An extension of TOPSIS for group decision making

A new approach for ranking fuzzy numbers by distance method

In this ever-changing world, information technology (IT) is a must for the survival of a company, and the functions of IT department is becoming increasingly important. The assessment of IT department is critical to understand how the department contributes to organizational and strategic goals. Because IT department performs many tasks that cannot simply be measured by monetary units, evaluation methods that solely rely on financial measures are not adequate. The objective of this study is to construct an approach based on the fuzzy analytic hierarchy process (FAHP) and balanced scorecard (BSC) for evaluating an IT department in the manufacturing industry in Taiwan. The BSC concept is applied to define the hierarchy with four major perspectives (i.e. financial, customer, internal business process, and learning and growth), and performance indicators are selected for each perspective. A fuzzy AHP (FAHP) approach is then proposed in order to tolerate vagueness and ambiguity of information. A FAHP information system is finally constructed to facilitate the solving process. The results provide guidance to IT departments in the manufacturing industry in Taiwan regarding strategies for improving department performance. The constructed information system is suggested to be a good tool for solving other multiple-criteria decision-making problems.

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A fuzzy AHP and BSC approach for evaluating performance of IT department in the manufacturing industry in Taiwan

Environmental sustainability of a supply chain depends on the purchasing strategy of the supply chain members. Most of the earlier models have focused on cost, quality, lead time, etc. issues but not given enough importance to carbon emission for supplier evaluation. Recently, there is a growing pressure on supply chain members for reducing the carbon emission of their supply chain. This study presents an integrated approach for selecting the appropriate supplier in the supply chain, addressing the carbon emission issue, using fuzzy-AHP and fuzzy multi-objective linear programming. Fuzzy AHP (FAHP) is applied first for analyzing the weights of the multiple factors. The considered factors are cost, quality rejection percentage, late delivery percentage, green house gas emission and demand. These weights of the multiple factors are used in fuzzy multi-objective linear programming for supplier selection and quota allocation. An illustration with a data set from a realistic situation is presented to demonstrate the effectiveness of the proposed model. The proposed approach can handle realistic situation when there is information vagueness related to inputs.

Supplier selection using fuzzy AHP and fuzzy multi-objective linear programming for developing low carbon supply chain

To improve the ranking method of Lee and Li [1], Cheng [2] proposed the coefficient of variation (CV index). Shortcomings are also found in the CV index. Cheng [2] also proposed the distance method to improve the ranking method of Murakami et al. However, the distance method is not sound either. Moreover, the CV index contradicts the distance method in ranking some fuzzy numbers. Therefore, to overcome the above shortcomings, we propose ranking fuzzy numbers with the area between the centroid point and original point.

Ranking fuzzy numbers with an area between the centroid point and original point

Most approaches for ranking fuzzy numbers proposed in the literature are based on fuzzy sets theory only, and suffer from lack of discrimination and occasionally conflict with intuition. It is true that fuzzy numbers are frequently partial order and cannot be compared. However,this does not alleviate the need for comparison in practical applications. In this paper the order of fuzzy numbers are determined based on the concept of probability measure of fuzzy events due to Zadeh. It considers both the mean and dispersion of alternatives and gives two groups of indices based on the uniform and the proportional probability distributions. The approach is also extended to the comparison of random fuzzy numbers by means of a mean fuzzy number. It is shown that several comparison indices in the literature can be obtained based on the probability present measure approach. Finally some typical examples are used to compare the various different approaches. The different interpretations of the dispersion index under different physical situations are emphasized.

Comparison of fuzzy numbers based on the probability measure of fuzzy events

A general approach for queuing systems in a fuzzy environment is proposed based on Zadeh's extension principle, the possibility concept and fuzzy Markov chains. To illustrate the approach, analytical results for M/F/1 and FM/FM/1 systems are presented. Fuzzy queues are much more realistic than the commonly used crisp queues in many practical situations. A simple numerical example is also presented.

Analysis of fuzzy queues

Various approaches have been proposed for the comparison or ranking of fuzzy sets. However, due to the complexity of the problem, a general method which can be used for any situation still does not exist. This paper formalizes the concept of existence for the ranking of fuzzy sets. Many of the existing fuzzy ranking methods are shown to be some application of this concept. An improved fuzzy ranking method is then introduced, based on this concept. This newly introduced method is expanded for treating both normal and nonnormal, convex and nonconvex fuzzy sets. Emphasis is placed on the use of the subjectivity of the decision maker, such as the optimistic or the pessimistic view points. An improved procedure for obtaining linguistic conclusions is also developed. Finally, some numerical examples are given to illustrate the approach.

Ranking of fuzzy sets based on the concept of existence

In practice, processing times can be more accurately represented as intervals with the most probable completion time somewhere near the middle of the interval. A fuzzy number which is essentially a generalized interval can represent this processing time interval exactly and naturally. In this work, triangular and trapezoidal fuzzy numbers are used to represent those vague job processing times in job shop production systems. The job sequencing algorithms of Johnson and Ignall and Schrage are modified to accept fuzzy job processing times. Fuzzy makespans and fuzzy mean flow times are then calculated for greater decision-making information. Numerous examples are used to illustrate the approach.

Job sequencing with fuzzy processing times

By the use of actual examples, it is shown that when the two trends, namely the fuzzy spread trend and the center line, or modal, trend, are in conflict or inconsistent, the results of the fuzzy linear regression (FLR) model based on the approach of Tanaka and coworkers frequently misinterprets the data. To avoid this misinterpretation, a modification of the FLR procedure, by allowing the spreads of the parameter to be unrestricted in sign, is proposed. It is shown that by the use of this unrestricted fuzzy linear regression (UFLR) model, correct prediction of the trends are obtained.

E.S. Lee

Papers

Comparison of fuzzy numbers based on the probability measure of fuzzy events

Analysis of fuzzy queues

Ranking of fuzzy sets based on the concept of existence

Job sequencing with fuzzy processing times

Fuzzy linear regression with spreads unrestricted in sign