Issue:Intuitionistic fuzzy estimations of biological interactions

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to: navigation, search
Title of paper: Intuitionistic fuzzy estimations of biological interactions
Hristo Aladjov
Institute of Biophysics and Biomedical Engineering, BAS, Acad. G. Bonchev Str., bl.105, 1113 Sofia, Bulgaria
Presented at: 7th IWIFS, Banska Bystrica, 27 September 2011
Published in: Conference proceedings, "Notes on IFS", Volume 17 (2011) Number 4, pages 29—38
Download: Download-icon.png PDF (576  Kb, Info) Download-icon.png
Abstract: All living organisms sustain their life, reproduce and evolve through interaction with the biotic and abiotic components of their ecosystems. Therefore, the mathematical formalism chosen to describe interactions generally predetermines the scope and properties of the ecological models it is part of. The goal of the present paper is to introduce intuitionistic fuzzy estimations of the interaction between two living organisms capable of aggregating the positive and negative aspects of the interaction, as well as the uncertainty with which they can be determined. Using the concept of intuitionistic fuzzy sets, new continuous formulation of the six basic types of biological interactions (neutralism, amensalism, commensalism, competition, mutualism, predation or parasitism) is presented. This formulation is capable of incorporating different sources of uncertainty, including the ambiguity in the discrimination of direct and environment mediated effects. In the special case when the uncertainty of interaction between two living organisms comes from unaccounted small changes in their relatively constant environment, a method for estimation the interaction components based on observations of interacting objects is provided. A simple averaging algorithm is presented for generalizing the results of multiple observations. Future extensions and possible applications of the intuitionistic fuzzy estimations of biological interactions are also discussed.
Keywords: Biological interactions, Intuitionistic fuzzy sets, Forward and inverse problems in ecology, Neutralism, Amensalism, Commensalism, Competition, Mutualism, Predation, Parasitism
AMS Classification: 92D40, 03B52
  1. Atanassov K. (1987). Generalized index matrices, Comptes rendus de l'Academie bulgare des Sciences, Vol. 40, No.11, 15–18.
  2. Atanassov K. (1991). Temporal intuitionistic fuzzy sets. Comptes rendus de l'Academie bulgare des Sciences, Vol. 44, No. 7, 5–7.
  3. Atanassov, K. (1999) Intuitionistic Fuzzy Sets, Springer Physica-Verlag, Heidelberg.
  4. Atanassov, K. (2007). Remark on intuitionistic fuzzy numbers. Notes on Intuitionistic Fuzzy Sets, Vol. 13, No. 3, 29–32.
  5. Atanassov, K. (2010). On index matrices. Part 1: Standard cases. Advanced Studies in Contem¬porary Mathematics, Vol. 20, No. 2, 291–302.
  6. Atanassov, K. (2010). On index matrices. Part 2: Intuitionistic fuzzy case. Proceedings of the Jangjeon Mathematical Society, Vol. 13, No. 2, 121–126.
  7. Bellman, R., Kagiwada, H., Kalaba, R., (1966). Inverse problems in ecology Journal of Theoretical Biology Vol. 11, Issue 1, May 1966, 164–167
  8. Bender E., Case T., Gilpin M., (1984). Perturbation Experiments in Community Ecology: Theory and Practice. Ecology, Vol. 65, No. 1, 1–13.
  9. Berlow, E., Navarrete, S., Briggs, C., Power, M., Menge, B., (1999). Quantifying variation in the strengths of species interactions. Ecology 80, 2206–2224.
  10. Bone, C., Dragicevic, S., Roberts, A., (2006). A fuzzy-constrained cellular automata model of forest insect infestations, Ecological Modelling, 192(1-2), 107–125.
  11. Cao, G., (1995) The definition of the niche by fuzzy set theory, Ecological Modelling, 77(1), 65–71.
  12. Cardinale, B. J., M. A. Palmer, and S. L. Collins. 2002. Species diversity enhances ecosystem functioning through interspecific facilitation. Nature 415, 426–429.
  13. Dambacher, J., Li H., Rossignol, P., (2003). Qualitative predictions in model ecosystems, Ecological Modelling, 161(1-2), 79-93.
  14. Darwen, P., Green, D., (1996) Viability of populations in a landscape. Ecol. Model. 85, 165–171.
  15. Diederich, S., Opper, M., (1989). Replicators With Random Interactions - A Solvable Model. Physical review. A, Atomic, molecular, and optical physics, 39(8), 4333-4336.
