Peterson Julian

On the Mitchell similarity measure and its application to pattern recognition

This paper is a response to the similarity measure and pattern recognition problem of Mitchell that was published in Pattern Recognition Letters, 2003. The purpose of this paper is threefold. First, we reviewed and revised her computation for similarity measures. Second, we proved that the similarity values for the one-norm should be larger than that for the two-norm for her pattern recognition problem. Third, we proposed a more scattered similarity measure to help researchers determine patterns. Our findings may shed light on the ongoing debate between Li and Cheng (2002) and Mitchell (2003).

A decision support system for engineering design based on an enhanced fuzzy MCDM approach

Design concept is an important wealth-creating activity in companies and infrastructure. However, the process of designing is very complex. Besides, the information required during the conceptual stage is incomplete, imprecise, and fuzzy. Hence, fuzzy set theory should be used to handle linguistic problem at this stage. This paper presents a fuzzy integrated approach to assess the performance of design concepts. And those criteria rating, relative weights and performance levels are captured by fuzzy numbers, and the overall performance of each alternative is calculated through an enhanced fuzzy weighted average (FWA) approach. A practical numerical example is provided to demonstrate the usefulness of this study. In addition, this paper, in order to make computing and ranking results easier to increase the recruiting productivity, develops a computer-based decision support system to help make decisions more efficiently.

A complete pattern recognition approach under Atanassov's intuitionistic fuzzy sets

This research is aimed at developing a method for solving pattern recognition problems under the Atanassovs intuitionistic fuzzy sets based on similarity measures. First we proposed two similarity measures and then developed a method based on our similarity measures. We also proved that our method is able to solve the pattern recognition problems. Finally, a fault diagnosis example of the turbine vibration has been examined by our method. The example demonstrates that the proposed method cannot only diagnose the main faults of the turbine generator but also it can detect useful information for future trends and multi-fault analysis. In addition, for the convenience of computing and ranking processes, a computer interface decision support system is also developed to help decision maker make diagnoses more efficiently.

Solution Structure for an Analytic Model of Bus Service Zones

This paper points out questionable derivations for the formulated solution in the algebraic approach for the optimal length of local bus route of a traffic model for bus service zones. It also provides revisions for the algebraic approach to prove the existence and uniqueness for the formulated optimal solution. An iterative method was then applied to obtain an alternative sequence that converges to the optimal solution. The same numerical examples in the literature are examined to support the findings.

Note on inexact optimal solution of fuzzy mathematical programming

Abstract In Tang and Wang (Computers and Operations Research, pp. 413–422, 1997), they tried to develop an interactive approach for quadratic programming problems with fuzzy objective and resources. Based on their approach, they claimed that the exact optimal solution for inventory model under fuzzy objective and resources is useless. We will point out that their approach is questionable, from complete and contains severe drawbacks so that their comments about the exact optimal solution should be treated as seriously questionable.

Note on inventory model with net present value

Abstract We study the paper of Hadley to compare the order quantities for inventory models using the average annual cost and the discounted cost. The purpose of this note is threefold. First, we show that the solution for the discounted cost inventory model is exist and unique. Second, we provide a formulated approximation for the discounted cost inventory model. Third, we use our approximation to explain why two solutions by the average annual cost and the discounted cost are close each other such that the numerical analysis in Hadley’s examples to demonstrate a negligible difference between them is explained. Our findings will undoubtedly improve the theoretical base for inventory models and develop new practical application for operational research.

Note on the merge of two maximum models under same constraints

Abstract In this note, we reviewed a popular paper of Li that published in Journal of Computer and System Sciences 70 (2005) 73-85. His paper had been referred more than two hundred and twenty six times. Based on the high citation, a detailed examination of his paper is necessary. We pointed out that the core of his solution method is merged two maximum problems into one which have the same constraints. We provided a counter example to reveal that his merge is questionable so that his proposed maximum problem needs revision. Moreover, we offered a possible outlet for his original two maximum problems.

Inventory system of deteriorating items with exponential declining demand and partial backlogging

Abstract We study the inventory model of Ouyang, Wu and Cheng that published in Yugoslav Journal of Operations Research, 2005, pp.277-288 to point out some questionable results in their solution procedure and then provide our new solution procedure to demonstrate that the interior minimum is exist and unique. Moreover, we point out that there are two local minimums on the boundaries. Our findings will shed the light of the solution structure for their interesting inventory model.

Monotonic Approach for Optimal Route Length of Bus Service Zoom Model

Abstract In this paper, we derive two new iterative algorithms to simplify the complicated alternative sequence approach of Yang et al. (2013). The purpose of this paper is threefold. First, we prove our approach generates monotonic and convergent sequences. Second, based on the same numerical example, we demonstrate that our monotonic sequence will converge faster than that of Yang et al. (2013). Third, we provide a reasonable explanation to the inconsistent results derived by our increasing sequence and decreasing sequence, with different starting point. Our findings will help researcher in the future construct faster iterative method to locate the optimal solution for traffic model.

Improved solution process for inventory model with ramp-type demand under stock-dependent consumption rate

We use the smoothly connected property to simplify the solution process for inventory model with ramp-type demand under stock-dependent consumption rate. This article is a response to a complicated solution process of Wu et al. [“Retailers optimal ordering policy for deteriorating items with ramp-type demand under stock-dependent consumption rate,” International Journal of Information and Management Sciences, 19, 245–262 (2008)]. They extended a minimum cost inventory model to a maximized profit problem and presented a detailed analysis for the solution procedure. However, their solution process may be too lengthy to involve many right but unnecessary results. In this article, we use the smooth connected property to dramatically simplify their solution structure. Our approach is also applied to minimum cost inventory models that were demonstrated by simplifying the paper of Deng et al. [“A note on the inventory models for deteriorating items with ramp type demand rate,” European Journal of Operational Research, 178, 112–120 (2007)]. Our findings will help ordinary readers to understand their important inventory models.