Representing qualitative variables and their interactions with fuzzy logic in system dynamics modeling

Abstract

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.

Fuzzy rule‐based inference in system dynamics formulations

“…They conclude that despite the increased complexity of their formulation, the results are improved with respect to the bullwhip effect and fluctuations in the inventory. Liu et al (2010) The fuzzy logic approach was proposed as a way to incorporate linguistic variables into dynamic modeling to study the dynamic consequences of congestion pricing and travel demand management strategies.…”

“…Additionally, this paper builds on a previously developed method (Liu et al, 2010;Sabounchi et al, 2011) where the authors proposed a fuzzy logic approach as a way to incorporate linguistic variables into dynamic modeling. The motivation for this research paper originated in part by the implementation and interpretation difficulties that the authors identified with the use of the LOM defuzzification method within a fuzzy logic inference approach where the authors studied the dynamic consequences of congestion pricing.…”

The stock-flow model of spatial data infrastructure development refined by fuzzy logic

“…Campuzano et al ( 2010 ) used fuzzy logic in a customer–producer–employment model in a system dynamics contest. Liu et al ( 2011 ) also elaborately explained the implementation of fuzzy logic for modeling the combination of two linguistic variables, “delivery timeliness” and “customer service”, in a variant of a sales and service model. Neither study explained the effect of various fuzzy models on the results of their simulations.…”

“…Taking into account the characteristic of such variables and the way they are approximated or interpreted could be the main concern for improving a simulation model (Mutingi and Mbohwa 2012 ; Sabounchi et al 2011 ; Kunsch and Springael 2008 ). A common way is to employ fuzzy logic (Kunsch and Springael 2008 ; Liu et al 2011 ; Sabounchi et al 2011 ). Thus, the vagueness and uncertainty of linguistic variables as another complexity in SDI development can be modeled by integrating fuzzy logic into SMSID.…”

A Rough Programming Model Based on the Greatest Compatible Classes and Synthesis Effect

“…To deal with the uncertainties, rough set theory, fuzzy set theory, stochastic probability theory and grey systems theory have been developed (Zuo et al ., ; Li et al ., ; Liu et al . ). The rough set theory was proposed by Pawlak () as a powerful mathematical tool to tackle with the uncertainties of roughness.…”