  16. Dimakis, A., Müller-Hoissen, F., (2002). On generalized Lotka-Volterra lattices. Czechoslovak journal of physics, 52(11), 1187–1193.
  17. Dowd, M. (2003). A Bayesian approach to the ecosystem inverse problem. Ecological modelling. Vol. 168, 39–55.
  18. Ellis, C., Ramankutty N., (2008). Putting people in the map: anthropogenic biomes of the world. Frontiers in ecology and the environment. Vol. 6, 439–447.
  19. Fasham, M., Evans, G. (1995). The use of optimization techniques to model marine ecosystem dynamics at the JGOFS station at 47 degrees N 20 degrees W. Philos. Trans. R. Soc. Lond., B 348, 203–209.
  20. Fontanari, J, de Oliveira, V. (2000). Random replicators with high-order interactions. Physical review letters, 85(23), 4984–4987.
  21. Gléria, I., Figueiredo A., Brenig, L., Filho, T. (2005). The Lotka-Volterra canonical format. Ecological modelling, 183(1), 95–106.
  22. Goudard, A., Loreau, M., (2008). Nontrophic Interactions, Biodiversity, and Ecosystem Functioning: An Interaction Web Model. The American naturalist, 171(1), 91–106.
  23. Hernandez, M. (2009-01-01). Disentangling nature, strength and stability issues in the characterization of population interactions. Journal of theoretical biology, 261(1), 107–119.
  24. Hoekstra, A., Kroc, J., Sloot, M., (2010). Simulating Complex Systems by Cellular Automata, Chapter 7, Springer, Berlin.
  25. Holland, E., Burrow, J., Dytham, C., Aegerter, J., (2009). Modelling with uncertainty: Introducing a probabilistic framework to predict animal population dynamics, Ecological Modelling, 220(9-10), 1203–1217.
  26. Kokkoris, G., Jansen, A., (2003). Complexity and stability revisited. Ecology letters, 6(6), 498–502.
  27. Laska, M.,Wootton, J. (1998). Theoretical concepts and empirical approaches to measuring interaction strength. Ecology 79, 461–76
  28. Levins, R. Evolution in Changing Environments, Princeton University Press, 1968.
  29. Mobley C., (1973). A systematic approach to ecosystems analysis, Journal of Theoretical Biology, 42(1), 119–136.
  30. Molofsky, J., Bever, J. 2004. A new kind of ecology? BioScience, 54, 440–446.
  31. Moon, D. Moon, J., (2011) Abiotically-Mediated Direct and Indirect Effects. Nature Education Knowledge 2(1):9
  32. Neuhauser, C., Fargione J., (2004). A mutualism–parasitism continuum model and its application to plant–mycorrhizae interactions, Ecological Modelling. 177 (2004), 337–352.
  33. Paine, R. T. (1992). Food-web analysis through field measurement of per capita interaction strength. Nature (London), 355(6355), 73–75.
  34. Poderoso, F., (2005). The random replicator model at nonzero temperature. The European physical journal. B, Condensed matter physics, 48(4), 557–565.
  35. Poderoso F., Fontanari J. 2007 Model ecosystem with variable interspecies interactions. Journal of Physics A: Mathematical and Theoretical, 40(30), 8723-8738.
  36. Reiter, C., (2002). Fuzzy automata and life. Complexity (New York, N.Y.), 7(3), 19-29. Res. 23 (4), 389–413.
  37. Snyder, W., Prasad, P. (2010). A non-trophic interaction chain links predators in different spatial niches. Oecologia, 162(3), 747–753.
  38. Wolfram, S. (1986). Theory and Application of Cellular Automata. World Scientific.
  39. Wootton, J., (2001). Local interactions predict large-scale pattern in empirically derived cellular automata. Nature (London), 413(6858), 841–844.
  40. Wootton, J., Emmerson M. (2005). Measurement of Interaction Strength in Nature. Annual review of ecology, evolution, and systematics, 36(1), 419–444.
  41. Wootton, J. (1994). The Nature and Consequences of Indirect Effects in Ecological Communities. Annual review of ecology and systematics, 25, 443–466.
  42. Yimin, L., Hua J., (2008). Type-2 fuzzy mathematical modeling and analysis of the dynamical behaviors of complex ecosystems, Simulation Modelling Practice and Theory, 16(9), 1379–1391.

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.