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Öncü verinin belirsizliği durumunda biyoçeşitliğin belirlenmesinde Shannon entropisinin Deng entropisi ve geliştirilmiş Deng Entropisi ile karşılaştırılması

Year 2018, Volume: 68 Issue: 2, 136 - 140, 20.07.2018

Abstract

DOI: 10.26650/forestist.2018.340634

Biyolojik çeşitliliğin belirlenmesinde
Margalef indeksi, McIntosh indeksi, Simpson indeksi, Brillouin indeksi ve
Shannon entropisi gibi birçok çeşitlilik indisi kullanılmaktadırlar. Bu
indisler arasındaki en popular olanı Shannon entropisidir. Bu çalışma biyolojik
çeşitliğin ölçümüne yönelik olarak bilgi teorisinin temel eşitliği olan Shannon
entropis ile Demster-Shafer Delil Teorisi’nin ölçümlerinden olan Deng entropisi
ve Geliştirilmiş Deng entropisini karşılaştırmak için gerçekleştirilmiştir.
Çalışmada 3 kompleksten oluşan hipotetik bir veri kullanılmıştır. Kullanılan
hipotetik veri ile gerçekleştirilen hesaplamaların sonucunda, ekolojik açıdan
en makul sonuçlar Geliştirilmiş Deng entropisi ile elde edilmiştir. Bu sonucun
iki sebebi bulunmaktadır. Birincisi Shannon entropisi hesaplanırken kütle
fonksiyonları kullanılamamaktadır. İkincisi ise Deng entropisinin sezgisel yapı
ölçeğini dikkate almamasıdır.

