#### DMCA

## Mathematical modeling of observed natural behavior: a fuzzy logic approach (2004)

Venue: | Fuzzy Sets Systems |

Citations: | 14 - 10 self |

### Citations

6238 |
Fuzzy sets
- Zadeh
(Show Context)
Citation Context ...itable when modeling with accurate, yet incomplete, knowledge rather than with linguistic knowledge. Zadeh laid down the foundations of fuzzy sets and fuzzy logic and linked them to human linguistics =-=[31-=-] [32]. Mamdani designed the rst fuzzy controller based on a linguistic control protocol [15]. His work demonstrated the applicability of fuzzy expert systems and led the way to numerous applications ... |

892 |
Outline of a New Approach to the Analysis of Complex Systems and Decision Processes
- Zadeh
- 1973
(Show Context)
Citation Context ...e when modeling with accurate, yet incomplete, knowledge rather than with linguistic knowledge. Zadeh laid down the foundations of fuzzy sets and fuzzy logic and linked them to human linguistics [31] =-=[32-=-]. Mamdani designed the rst fuzzy controller based on a linguistic control protocol [15]. His work demonstrated the applicability of fuzzy expert systems and led the way to numerous applications (see,... |

644 |
Sociobiology: The New Synthesis,
- Wilson
- 1975
(Show Context)
Citation Context ...istic description of both their observations and interpretations. Thus, we demonstrate the fuzzy modeling approach using an example from ethology. Territory has a major role in social animal behavior =-=[-=-29] and results in a rich set of phenomena, but how is the territory created? Nobel Laureate Konrad Lorenz describes a specic example: . . . a real stickleback ght can be seen only when two males are ... |

488 |
Neuro-fuzzy and soft computing: A computational approach to learning and machine intelligence,” Upper Saddle River,
- Jang, Sun, et al.
- 1997
(Show Context)
Citation Context ...s case, methods such as fuzzy clustering, neural learning, or least squares can be used to ne-tune the model using the discrepancy between the measurements and the model's output (see, e.g., [8] [3] [=-=9-=-] and the references therein). 4 An example: territorial behavior There are at least two reasons for modeling the behavior of animals (and humans) using fuzzy sets and fuzzy logic. The rst is that for... |

448 |
Neural networks and fuzzy systems, a dynamical systems approach to machine intelligence
- Kosko
- 1992
(Show Context)
Citation Context ... modeling dynamic systems the amount of fuzziness (or uncertainty) increases with every iteration. This implies that the system can be simulated eectively only for relatively short time spans. Kosko [=-=12]-=- suggested fuzzy cognitive maps (FCMs) as a tool for the representation of causal relationships between various linguistic concepts. FCMs were used to model several interesting real world phenomena (s... |

382 | The Study of Instinct - Tinbergen - 1951 |

354 |
Qualitative Reasoning: modeling and simulation with incomplete knowledge
- �Kuipers
- 1994
(Show Context)
Citation Context ...es (e.g., a temperature of 30 Celsius) are modeled in precisely the same way as fuzzy terms (e.g., warm weather). A more systematic approach to modeling physical systems is qualitative reasoning (QR) =-=[13-=-] which allows transforming qualitative descriptions of a system into qualitative dierential equations. These are generalizations of 2 To date, more than 30 books on system dynamics appeared. A very r... |

272 |
Filev, "Essentials of fuzzy modelling and control
- Yager, P
- 1994
(Show Context)
Citation Context ...e rst fuzzy controller based on a linguistic control protocol [15]. His work demonstrated the applicability of fuzzy expert systems and led the way to numerous applications (see, e.g., [7] [24] [25] [=-=30]-=- [23].) However, most of these applications are based not on modeling real world phenomena, but rather on transforming the knowledge of a human expert into a fuzzy expert system. Thus, the expert may ... |

212 |
Anticipatory Systems.
- Rosen
- 1985
(Show Context)
Citation Context ...e this using an example of territorial behavior of sh. keywords: Linguistic modeling, fuzzy system models, ethology. 2 1 Introduction Formal models play a crucial role in all elds of science. Rosen [2=-=0-=-] claims that they are based on the belief that . . . causal sequences in the world of phenomena can be faithfully imaged by implication in the formal world of propositions describing these phenomena.... |

202 |
Introduction to System Dynamics Modeling with Dynamo,
- Richardson, Pugh
- 1981
(Show Context)
Citation Context ...ransforming qualitative descriptions of a system into qualitative dierential equations. These are generalizations of 2 To date, more than 30 books on system dynamics appeared. A very readable one is [=-=19-=-]. The journal Systems Dynamics Review contains up-to-date papers 7 dierential equations that include two main ingredients: (1) Functional relationships between variables can be represented by functio... |

