A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory

Luca, Aldo de; Termini, Settimo

doi:10.1016/s0019-9958(72)90199-4

Cited by 1,917 publications

(493 citation statements)

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“…We are going to cite the following examp le for illustration purposes Let X= [4,16,25] be a fu zzy number with membership function defined as:…”

Section: Numerical Examplesmentioning

confidence: 99%

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On Some Properties of Entropy of Fuzzy Numbers

Dhar¹

2013

IJISA

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Abstract-Here at first we are going to give a brief history of the development of fuzzy entropy. Finally, new measures for entropy of fu zzy sets in continuous cases are introduced. In this art icle, our main purpose is to show that the entropy of fuzzy nu mber is very much dependent on the selection of intervals. Another important thing which can be observed from the cases discussed is that the entropy of triangular fu zzy numbers is the same for the same choice of interval length and for non triangular fuzzy nu mber this property does not hold.

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“…We are going to cite the following examp le for illustration purposes Let X= [4,16,25] be a fu zzy number with membership function defined as:…”

Section: Numerical Examplesmentioning

confidence: 99%

“…De Luca and Termin i [4] suggested as a measure of fuzziness of a fuzzy set, which they defined as follows:…”

Section: Introductionmentioning

confidence: 99%

On Some Properties of Entropy of Fuzzy Numbers

Dhar¹

2013

IJISA

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“…Following these approaches, we get a single nu mber or alternatively a fuzzy set as cardinality of fuzzy set. The first concept of this kind was proposed and discussed in De Luca and Termini [6]. In many applications, one prefers a simp le scalar appro ximation of cardinality of a fuzzy set.…”

Section: Cardinality Of Fuzzy Setsmentioning

confidence: 99%

“…Kosko ([8], [9]) has defined the entropy of a fuzzy set A as: De Luca and Termin i [6] suggested as a measure of fuzziness the -entropy‖ of a fu zzy set, which they defined as follows:…”

Section: Entropy Of Fuzzy Setsmentioning

confidence: 99%

The Complement of Normal Fuzzy Numbers: An Exposition

Dhar¹,

Baruah²

2013

IJISA

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Abstract-In this article, our main intention is to revisit the existing definit ion of co mplementation of fu zzy sets and thereafter various theories associated with it a re also commented on. The main contribution of this paper is to suggest a new definit ion of complementation of fuzzy sets on the basis of reference function. So me other results have also been introduced whenever possible by using this new definit ion of complementation.

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“…A functional defined on the class of generalised characteristic functions (fuzzy sets), called "entropy", is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets [7]. The meaning of this quantity is quite different from the one of classical entropy because no probabilistic concept is needed in order to define it.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Shannon Entropy: A Hybrid GIS-Based Landslide Susceptibility Mapping Method

Roodposhti

Aryal

Shahabi

et al. 2016

Entropy

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Assessing Landslide Susceptibility Mapping (LSM) contributes to reducing the risk of living with landslides. Handling the vagueness associated with LSM is a challenging task. Here we show the application of hybrid GIS-based LSM. The hybrid approach embraces fuzzy membership functions (FMFs) in combination with Shannon entropy, a well-known information theory-based method. Nine landslide-related criteria, along with an inventory of landslides containing 108 recent and historic landslide points, are used to prepare a susceptibility map. A random split into training (≈70%) and testing (≈30%) samples are used for training and validation of the LSM model. The study area-Izeh-is located in the Khuzestan province of Iran, a highly susceptible landslide zone. The performance of the hybrid method is evaluated using receiver operating characteristics (ROC) curves in combination with area under the curve (AUC). The performance of the proposed hybrid method with AUC of 0.934 is superior to multi-criteria evaluation approaches using a subjective scheme in this research in comparison with a previous study using the same dataset through extended fuzzy multi-criteria evaluation with AUC value of 0.894, and was built on the basis of decision makers' evaluation in the same study area.

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A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory

Cited by 1,917 publications

References 4 publications

On Some Properties of Entropy of Fuzzy Numbers

On Some Properties of Entropy of Fuzzy Numbers

The Complement of Normal Fuzzy Numbers: An Exposition

Fuzzy Shannon Entropy: A Hybrid GIS-Based Landslide Susceptibility Mapping Method

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