Fuzzy systems simulation: Models, foundations, and systems development

Simulations of modeled systems are effective tools for evaluating system attributes; fuzzy logic provides for simulation of systems with inherent uncertainties. This research to advance simulation of fuzzy systems involves several studies in a planned sequence. Continuous fuzzy system modeling activities constitute a first stage of research action, a natural flow from earlier work on modeling discrete fuzzy systems; the notion of using crisp simulation to carry out fuzzy computations is at the heart of the work. This activity requires choosing tools and problems with which to demonstrate feasibility and broad applicability of the approach. Some fundamental issues underlying the work provoke new departures for the second stage consisting of two substages. The first substage involves a new fuzzy number (FN) concept, that of a Bezier generated FN (BGFN). These numbers were conceived at a very basic level to illustrate that the approach we take is not rooted in or confined to simple triangular FNs (TFN) that are often used in modeling. Their potential lies in both previous discrete simulation and in continuous simulation. The second substage of continuous modeling pursues these numbers in relation to random FNs. The second stage includes these pursuits in parallel with investigations of sequences of random numbers (as they are required for fuzzy modeling). Sequences must be able to pass rigorous statistical inspection, for which we offer some new ideas, at least in the fuzzy domain. A final phase of work, a third stage, from software cost estimation's (SCE) COnstructive COst MOdel (COCOMO), concerns f-COCOMO(fuzzy COCOMO). Our f-COCOMO studies may be viewed as software engineering (SE) reflections on the entire modeling effort, but a broader tact is taken; that is, inherited from CO-COMO's broad perspective. Advances in fuzzy treatments of COCOMO open a new fuzzy modeling frontier relating to cost systems analysis. In our overview of the entire effort, we note the progression from discrete to continuous models, and address some theoretical and mathematical foundations as they arise. We also note that this progression that culminates in fundamental SE contributions, parallels for fuzzy systems, a similar workflow found in crisp systems.