Daud Mohamad

A Z-number-based decision making procedure with ranking fuzzy numbers method

The theory of fuzzy set has been in the limelight of various applications in decision making problems due to its usefulness in portraying human perception and subjectivity. Generally, the evaluation in the decision making process is represented in the form of linguistic terms and the calculation is performed using fuzzy numbers. In 2011, Zadeh has extended this concept by presenting the idea of Z-number, a 2-tuple fuzzy numbers that describes the restriction and the reliability of the evaluation. The element of reliability in the evaluation is essential as it will affect the final result. Since this concept can still be considered as new, available methods that incorporate reliability for solving decision making problems is still scarce. In this paper, a decision making procedure based on Z-numbers is proposed. Due to the limitation of its basic properties, Z-numbers will be first transformed to fuzzy numbers for simpler calculations. A method of ranking fuzzy number is later used to prioritize the altern...

Ranking fuzzy numbers using similarity measure with centroid

Ranking fuzzy numbers correctly is essential especially in decision making process. Many techniques of ranking fuzzy numbers have been investigated using variety of approaches. However, most of the techniques have weaknesses one way or another. In this paper, we propose a new method of ranking fuzzy numbers using similarity measure approach with centroid. We investigate its ranking consistency compares to other existing methods using a few benchmarking sets of fuzzy numbers. It is found that our proposed method is able to overcome some of the weaknesses of other methods.

A Jaccard-based similarity measure for soft sets

In this paper, we propose a novel similarity measure for soft sets which is based on Jaccard similarity coefficient. The proposed similarity measure takes into consideration two component i.e. similarity due to the compared parameter set, and similarity between approximate value sets of the overlapping parameters. The efficiency of the proposed measure is compared with existing soft set similarity measures through numerical examples. An application of the new similarity measure in solving a financial diagnostic problem is also illustrated in the paper.

On the Jaccard Index with Degree of Optimism in Ranking Fuzzy Numbers

Ranking of fuzzy numbers plays an important role in practical use and has become a prerequisite procedure for decision-making problems in fuzzy environment. Jaccard index similarity measure has been introduced in ranking the fuzzy numbers where fuzzy maximum, fuzzy minimum, fuzzy evidence and fuzzy total evidence are used in determining the ranking. However, the fuzzy total evidence is obtained by using the mean aggregation which can only represent the neutral decision maker’s perspective. In this paper, the degree of optimism concept which represents all types of decision maker’s perspectives is applied in calculating the fuzzy total evidence. Thus, the proposed method is capable to rank fuzzy numbers based on optimistic, pessimistic and neutral decision maker’s perspective. Some properties which can simplify the ranking procedure are also presented.

A Function Principle Approach to Jaccard Ranking Fuzzy Numbers

Ranking of fuzzy numbers plays an important role in practical use and has become a prerequisite procedure for decision-making problem in fuzzy environment. Various techniques of ranking fuzzy numbers have been developed and one of them is based on the similarity measure technique. Jaccard index similarity measure has been introduced in ranking the fuzzy numbers where the fuzzy maximum and fuzzy minimum are obtained by using the extension principle. However, this approach is only applicable to normal fuzzy numbers and therefore, fails to rank the non-normal fuzzy numbers. Besides that the extension principle does not preserve the type of membership function of the fuzzy numbers and also involves laborious mathematical operations. In this paper, a simple vertex fuzzy arithmetic operation namely function principle is applied in the Jaccard ranking index. This method is capable to rank both normal and non-normal fuzzy numbers in a simpler manner. It has also improved the ranking results by the original Jaccard ranking method and some of the existing ranking methods.

On arithmetic operations of G-number

Heterogeneity in decision making evaluation is inevitable due to different background, preference and experience of decision makers. One aspect of the heterogeneity can be the type of numerical scale used in the evaluation such as crisp, interval, fuzzy and the most recent is the z-number. The calculation will be simpler if these different scales can be represented in a single form. A general form of uncertain number known as granular number or simply denoted as G-number have been introduced to cater the problem. At present, two basic operations, which are the addition and multiplication have been given and implemented in AHP method and Djikstras algorithm. Nevertheless, in order to be further useful in some other decision making models, it is essential to introduce the other two arithmetic operations, which are the subtraction and division. In this paper, the negation and the reciprocal of G-number is determined in order to obtain the subtraction and division operations. Some numerical examples and the general formula are given at the end of the paper.

A set theoretic similarity measure for fuzzy soft sets and its application in group decision making

This paper introduces a new set theoretic-based similarity measure for fuzzy soft sets. A fuzzy soft set similarity aggregation procedure for aggregating individual fuzzy soft sets into a collective fuzzy soft set is proposed. The new similarity measure is used to determine the collective coefficient of individual fuzzy soft sets. A group decision making model is then presented and illustrated with numerical example.

Combining Mahalanobis and Jaccard to Improve Shape Similarity Measurement in Sketch Recognition

Mahalanobis, Jaccard and others are similarity measurements which are commonly used in sketch recognition. Attempts to improve similarity measurement can be made by manipulating formulae and reducing the testing data set used but less effort are attempted to propose algorithm. Hence, the purpose of this study is to propose a new algorithm for a better method in shape recognition. To do so, Mahalanobis and Jaccard distance measures were combined to improve the similarity measure. The pre-processing involved feature analysis, shape normalization and shape perfection and data conversion into a binary. In the new algorithm, each edge of the geometric shape was separated and measured using Jaccard distance. Shapes that passed the threshold value were measured by Mahalanobis distance. The results showed that the similarity percentage had increased from 61% to 84%, thus accrued an improved average of 21.6% difference. Having this difference, the three outcomes of this study were a combined algorithm, a new technique of separating the strokes in Jaccard, and lastly, the use of extreme vertices in Mahalanobis similarity measurement to reduce computation time.

Solving industrial decision making problems using fuzzy numbers

Human-based industrial decision making normally involves both quantitative and qualitative input factors. Subjectiveness in human evaluation is unavoidable in the decision making process. In fuzzy-based industrial decision making environment where fuzzy numbers are used to evaluate subjective factors, ranking of fuzzy numbers become one of the crucial component which need to be performed before the final decision can be reached. In this paper, a similarity-based method of ranking fuzzy numbers is proposed. The applicability of the proposed method in solving selected industrial-related decision making problems namely the risk evaluation and pattern recognition problems are illustrated.

Investigating Jaccard Distance similarity measurement constriction on handwritten pen-based input digit

This paper presents a preliminary study on conventional Jaccard Distance performance in recognizing shapes with and without pre processing tasks. This study also identified the pre processing tasks that should be conducted to improve recognition performance. Jaccard Distance is performed by measuring the asymmetric information on binary variable and the comparison between vectors component. It compared two objects and notified the degree of similarity of these objects. This study also evaluated recognition performance on hand writing on isolated digits written using pen-based device. The first part of the work showed low recognition performed by the conventional Jaccard Distance when there was no pre processing task done onto the input. However, after translation, rotation, invariance scale content and noise resistance were added it showed improvement on the recognition progress. However the improvement was not very significance. Result showed that the degree of accuracy only improve averagely by 20%. Therefore thorough pre-processing tasks are to be carried out for the pen-based input using Jaccard Distance measurement.