References

  • Chin, K.S., Fu, C., Wang, Y., 2015. A method of determining attribute weights in evidential reasoning approach based on incompatibility among attributes. Computers and Industrial Engineering vol. 87, pp. 150-162.
  • Deng, Y., 2016. Deng entropy. Chaos, Solitions and Fractals vol. 91, pp. 549-553.
  • Doyle, L.R., 2009. Quantification of Information in a One-Way Plant to Animal Communication System. Entropy 11, pp. 431-442.
  • Du, W.S., Hu, B.Q., 2016. Attribute reduction in ordered decision tables via evidence theory. Information Science vol. 364-365, pp. 91-110.
  • Dubois, D., Prade, H., 1985. A note on measures of specificity for fuzzy sets. International Journal of General Systems vol. 10, no. 4, pp. 279-283.
  • Fu, C., Wang, Y., 2015. An interval difference based evidential reasoning approach with unknown attribute weights and utilities of assessment grades. Computers and Industrial Engineering vol.81, pp. 109-117.
  • George, T., Pal, N.R., 1996. Quantification of conflict in Dempster-Shafer framework: a new approach. International Journal of General Systems vol. 24, no. 4, pp. 407-423.
  • Gorelick, R., 2006. Combining richness and abundance into a single diversity index using matrix analogues of Shannon’s and Simpson’s indices. Ecography 29, 525-530.
  • Jiang, W., Xie, C., Wei, B., Zhou, D., 2016a. A Improved method for risk evaluation in failure models and effects analysis of aircraft turbine rotor blades. Advances in Mechanical Enginnering vol. 8, no. 4, pp. 1-16.
  • Jiang, W, Wei, B, Xie, C, Zhou, D., 2016b. An evidential sensor fusion method in fault diagnosis. Advances in Mechanic Engineering vol 8(3), pp. 1-7.
  • Jiang, W., Wei, B., Qin, X., Zhan, J., Tang, Y., 2016c. Sensor data fusion based on a new conflict measure. Mathematical Problems in Engineering vol. 2016, p.11.
  • Jiang, W., Xie, C., Zhuang, M., Shou, Y., Tang, Y., 2016d. Sensor data fusion with z-numbers and its application in fault diagnosis. Sensor vol. 16, no. 9, p.1509. Jost, L., 2006. Entropy and diversity. Oikos 113, 363-375.
  • Klir, G.J., Ramer, A., 1990. Uncertainly in the Dempster-Shafer theory: a critical re-examination. International Journal of General Systems vol. 18, no.2, pp. 155-166.
  • Liu, Z., Pan, Q., Dezert, J., 2013. A new belief-based K-nearest neighbor classification method. Pattern Recognition vol. 46, no.3, pp. 834-844.
  • Liu, Z.G., Pan, Q., Dezert, J., Martin, A. 2016. Adaptive imputation of missing values for incomplete pattern classification. Pattern Recognition vol. 52, pp. 85-95.
  • Ma, J., Liu, W., Benferhat, S., 2015. A belief revision framework for revising epistemic states with partial epistemic states. International Journal of Approximate Reasoning 59; 20-40.
  • Özkan, K., 2016a. Application of Information Theory for an Entropic Gradient of Ecological Sites. Entropy 18: 340.
  • Özkan, K., 2016b. Biyolojik Çeşitlilik Bileşenleri (α, ß, γ) Nasıl Ölçülür. Süleyman Demirel Üniversitesi, Orman Fakültesi Yayın No: 98, ISBN: 976-9944-452-89-2, Isparta, 142 s.
  • Robinson, D.W., 2008. Entropy and uncertainty. Entropy 10(4): 493-506.
  • Shannon, C.E., 1948. A mathematical theory of communication. Bell Syst Tech J 27: 379-423.
  • Song, Y., Wang, X., Lei, L., Yue, S., 2016. Uncertainly measure for interval-valued belief structures. Measurement vol. 80, pp. 241-250.
  • Song, Y., Wang, X., Zhang, H., 2015. A distance measure between intuitionistic fuzzy belief functions. Knowlegde-Based Systems vol. 86, pp. 288-298.
  • Su, X., Deng, Y., Mahadevan, S., Bao, Q., 2012. An improved method for risk evaluation in failure models and effects analysis of aircraft engine rotor blades. Engineering Failure Analysis vol.26, pp.164-174.
  • Tang, Y., Zhou, D., Jiang, W., 2016. A new fuzzy-evidential controller for stabilization of the planar inverted pendulum systems. PLos ONE vol. 11, no. 8.
  • Wang, Y.M., Elhag, T.M.S., 2007. A comparison of neural network, evidential reasoning and multiple regression analysis in modelling bridge risks. Expert Systems with Applications vol. 32, no. 2, pp.336-348.
  • Wang, Y.M., Yang, J.B., Xu, D.L., Chin, K.S., 2009. Consumer preference prediction by using a hybrid evidential reasoning and belief rule-based methodology. Expert Systems with Applications vol. 36, no. 4, pp. 8421-8430.
  • Yager, R.R., 1983. Entropy and specificity in a mathematical theory of evidence. International Journal of General Systems vol. 9, no. 4, pp. 249-260.
  • Yager, R.R., Filev, D.P., 1995. Including probabilistic uncertainly in fuzzy logic controller modeling using dempster-shafer theory. IEEE Transactions on Systems, Man, and Cybernetics vol. 25, no. 8, pp.1221-1230.
  • Yang, Y., Han, D., 2016. A new distance-based total uncertainly measure in the theory of belief functions. Knowledge-Based Systems vol. 94, pp.114-123.
  • Yuan, K., Xiao, F., Fei, L., Kang, B., Deng, Y., 2016. Modelling sensor reliability in fault diagnosis based on evidence theory. Sensor vol. 16, no. 1, article 113.
  • Zhou, K., Martin, A., Pan, Q., Liu, Z.G., 2015. Medial evindential c-means algorithm and its application to community detection. Knowlegde-Based Systems vol. 74, pp. 69-88.
  • Zhou, D., Tang, Y., Jiang, W., 2017. A Improved belief entropy in Dempster-Shafer framework. PLoS ONE 12(5): e0176832.

Comparing Shannon entropy with Deng entropy and improved Deng entropy for measuring biodiversity when a priori data is not clear

Year 2018, Volume: 68 Issue: 2, 136 - 140, 20.07.2018

Abstract

DOI: 10.26650/forestist.2018.340634

The various diversity measures used to
measure biodiversity include the Margalef index, McIntosh index, Simpson index,
Brillouin index, and Shannon entropy. Of these measures, the most popular is
Shannon entropy (H). In this study, with respect to measuring biodiversity, we
compare Shannon entropy-the essential aspect of information theory-with the
Deng and improved Deng entropies, as proposed within the framework of the
Dempster–Shafer evidential theory. To do so, we used a hypothetical dataset of
three complexes. Based on this hypothetic data, ecologically speaking, we
obtained the most reasonable result from the improved Deng entropy. There are
two reasons for this result: 1) Mass functions cannot be used when computing
the Shannon entropy, and 2) Deng entropy does not take into consideration the
scale of the frame of discernment.

