Rough Interval Research Articles

An inexact rough-interval fuzzy linear programming method for generating conjunctive water-allocation strategies to agricultural irrigation systems

An inexact rough-interval fuzzy linear programming (IRFLP) method is developed for agricultural irrigation systems to generate conjunctive water allocation strategies. The concept of “rough interval” is introduced in the modeling framework to represent dual-uncertain parameters. After the modeling formulation, an agricultural water allocation management system is provided to demonstrate the applicability of the developed method. The results show that reasonable solutions and allocation strategies are obtained. Based on the analysis of alternatives obtained from different scenarios, the significant impact of dual uncertainties existing in the system is specified. Comparisons between the results from IRFLP and interval-valued fuzzy linear programming are also conducted. The obtained rough-interval solutions correspond to the management strategies under both normal and special system conditions, and thus more conveniences would be provided for decision makers. Compared to the previous modeling efforts, the proposed IRFLP shows uniqueness in addressing the interaction between dual intervals of highly uncertain parameters, as well as their joint impact on the system.

Fast Algorithm and Efficient Implementation of GMM-Based Pattern Classifiers

This paper proposes a fast decision algorithm in pattern classification based on Gaussian mixture models (GMM). Statistical pattern classification problems often meet a situation that comparison between probabilities is obvious and involve redundant computations. When GMM is adopted for the probability model, the exponential function should be evaluated. This work firstly reduces the exponential computations to simple and rough interval calculations. The exponential function is realized by scaling and multiplication with powers of two so that the decision is efficiently realized. For finer decision, a refinement process is also proposed. In order to verify the significance, experimental results on TI DM6437 EVM board and TED TB-3S-3400DSP-IMG board are shown through the application to a color extraction problem. It is verified that the classification was almost completed without any refinement process and the refinement process can proceed the residual decisions.

Integrating Rough Numbers with Interval Arithmetic: A Novel Approach to QFD Analysis

Quality function deployment (QFD) has been widely recognised as an effective means to develop quality products that can maximise customer satisfactions. Traditionally, fuzzy numbers and fuzzy arithmetic operations are employed to quantify and analyse the vague design information in QFD. However, besides the difficulties in determining an appropriate fuzzy membership function, the rapid enlargement of fuzzy boundary intervals due to fuzzy arithmetic operations is another important issue, which leads to low discerniblility of design objectives. In this work, two novel concepts termed rough number and rough boundary interval are proposed based on rough set theory and are integrated with interval arithmetic to formulate a novel approach to QFD analysis. A comparison between using rough numbers and fuzzy numbers in QFD analysis is conducted through a case study. The results show that the proposed rough number enabled QFD analysis is able to provide more insights into the design information and can significantl...