Quantified trapezoidal fuzzy numbers

The aim of this work is to construct quantified trapezoidal fuzzy numbers as an extension of trapezoidal fuzzy numbers, by using modal intervals and accepting the possibility that the α-cuts of a trapezoidal fuzzy number may also be improper intervals. In addition, this paper addresses the inclusion relationship which is deduced from the inclusion of modal intervals and is related to the classical set-inclusion relationship between trapezoidal fuzzy numbers. Moreover, in this paper we also study the extensions of real continuous functions over the set of quantified trapezoidal fuzzy numbers. Using the semantic interpretation of the calculations over modal intervals will enable us to interpret the meaning of the calculus accurately over quantified trapezoidal fuzzy numbers. With quantified trapezoidal fuzzy numbers, we will be able to overcome some operational limitations that are usually faced when working with trapezoidal fuzzy numbers from a classical point of view. In order to show the applicability of quantified trapezoidal fuzzy numbers, we propose fuzzy equations which have no solution in the set of proper fuzzy numbers yet do have solutions that are improper fuzzy numbers. We also propose two applications of quantified trapezoidal fuzzy numbers, one of them about financial calculations and the other one in an optical problem

Fault Detection in Systems-A Fuzzy Approach

The task of fault detection is important when dealing with failures of crucial nature. After detection of faults in a system, it is advisable to suggest maintenance action before occurrenceof a failure. Fault detection may be done by observing various symptoms of the system during its operational stage. Sometimes, symptoms cannot be quantified easily but can be expressedin linguistic terms. Since linguistic terms are fuzzy quantifiers, these can be represented by fuzzy numbers. In this paper, two cases have been discussed, where a fault likely to affect a particular systemlsystems, is detected. In the first case, this is done by means of a compositional rule of inference. The second case is based on modified similarity measure. For both these  cases, linguistic terms have been expressed as trapezoidal fuzzy number

On the dialog between experimentalist and modeler in catchment hydrology

The dialog between experimentalist and modeler in catchment hydrology has been minimal to date. The experimentalist often has a highly detailed yet highly qualitative understanding of dominant runoff processes—thus there is often much more information content on the catchment than we use for calibration of a model. While modelers often appreciate the need for 'hard data' for the model calibration process, there has been little thought given to how modelers might access this 'soft' or process knowledge. We present a new method where soft data (i.e., qualitative knowledge from the experimentalist that cannot be used directly as exact numbers) are made useful through fuzzy measures of model-simulation and parameter-value acceptability. We developed a three-box lumped conceptual model for the Maimai catchment in New Zealand, a particularly well-studied process-hydrological research catchment. The boxes represent the key hydrological reservoirs that are known to have distinct groundwater dynamics, isotopic composition and solute chemistry. The model was calibrated against hard data (runoff and groundwater-levels) as well as a number of criteria derived from the soft data (e.g. percent new water, reservoir volume, etc). We achieved very good fits for the three-box model when optimizing the parameter values with only runoff (Reff=0.93). However, parameter sets obtained in this way showed in general a poor goodness-of-fit for other criteria such as the simulated new-water contributions to peak runoff. Inclusion of soft-data criteria in the model calibration process resulted in lower Reff-values (around 0.84 when including all criteria) but led to better overall performance, as interpreted by the experimentalist’s view of catchment runoff dynamics. The model performance with respect to soft data (like, for instance, the new water ratio) increased significantly and parameter uncertainty was reduced by 60% on average with the introduction of the soft data multi-criteria calibration. We argue that accepting lower model efficiencies for runoff is 'worth it' if one can develop a more 'real' model of catchment behavior. The use of soft data is an approach to formalize this exchange between experimentalist and modeler and to more fully utilize the information content from experimental catchments

Enhanced genetic algorithm-based fuzzy multiobjective strategy to multiproduct batch plant design

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessary involves how equipment may be utilized, which means that plant scheduling and production must constitute a basic part of the design problem. Rather than resorting to a traditional probabilistic approach for modeling the imprecision on product demands, this work proposes an alternative treatment by using fuzzy concepts. The design problem is tackled by introducing a new approach based on a multiobjective genetic algorithm, combined wit the fuzzy set theory for computing the objectives as fuzzy quantities. The problem takes into account simultaneous maximization of the fuzzy net present value and of two other performance criteria, i.e. the production delay/advance and a flexibility index. The delay/advance objective is computed by comparing the fuzzy production time for the products to a given fuzzy time horizon, and the flexibility index represents the additional fuzzy production that the plant would be able to produce. The multiobjective optimization provides the Pareto's front which is a set of scenarios that are helpful for guiding the decision's maker in its final choices. About the solution procedure, a genetic algorithm was implemented since it is particularly well-suited to take into account the arithmetic of fuzzy numbers. Furthermore because a genetic algorithm is working on populations of potential solutions, this type of procedure is well adapted for multiobjective optimization

Valuation of real estate investments through Fuzzy Logic

This paper aims to outline the application of Fuzzy Logic in real estate investment. In literature, there is a wide theoretical background on real estate investment decisions, but there has been a lack of empirical support in this regard. For this reason, the paper would fill the gap between theory and practice. The fuzzy logic system is adopted to evaluate the situations of a real estate market with imprecise and vague information. To highlight the applicability of the Possibility Theory, we proceeded to reconsider an example of property investment evaluation through fuzzy logic. The case study concerns the purchase of an office building. The results obtained with Fuzzy Logic have been also compared with those arising from a deterministic approach through the use of crisp numbers