References

  • Chin, K.S., Fu, C., Wang, Y., 2015. A method of determining attribute weights in evidential reasoning approach based on incompatibility among attributes. Computers and Industrial Engineering vol. 87, pp. 150-162.
  • Deng, Y., 2016. Deng entropy. Chaos, Solitions and Fractals vol. 91, pp. 549-553.
  • Doyle, L.R., 2009. Quantification of Information in a One-Way Plant to Animal Communication System. Entropy 11, pp. 431-442.
  • Du, W.S., Hu, B.Q., 2016. Attribute reduction in ordered decision tables via evidence theory. Information Science vol. 364-365, pp. 91-110.
  • Dubois, D., Prade, H., 1985. A note on measures of specificity for fuzzy sets. International Journal of General Systems vol. 10, no. 4, pp. 279-283.
  • Fu, C., Wang, Y., 2015. An interval difference based evidential reasoning approach with unknown attribute weights and utilities of assessment grades. Computers and Industrial Engineering vol.81, pp. 109-117.
  • George, T., Pal, N.R., 1996. Quantification of conflict in Dempster-Shafer framework: a new approach. International Journal of General Systems vol. 24, no. 4, pp. 407-423.
  • Gorelick, R., 2006. Combining richness and abundance into a single diversity index using matrix analogues of Shannon’s and Simpson’s indices. Ecography 29, 525-530.
  • Jiang, W., Xie, C., Wei, B., Zhou, D., 2016a. A Improved method for risk evaluation in failure models and effects analysis of aircraft turbine rotor blades. Advances in Mechanical Enginnering vol. 8, no. 4, pp. 1-16.
  • Jiang, W, Wei, B, Xie, C, Zhou, D., 2016b. An evidential sensor fusion method in fault diagnosis. Advances in Mechanic Engineering vol 8(3), pp. 1-7.
  • Jiang, W., Wei, B., Qin, X., Zhan, J., Tang, Y., 2016c. Sensor data fusion based on a new conflict measure. Mathematical Problems in Engineering vol. 2016, p.11.
  • Jiang, W., Xie, C., Zhuang, M., Shou, Y., Tang, Y., 2016d. Sensor data fusion with z-numbers and its application in fault diagnosis. Sensor vol. 16, no. 9, p.1509. Jost, L., 2006. Entropy and diversity. Oikos 113, 363-375.
  • Klir, G.J., Ramer, A., 1990. Uncertainly in the Dempster-Shafer theory: a critical re-examination. International Journal of General Systems vol. 18, no.2, pp. 155-166.
  • Liu, Z., Pan, Q., Dezert, J., 2013. A new belief-based K-nearest neighbor classification method. Pattern Recognition vol. 46, no.3, pp. 834-844.
  • Liu, Z.G., Pan, Q., Dezert, J., Martin, A. 2016. Adaptive imputation of missing values for incomplete pattern classification. Pattern Recognition vol. 52, pp. 85-95.
  • Ma, J., Liu, W., Benferhat, S., 2015. A belief revision framework for revising epistemic states with partial epistemic states. International Journal of Approximate Reasoning 59; 20-40.
  • Özkan, K., 2016a. Application of Information Theory for an Entropic Gradient of Ecological Sites. Entropy 18: 340.
  • Özkan, K., 2016b. Biyolojik Çeşitlilik Bileşenleri (α, ß, γ) Nasıl Ölçülür. Süleyman Demirel Üniversitesi, Orman Fakültesi Yayın No: 98, ISBN: 976-9944-452-89-2, Isparta, 142 s.
  • Robinson, D.W., 2008. Entropy and uncertainty. Entropy 10(4): 493-506.
  • Shannon, C.E., 1948. A mathematical theory of communication. Bell Syst Tech J 27: 379-423.
  • Song, Y., Wang, X., Lei, L., Yue, S., 2016. Uncertainly measure for interval-valued belief structures. Measurement vol. 80, pp. 241-250.
  • Song, Y., Wang, X., Zhang, H., 2015. A distance measure between intuitionistic fuzzy belief functions. Knowlegde-Based Systems vol. 86, pp. 288-298.
  • Su, X., Deng, Y., Mahadevan, S., Bao, Q., 2012. An improved method for risk evaluation in failure models and effects analysis of aircraft engine rotor blades. Engineering Failure Analysis vol.26, pp.164-174.
  • Tang, Y., Zhou, D., Jiang, W., 2016. A new fuzzy-evidential controller for stabilization of the planar inverted pendulum systems. PLos ONE vol. 11, no. 8.
  • Wang, Y.M., Elhag, T.M.S., 2007. A comparison of neural network, evidential reasoning and multiple regression analysis in modelling bridge risks. Expert Systems with Applications vol. 32, no. 2, pp.336-348.
  • Wang, Y.M., Yang, J.B., Xu, D.L., Chin, K.S., 2009. Consumer preference prediction by using a hybrid evidential reasoning and belief rule-based methodology. Expert Systems with Applications vol. 36, no. 4, pp. 8421-8430.
  • Yager, R.R., 1983. Entropy and specificity in a mathematical theory of evidence. International Journal of General Systems vol. 9, no. 4, pp. 249-260.
  • Yager, R.R., Filev, D.P., 1995. Including probabilistic uncertainly in fuzzy logic controller modeling using dempster-shafer theory. IEEE Transactions on Systems, Man, and Cybernetics vol. 25, no. 8, pp.1221-1230.
  • Yang, Y., Han, D., 2016. A new distance-based total uncertainly measure in the theory of belief functions. Knowledge-Based Systems vol. 94, pp.114-123.
  • Yuan, K., Xiao, F., Fei, L., Kang, B., Deng, Y., 2016. Modelling sensor reliability in fault diagnosis based on evidence theory. Sensor vol. 16, no. 1, article 113.
  • Zhou, K., Martin, A., Pan, Q., Liu, Z.G., 2015. Medial evindential c-means algorithm and its application to community detection. Knowlegde-Based Systems vol. 74, pp. 69-88.
  • Zhou, D., Tang, Y., Jiang, W., 2017. A Improved belief entropy in Dempster-Shafer framework. PLoS ONE 12(5): e0176832.
There are 32 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Kürşad Özkan

