Fuzzy qualitative simulation

Simulation Practice and Theory, 1996

A procedure for building fuzzy-qualitative models of dynamical systems is described and the influence on the modelling accuracy of several factors related to quantity spaces and membership functions involved in fuzzification and/or defuzzification interfaces is investigated via a simulation analysis. It is shown that using multi-valued universes of discourse and introducing fuzziness allow accurate fuzzy-qualitative simulations. Simulation results for linear and nonlinear first-order systems and for second-order systems with real or complex poles are presented and discussed. ]. Such models are also useful for teaching and instruction purposes, in particular as explanatory tools for process operators or for scientists with a low mathematical background; see e.g. [10,38,39,42]. There are several approaches to building qualitative models, depending on the purpose of the model and some behavioural properties such as precision, accuracy and uncertainty [5,28] ; one of these approaches is based on the use of a fuzzy-qualitative transposition of numerical discrete-time models [ 19,30,40], which can be an answer to some problems presented in the original purely qualitative approach . An attractive feature of this fuzzy-qualitative approach is that it can be used in model-based control systems [18] as well as for relatively accurate simulation of dynamical systems [ 19,36]. Obviously, the accuracy of such a qualitative simulation, in other words the closeness of the model behaviour to that of the modelled system, depends on several factors, in particular on the number of distinctions supported by the description of the behaviour [37] and on the functions and operators used in fuzzification and defuzzification processes [1,19], as it will be shown in the next sections.

ACM transactions on modeling and …, 1994

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2011

Fuzzy systems properly integrated with Qualitative Reasoning approaches yield a hybrid identification method, called FS-QM, that outperforms traditional data-driven approaches in terms of robustness, interpretability and efficiency in both rich and poor data contexts. This results from the embedment of the entire system dynamics predicted by the simulation of its qualitative model, represented by fuzzy-rules, into the fuzzy system. However, the intrinsic limitation of qualitative simulation to scale up to complex and large systems significantly reduces its efficient applicability to real-world problems. The novelty of this paper deals with a divide-and-conquer approach that aims at making qualitative simulation tractable and the derived behavioural description comprehensible and exhaustive, and consequently usable to perform system identification. The partition of the complete model into smaller ones prevents the generation of a complete temporal ordering of all unrelated events, th...

2007

Fuzzy qualitative simulation combines the features of qualitative simulation and fuzzy reasoning in order to gain advantages from both. However, the output of a fuzzy qualitative simulation process is a behaviour tree which for complex systems will be large. In order to overcome this and permit focussing on preferred behaviours priortisation was developed. In this paper a new prioritisation scheme is presented that makes use of both constraint and temporal information to perform the prioritisation.

1990

This paper presents a methodology for integrating common-sense and qualitative simulation of physical systems by the use of Fuzzy Sets. This allows a semi-quantitative extension to qualitative simulation that provides three significant advantages over existing techniques. Firstly, it allows a more detailed description of physical variables, through an arbitrary, but finite, discretisation of the quantity space, thereby reducing qualitative ambiguity at source. The adoption of Fuzzy Sets also allows common-sense knowledge to be utilised in defining values through the use of graded membership. Secondly, the fuzzy quantity space allows more detailed description of functional relationships in that both strength and sign information can be represented by fuzzy relations held against two or multi-variables. Thirdly, the quantity space allows ordering information on rates of change to be used to compute temporal durations of system states and the possible transitions. Thus, an ordering of the

Systems Research and Behavioral Science, 2010

We propose a method for incorporating multiple linguistic or soft variables into a system dynamics framework. A simple example is used to illustrate the procedures necessary to define linguistic variables using triangular membership functions within the VENSIM Simulation Environment. We illustrate the operations of linguistic variables through a sales and service model where two linguistic variables, i.e. customer's satisfaction with respect to service, and lead time associated with a product, impact the conversion of potential customers into customers. After having created fuzzy triangular membership functions, we obtain the combined effect of the two linguistic variables using the max-min inference procedure. For defuzzification we use the notion of the largest of maximum to translate the fuzzy representation of the combined effect into a crisp value. Finally, we provide simulation results pertaining to the probability of generating new customers and profits by considering pessimistic, optimistic and intermediate fuzzy rules for our model.

2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2014

In this research we focus on dealing with fuzzy multivariate relations and how we could perform fuzzy qualitative simulation with models containing such relations. To achieve this, we extended Morven, a fuzzy qualitative reasoning framework, and proposed novel types of constraints for the framework. We first introduced fuzzy multivariate function (F MF) constraints, and presented their corresponding constraints in higher differential planes of a Morven model. We then implemented the fuzzy multivariate monotonicity (F MM) relations by F MF constraints and MM add constraints, another kind of constraints we proposed for Morven. In addition, we employed alpha-cut to determine the "strictness" of qualitative signs in the MM add constraints. Finally, proof-of-concept experiments were performed to validate the proposed constraints, and both fuzzy and non-fuzzy situations were considered in these experiments.

Proceedings of the European Simulation Multiconference ESM, 1996

This paper presents a software tool (Qua. Si. III) for the simulation of continuous dynamical systems whose parameters and/or initial conditions are modelled by fuzzy distributions. The tool, which is the last version of the qualitative simulator Qua. Si.(Bonarini, Bontempi, 1994a), implements a new approach to the numerical integration of fuzzy dynamical systems, where the problem of propagating a fuzzy distribution in the phase space is solved as a problem of constrained multivariable optimisation. Numerical ...

Qualitative simulation is a well-known reasoning technique that involves the use of simulation technologies. Reasoning is made to determine qualitative values and change directions of system variables, and it is done for each time point and time interval following the time point. Qualitative variables possess continuous qualitative value sets that are discretized by landmark points. Qualitative simulation uses qualitative time representation and its quantitative value is of no interest. The main purpose of this study was to develop a technique to determine time steps for a quantitative simulation under guidance of qualitative information. The proposed technique determined time advances using qualitative and quantitative information together to obtain a robust time step as wide as possible for simulation time advances. For this purpose, sign algebraic properties and derivation roots of quantitative equations and qualitative variable values with their change directions were used to compute time advances. In the approach, qualitative simulation determined landmark points to be advanced, and quantitative simulation calculated the duration required. Using the proposed algorithm, the simulation is advanced instead of iterating simulation time for a predefined time step and checking whether or not there is any activity in the interval, directly to the time points that are qualitatively different.

European Society for Fuzzy Logic and Technology, 2003

The aim of this paper is to present the Temporal Fuzzy Chains (TFCs) [3] to model the dynamic,systems in a linguistic manner. TFCs make,use of two different concepts: the traditional method,to represent the dynamic systems named state vectors [6], and the linguistic variables [8] used in fuzzy logic [7]. Thus, TFCs are qualitative and represents the ”temporal zones” using