107 |
Applications of fuzzy algorithms for simple dynamic plant
- Mamdani
- 1974
(Show Context)
Citation Context ...wledge. Zadeh laid down the foundations of fuzzy sets and fuzzy logic and linked them to human linguistics [31] [32]. Mamdani designed the rst fuzzy controller based on a linguistic control protocol [=-=15]-=-. His work demonstrated the applicability of fuzzy expert systems and led the way to numerous applications (see, e.g., [7] [24] [25] [30] [23].) However, most of these applications are based not on mo... |

88 | 2001, Designing fuzzy inference systems from data: an interpretability-oriented review
- Guillaume
(Show Context)
Citation Context .... In this case, methods such as fuzzy clustering, neural learning, or least squares can be used to ne-tune the model using the discrepancy between the measurements and the model's output (see, e.g., [=-=8-=-] [3] [9] and the references therein). 4 An example: territorial behavior There are at least two reasons for modeling the behavior of animals (and humans) using fuzzy sets and fuzzy logic. The rst is ... |

29 |
Simplification and scaling.
- Segel
- 1972
(Show Context)
Citation Context ...ed to a model based on Zadeh's compositional rule of inference. When modeling real-worlds systems, the variables are physical quantities with dimensions (e.g., length, time.) Dimensional analysis [2] =-=[21]-=-, that is, 12 the process of introducing dimensionless variables, can many times simplify the resulting equations and decrease the number of parameters. For example, suppose that the fuzzy model inclu... |

29 |
Applied fuzzy systems,”
- Terano, AsaI, et al.
- 1994
(Show Context)
Citation Context ...ed the rst fuzzy controller based on a linguistic control protocol [15]. His work demonstrated the applicability of fuzzy expert systems and led the way to numerous applications (see, e.g., [7] [24] [=-=25]-=- [30] [23].) However, most of these applications are based not on modeling real world phenomena, but rather on transforming the knowledge of a human expert into a fuzzy expert system. Thus, the expert... |

27 |
King Solomon’s ring.
- Lorenz
- 1952
(Show Context)
Citation Context ...ry. In fact, this too is congruent with the behavior observed in nature: . . . the relative ghting potential of the individual is shown by the size of the territory which he keeps clear of rivals. [14=-=]-=- 4.4 Prediction We can also use the mathematical model, such as (1), to analyze and simulate new scenarios that were not described by the observer. The results can be regarded as predictions of the be... |

25 |
Adventures in Modeling: Exploring Complex, Dynamic Systems with StarLogo
- Colella, Klopfer, et al.
- 2001
(Show Context)
Citation Context ...erns of birds, and the behavior of human drivers in congested highways. An interesting research topic is the implementation of fuzzy modeling tools in existing simulation environments (e.g., StarLogo =-=[5]-=-) allowing the observer to intuitively program, simulate, and re ne her verbal model. This can make fuzzy modeling more accessible to researchers in many elds of science. Acknowledgements We thank the... |

19 | M.: The Local Paradigm for Modeling and Control: From NeuroFuzzy to Lazy Learning
- Bontempi, Bersini, et al.
- 2001
(Show Context)
Citation Context ... this case, methods such as fuzzy clustering, neural learning, or least squares can be used to ne-tune the model using the discrepancy between the measurements and the model's output (see, e.g., [8] [=-=3-=-] [9] and the references therein). 4 An example: territorial behavior There are at least two reasons for modeling the behavior of animals (and humans) using fuzzy sets and fuzzy logic. The rst is that... |

17 |
Fuzzy Information Engineering,
- Dubois, Prade, et al.
- 1997
(Show Context)
Citation Context ...ni designed the rst fuzzy controller based on a linguistic control protocol [15]. His work demonstrated the applicability of fuzzy expert systems and led the way to numerous applications (see, e.g., [=-=7]-=- [24] [25] [30] [23].) However, most of these applications are based not on modeling real world phenomena, but rather on transforming the knowledge of a human expert into a fuzzy expert system. Thus, ... |

16 |
Introduction : The real contribution of fuzzy systems”, in: Fuzzy systems: Modelling and control
- Dubois, Nguyen, et al.
- 1998
(Show Context)
Citation Context ...rm linguistic 4 observations into mathematical entities. Fuzzy modeling is the most eective approach for transforming linguistic data into mathematical formulas and vice-versa. Indeed, Dubois et al. [=-=6]-=- state that the real power of fuzzy logic lies in its ability to combine modeling (constructing a function that accurately mimics given data) and abstracting (articulating knowledge from the data) 1 .... |