Publication Date July 20, 2018
Published in Issue Year 2018 Volume: 68 Issue: 2

Cite

APA Özkan, K. (2018). Comparing Shannon entropy with Deng entropy and improved Deng entropy for measuring biodiversity when a priori data is not clear. Forestist, 68(2), 136-140.
AMA Özkan K. Comparing Shannon entropy with Deng entropy and improved Deng entropy for measuring biodiversity when a priori data is not clear. FORESTIST. July 2018;68(2):136-140.
Chicago Özkan, Kürşad. “Comparing Shannon Entropy With Deng Entropy and Improved Deng Entropy for Measuring Biodiversity When a Priori Data Is Not Clear”. Forestist 68, no. 2 (July 2018): 136-40.
EndNote Özkan K (July 1, 2018) Comparing Shannon entropy with Deng entropy and improved Deng entropy for measuring biodiversity when a priori data is not clear. Forestist 68 2 136–140.
IEEE K. Özkan, “Comparing Shannon entropy with Deng entropy and improved Deng entropy for measuring biodiversity when a priori data is not clear”, FORESTIST, vol. 68, no. 2, pp. 136–140, 2018.
ISNAD Özkan, Kürşad. “Comparing Shannon Entropy With Deng Entropy and Improved Deng Entropy for Measuring Biodiversity When a Priori Data Is Not Clear”. Forestist 68/2 (July 2018), 136-140.
JAMA Özkan K. Comparing Shannon entropy with Deng entropy and improved Deng entropy for measuring biodiversity when a priori data is not clear. FORESTIST. 2018;68:136–140.
MLA Özkan, Kürşad. “Comparing Shannon Entropy With Deng Entropy and Improved Deng Entropy for Measuring Biodiversity When a Priori Data Is Not Clear”. Forestist, vol. 68, no. 2, 2018, pp. 136-40.
Vancouver Özkan K. Comparing Shannon entropy with Deng entropy and improved Deng entropy for measuring biodiversity when a priori data is not clear. FORESTIST. 2018;68(2):136-40.