A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers

Zhang, Xu; Shang, Shichao; Qian, Wei; Shu, Wenhao

doi:10.1016/j.eswa.2009.07.015

Cited by 120 publications

(89 citation statements)

References 13 publications

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“…Like the measure proposed by Chen and Chen [2], this new measure also verifies the four properties but again has the above drawback. This was the ground proffered by Xu et al [13] for proposing a new measure based, like the measure published by Chen and Chen [2], on the concept of center of gravity. Xu et al consider two weights w, 1 -w G (0,1) to attach more or less importance to the concepts used:…”

Section: Overview Of Similarity Measuresmentioning

confidence: 99%

“…We demonstrate that the new similarity measure has the same good properties as earlier measures and other additional properties that overcome their drawbacks. In Section 4, we compare the proposed measure with the measures outlined in this section, taking as a reference the set of 30 pairs of generalized fuzzy numbers provided in [13]. Finally, some conclusions are provided in Section 5.…”

Section: Introductionmentioning

confidence: 99%

“…Fuzzy number arithmetic, defined in conformity with the model in question, is then used to make computations (addition, multiplication, substraction, ranking...) using the fuzzy information provided by experts (see, e.g. 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%

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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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Section: Overview Of Similarity Measuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Similarity Function for Generalized Trapezoidal Fuzzy Numbers

Vicente

Mateos

Jiménez

2013

Artificial Intelligence and Soft Computing

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“…As shown, we consider the set of trapezoidal fuzzy numbers with support on [0, 1]. The arithmetic proposed in (Xu et al, 2010) on TF [0, 1] is used to make computations. The resulting fuzzy number from such a computation is usually translated into a linguistic term in the previously defined scale by means of a similarity function (Vicente et al, 2013).…”

Section: A Fuzzy Mcda Approachmentioning

confidence: 99%

“…The operators are those proposed in Xu et al 2010. If the linguistic scale is used to value remediation alternatives in respect of a particular attribute, then the corresponding trapezoidal fuzzy numbers (Fig.1) are used as fuzzy component utilities.…”

Section: Fuzzy Evaluation Of Remediation Alternativesmentioning

confidence: 99%

Fuzzy MCDA for remediation of a Uranium tailing

Pérez-Sánchez¹,

Jiménez²,

Mateos³

et al. 2014

Uranium - Past and Future Challenges

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Abstract. The Pridneprovsky Chemical Plant was a largest uranium processing enterprises, producing a huge amount of uranium residues. The Zapadnoe tailings site contains the majority of these residues. We propose a theoretical framework based on Multi-Criteria Decision Analysis and fuzzy logic to analyse different remediation alternatives for the Zapadnoe tailings, in which potentially conflicting economic, radiological, social and environmental objectives are simultaneously taken into account. An objective hierarchy is built that includes all the relevant aspects. Fuzzy rather than precise values are proposed for use to evaluate remediation alternatives against the different criteria and to quantify preferences, such as the weights representing the relative importance of criteria identified in the objective hierarchy. Finally, it is proposed that remediation alternatives should be evaluated by means of a fuzzy additive multi-attribute utility function and ranked on the basis of the respective trapezoidal fuzzy number representing their overall utility.

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Similarity Measures and Measures of Fuzziness

2019

Fuzzy Set and Its Extension

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A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers

Cited by 120 publications

References 13 publications

A New Similarity Function for Generalized Trapezoidal Fuzzy Numbers

A New Similarity Function for Generalized Trapezoidal Fuzzy Numbers

Fuzzy MCDA for remediation of a Uranium tailing

Similarity Measures and Measures of Fuzziness

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