16 |
New Approaches to Fuzzy Modeling
- Margaliot, Langholz
- 2000
(Show Context)
Citation Context ...o build mathematical models quickly, focusing on the 'what' instead of the 'how'. The 1 This is well demonstrated in the computing with words version of Lyapunov synthesis developed in [16] (see also =-=[17-=-]) 5 resulting mathematical model allows the observer to enjoy all the benets of a mathematical model and, in particular, can be used to prove or refute the modeler's ideas as to how the natural syste... |

16 |
Fuzzy Decision Making in Modeling and Control
- Kaymak
- 2002
(Show Context)
Citation Context ... logical operators, inferencing method, and the values of the dierent parameters. We now discuss several guidelines that can assist in selecting the dierent ingredients of the fuzzy model (see also [2=-=-=-2] for details on how the dierent elements in the fuzzy model inuence its behavior). It is important that the resulting mathematical model will have a simple (as possible) form, and that it will be am... |

13 | Fuzzy Lyapunov Based Approach to the Design of Fuzzy Controllers”,
- Margaliot, Langholz
- 1999
(Show Context)
Citation Context ...various elds to build mathematical models quickly, focusing on the 'what' instead of the 'how'. The 1 This is well demonstrated in the computing with words version of Lyapunov synthesis developed in [=-=16-=-] (see also [17]) 5 resulting mathematical model allows the observer to enjoy all the benets of a mathematical model and, in particular, can be used to prove or refute the modeler's ideas as to how th... |

9 |
Adaptive random fuzzy cognitive maps
- Aguilar
- 2002
(Show Context)
Citation Context ...ggested fuzzy cognitive maps (FCMs) as a tool for the representation of causal relationships between various linguistic concepts. FCMs were used to model several interesting real world phenomena (see =-=[1-=-] and the references therein). However, the inferencing process used in FCMs yields a discrete-time linear system in the form x(k + 1) = Ax(k), which is clearly too simplied to faithfully depict many ... |

7 |
Deductive verbal models of organizations,
- Wenstop
- 1976
(Show Context)
Citation Context ...on modeling real world phenomena, but rather on transforming the knowledge of a human expert into a fuzzy expert system. Thus, the expert may be replaced by a computer. The pioneering work of Wenstop =-=[2-=-8] [27] was aimed at building verbal models that can represent and process linguistic information. The basic ingredients of this model include (1) generative grammarused for dening the 8 semantics of ... |

7 |
Fuzzy Decision Making in Modeling and Control. World Scientific,
- Sousa, Kaymak
- 2002
(Show Context)
Citation Context ... logical operators, inferencing method, and the values of the di erent parameters. We now discuss several guidelines that can assist in selecting the di erent ingredients of the fuzzy model (see also =-=[22]-=- for details on how the di erent elements in the fuzzy model in uence its behavior). It is important that the resulting mathematical model will have a simple (as possible) form, and that it will be am... |

5 |
New approaches to Fuzzy modeling and control design and analysis
- Margaliot, Langholz
- 2000
(Show Context)
Citation Context ...er’s ideas as to how the natural system behaves and why. This approach eliminates the 1 This is well demonstrated in the computing with words version of Lyapunov synthesis developed in [16] (see also =-=[17]-=-).E. Tron, M. Margaliot / Fuzzy Sets and Systems 146 (2004) 437–450 439 arti cial distance between the observer who studied the actual system and the mathematician who creates a suitable mathematical... |

4 |
Fuzzy pharmacology: theory and applications
- Sproule, Naranjo, et al.
- 2002
(Show Context)
Citation Context ...t fuzzy controller based on a linguistic control protocol [15]. His work demonstrated the applicability of fuzzy expert systems and led the way to numerous applications (see, e.g., [7] [24] [25] [30] =-=[23]-=-.) However, most of these applications are based not on modeling real world phenomena, but rather on transforming the knowledge of a human expert into a fuzzy expert system. Thus, the expert may be re... |

3 |
An example of linguistic modeling: the case of Mulder’s theory of power
- Kickert
- 1979
(Show Context)
Citation Context ...e implemented using the APL computer language so the entire process was automated. Wenstop and Kickert developed verbal models of several interesting systems from the social sciences [28] [10, Ch. 7] =-=[11-=-]. However, verbal models are not standard mathematical models as their input and output are linguistic values rather than numerical values. As such, verbal models suer from two drawbacks. First, ther... |

2 |
Anco: Symmetry and integration methods for dierential equations
- Bluman, C
- 2002
(Show Context)
Citation Context ...ferred to a model based on Zadeh's compositional rule of inference. When modeling real-worlds systems, the variables are physical quantities with dimensions (e.g., length, time.) Dimensional analysis =-=[2]-=- [21], that is, 12 the process of introducing dimensionless variables, can many times simplify the resulting equations and decrease the number of parameters. For example, suppose that the fuzzy model ... |

