Mathematical Modeling of Natural Phenomena: A Fuzzy Logic Approach

Abstract

Summary. In many fields of science human observers have provided verbal descriptions and explanations of various systems. A formal mathematical model is indispensable when we wish to rigorously analyze these systems. In this chapter, we survey some recent results on transforming verbal descriptions into mathematical models using fuzzy modeling. This is a simple and direct approach that offers a unique advantage-the close relationship between the verbal description and the mathematical model can be used to verify the validity of the verbal explanation suggested by the observer. We review two applications of this approach from the field of ethology: the territorial behavior of the fish and the orientation to light of a flat worm. We believe that the fuzzy modeling approach demonstrated here may supply a suitable framework for biomimicry, that is, the design of artificial systems based on mimicking a natural behavior observed in nature.keywords: Linguistic modeling, animal and human behavior, territorial behavior, mathematical modeling in biology, hybrid systems, discrete-event systems, biomimicry.

Mathematical modeling of the lambda switch: A fuzzy logic approach

“…Recently, FM has been used in the modeling and analysis of biological phenomena and, in particular, in deriving mathematical models of animal behavior Margaliot, 2004, 2005;Bajec et al, 2005;Rashkovsky and Margaliot, 2007;Rozin and Margaliot, 2007;Margaliot, 2007). This application of FM is somewhat different than the typical approach applied in the construction of AESs.…”

Evaluation of Neoergasilus japonicus (Ergasilidae) Occurrence on Rudd Scardinius erythrophthalmus Using Fuzzy Logic Approach

“…Fuzzy Logic (FL) theory, which emerged during the twentieth century, was predicted to apply to many areas and disciplines such as economics, control systems evaluation of student performance, and many others (Allahverdi, 2009;Badwawi, Issa, Mallick, ve Abusara, 2016;Bassford ve Painter, 2016;Buemi, Giacalone, Naccari, ve Spampinato, 2016;Cordón, 2011;Fat, Mic, Kilyen, Santa, ve Letia, 2016;Gokmen et al, 2010;Katbab, 1995;Michalczuk, Ufnalski, ve Grzesiak, 2016;Setyaningrum ve Swarinata, 2014;Turksen, 1997). There are also some scientific articles about the application of fuzzy logic in the fishery industry (Boavida, Dias, Ferreira, ve Santos, 2014;Carbajal-Hernández, Sánchez-Fernández, Carrasco-Ochoa, ve Martínez-Trinidad, 2012;Cheung, Pitcher, ve Pauly, 2005;Farghally, Atia, Elmadany, ve Fahmy, 2014;Hattab et al, 2013;Jarre et al, 2008;Lea et al, 1998;Margaliot, 2007;Mendel, 1995;Van Rijn, Tal, ve Schreier, 2006). In this original research article, by using a fuzzy logic approach, we were able to model a system that predicts the existence of N. japonicus on S. erythrophthalmus and the results were compared with data obtained from another experiment to show that the results are compatible.…”