaluating their judgments. According to MAUT, the overall evaluation U(x) of an object x is defined as a weighted addition of its evaluation with respect to its relevant value dimensions. The recent years have witnessed a huge concentration and interest in intelligent buildings' performance that is increasingly evidenced in building design and construction. Intelligent buildings (IBs) are also under assessment according to their IB related characteristics and actual circumstances. For this aim, in this paper a fuzzy multiple attribute utility model for intelligent building assessment is proposed and three alternative intelligent buildings for a business center in Istanbul are evaluated.

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Section: Fig 5 the Membership Functions Of Intelligent Building Altmentioning

confidence: 99%

A Fuzzy Multiple Attribute Utility Model for Intelligent Building Assessment

Kahraman

Kaya

2012

Journal of Civil Engineering and Management

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“…The first ideas about the similarity of normalized fuzzy numbers with support in Tran and Duckstein [11] defined a distance, which was computed as a weighted sum of distances between two intervals across all the a-cuts from 0 to 1. This distance was also used in [8] to measure the intensity of dominance between trapezoidal fuzzy weights representing the preferences of DMs within MAUT.…”

Section: Overview Of Similarity Measuresmentioning

confidence: 99%

“…the arithmetic proposed in [13] for linguistic values trapezoidal fuzzy numbers or the one in [4,6] for generalized trapezoidal fuzzy numbers). For advance in research in fuzzy number arithmetic and logical operators, see [11].…”

Section: Introductionmentioning

confidence: 99%

A New Similarity Function for Generalized Trapezoidal Fuzzy Numbers

Vicente

Mateos

Jiménez

2013

Artificial Intelligence and Soft Computing

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Abstract. Numerous authors have proposed functions to quantify the degree of similarity between two fuzzy numbers using various descriptive parameters, such as the geometric distance, the distance between the centers of gravity or the perimeter. However, these similarity functions have drawbacks for specific situations. We propose a new similarity measure for generalized trapezoidal fuzzy numbers aimed at overcoming such drawbacks. This new measure accounts for the distance between the centers of gravity and the geometric distance but also incorporates a new term based on the shared area between the fuzzy numbers. The proposed measure is compared against other measures in the literature.

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“…Table 4 is the result of comparison with previous works, in which, the methods refer to [15], [16], [17], [4], [19], [12], [18], [10] and [6], respectively, the content of Table 4 partly comes from [6].…”

Section: Numeric Examples and Comparison With Previous Workmentioning

confidence: 99%

“…Because of the suitability for representing uncertain values, fuzzy numbers have been widely used in many applications. Since fuzzy numbers represent uncertain numeric values, it is difficult to rank them according to their magnitude, Many methods for ranking fuzzy numbers have been proposed [1]- [5], such as, representing them with real numbers [6]- [12]. The results of studies on ranking fuzzy numbers have been used in application areas such as decision making [13]- [22].…”

Section: Introductionmentioning

confidence: 99%

A Method for Ranking Fuzzy Numbers and Its Application to Game with Fuzzy Profit

Shao¹,

Pei²

2007

Proceedings on Intelligent Systems and Knowledge Engineering (ISKE2007)

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In this paper, a new method for ranking fuzzy numbers is proposed. Based on decomposition theorem of fuzzy set, firstly, the method considers interval numbers, the relation between lines and interval numbers is discussed in Cartesian coordinates, the distance of dot A to lines l is used as evaluation of interval number. Then, integral of all distances is used as evaluation of fuzzy number. Finally, ranking fuzzy numbers is implemented by the evaluations of fuzzy numbers. In order to illustrate the ranking method, numeric example is shown, and for the comparative study, our method is compared with four existing ranking methods. As an example of potential applications, the proposed method is applied to game with Fuzzy Profit.

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Comparison of fuzzy numbers using a fuzzy distance measure

Cited by 339 publications

References 18 publications

A Fuzzy Multiple Attribute Utility Model for Intelligent Building Assessment

A Fuzzy Multiple Attribute Utility Model for Intelligent Building Assessment

A New Similarity Function for Generalized Trapezoidal Fuzzy Numbers

A Method for Ranking Fuzzy Numbers and Its Application to Game with Fuzzy Profit

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