2 |
Fuzzy Modeling and
- Sugeno, Kang
- 1986
(Show Context)
Citation Context ...esigned the rst fuzzy controller based on a linguistic control protocol [15]. His work demonstrated the applicability of fuzzy expert systems and led the way to numerous applications (see, e.g., [7] [=-=24]-=- [25] [30] [23].) However, most of these applications are based not on modeling real world phenomena, but rather on transforming the knowledge of a human expert into a fuzzy expert system. Thus, the e... |

2 |
Türksen: Fuzzy pharmacology: theory and applications. Trends Pharmacol. Sci.
- Sproule, Naranjo, et al.
- 2002
(Show Context)
Citation Context ...ani designed the rst fuzzy controller based on a linguistic control protocol [15]. His work demonstrated the applicability of fuzzy expert systems and led the way to numerous applications (see, e.g., =-=[7,24,25,30,23]-=-). However, most of these applications are based not on modeling real-world phenomena, but rather on transforming the knowledge of a human expert into a fuzzy expert system. Thus, the expert may be re... |

1 |
to Aristotle: Toward a Theory of Models for Living Systems
- Introduction
- 1989
(Show Context)
Citation Context ...imaged by implication in the formal world of propositions describing these phenomena. Thus, inference in a formal model parallels causality in the natural world. Mathematical models, dened by Casti [4=-=]-=- as a program or algorithm that encapsulates the order present in a given natural system, play a fundamental role in science. The derivation of a mathematical model forces the researcher to formalize ... |

1 | The Routh–Hurwitz array and realization of characteristic polynomials
- Margaliot, Langholz
- 2000
(Show Context)
Citation Context ... = s 4 + 2s 3 + ( t 1 2 + t 2 2 t 1 t 2 4 + 2t 1 log 2 a 1 + 2t 2 log 2 a 2 )s 2 +( 2t 1 log 2 a 1 + 2t 2 log 2 a 2 )s + 4t 1 t 2 log 2 2 a 1 a 2 ; and the rst column of the Routh-Hurwitz array (see [=-=18]-=- and the references therein) of P (s) is 1; 2; t 1 2 + t 2 2 t 1 t 2 4 + t 1 log 16 4a 1 + t 2 log 16 4a 2 ; num den ; 4 t 1 t 2 log 2 2 a 1 a 2 where den = t 1 2 + t 2 2 t 1 t 2 4 + t 1 log 2 a1 + t ... |

1 |
Quantitative analysis with linguistic rules, Fuzzy Sets and Systems 4
- Wenstop
- 1980
(Show Context)
Citation Context ...deling real world phenomena, but rather on transforming the knowledge of a human expert into a fuzzy expert system. Thus, the expert may be replaced by a computer. The pioneering work of Wenstop [28] =-=[2-=-7] was aimed at building verbal models that can represent and process linguistic information. The basic ingredients of this model include (1) generative grammarused for dening the 8 semantics of the l... |

1 |
Karlqvist (Eds.), Newton to Aristotle: Toward a Theory of Models for Living Systems
- Casti, Introduction, et al.
- 1989
(Show Context)
Citation Context ... - see front matter c○ 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.fss.2003.09.005438 E. Tron, M. Margaliot / Fuzzy Sets and Systems 146 (2004) 437–450 Mathematical models, de ned by Casti =-=[4]-=- as a program or algorithm that encapsulates the order present in a given natural system, play a fundamental role in science. The derivation of a mathematical model forces the researcher to formalize ... |

1 |
Fuzzy Theories on Decision-Making, Martinus Nijho
- Kickert
- 1978
(Show Context)
Citation Context ...tic approximation—used for attaching linguistic labels to the outputs. These ingredients were implemented using the APL computer language so the entire process was automated. Wenstop [28] and Kickert =-=[10,11]-=- developed verbal models of several interesting systems from the social sciences. However, verbal models are not standard mathematical models as their input and output are linguistic values rather tha... |

1 |
Simpli cation and scaling
- Segel
- 1972
(Show Context)
Citation Context ...ferred to a model based on Zadeh’s compositional rule of inference. When modeling real-worlds systems, the variables are physical quantities with dimensions (e.g., length, time). Dimensional analysis =-=[2,21]-=-, that is, the process of introducing dimensionless variables, can many times simplify the resulting equations and decrease the number of parameters. For example, suppose that the fuzzy model includes... |

1 |
Deductive verbal models of organizations, in: E.H
- Wenstop
- 1981
(Show Context)
Citation Context ...ared. A very readable one is [19]. The journal Systems Dynamics Review contains up-to-date papers.440 E. Tron, M. Margaliot / Fuzzy Sets and Systems 146 (2004) 437–450 The pioneering work of Wenstop =-=[28,27]-=- was aimed at building verbal models that can represent and process linguistic information. The basic ingredients of this model include (1) generative grammar—used for de ning the semantics of the lin... |