Nazirah Ramli

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.

Fuzzy evaluation in IT supplier selection

Supplier selection is crucial as it involves in-depth research process whereby multiple criteria should be considered. With the rising cost of raw materials and products, the management is forced to make better choices when selecting supplier. This paper proposed a fuzzy evaluation technique by using fuzzy linguistic terms in selecting the best IT supplier based on certain criteria. Fuzzy grade matrices and centroid ranking were utilized in the evaluation process. Result shows that Supplier 1 is the best supplier among the choice of four suppliers. Conclusion suggests the applicability of the proposed method to improve future decision making in supplier selection.

Jaccard Ranking Index with Algebraic Product t-Norm Based on Second Function Principle in Handling Fuzzy Risk Analysis Problem

Jaccard set theoretic index based on the first function principle approach has been proposed for ranking fuzzy numbers. However, the arithmetic operations of the first function principle is not straightforward which consists of determining both the lower and upper limit of the fuzzy numbers and also the minimum and maximum values of the fuzzy numbers’ domain. In this paper, a simple point-wise arithmetic operation, namely the second function principle is applied in developing the Jaccard ranking index with algebraic product t-norm. Based on the proposed ranking index, a fuzzy risk analysis (FRA) is presented in dealing with FRA problem. The behavior of the proposed risk’s ranking order is investigated and compared with some of the previous studies.

The Existence of Golden Section in the Traditional Malay Architecture

Since the ancient times, architects have relied on mathematical principles such as symmetry, proportion, geometry, Fibonacci, and golden section in designing buildings, monuments, and mosques. As such, the golden section which has aesthetically pleasing properties has been found to exist in the proportion of overall plan of Parthenon and Great Mosque of Kairouan. In this study, we investigate the existence of golden section element in the traditional Malay architecture. In order to obtain the element, the geometrical analysis is conducted based on building measurements and observations. The results show that the element of the golden section exists in some parts of the traditional Malay architecture.

Integrated Fuzzy Time Series Model for Forecasting Tourist Arrivals

Tourism is one of the major contributing sectors for most countries including Malaysia. In order to have a well-organized tourism strategy, tourism forecasting is important to satisfy the country demand. Various models based on fuzzy time series have been proposed. However, most of the models define the historical data in terms of discrete fuzzy sets, which is only based on a single-point value. In this paper, tourist fuzzy forecasting model based on fuzzy time series with data in trapezoidal form is proposed. The forecasting procedure involved three phases which are test data for seasonality and trend pattern, model development using trapezoidal fuzzy numbers and deterministic length interval, and verifying the forecasting accuracy. This integrated fuzzy forecasting model is implemented for predicting tourist arrivals to the state of Sabah, Malaysia. The result shows that the data have seasonal and trend pattern with eleven linguistic values in terms of trapezoidal fuzzy numbers. Thus, the forecasted values under different degrees of confidence can be obtained.

Formulation of Evidences in Pointwise Form for Some Jaccard Ranking Fuzzy Numbers

The ranking of fuzzy numbers becomes an important part of the component in the decision-making process and procedure. Various ranking methods have been developed but some of the methods have a lengthy calculation, computationally complex and difficult to implement. In this paper, the formulation of evidences in pointwise form for Jaccard ranking index is proposed. Generalized trapezoidal fuzzy numbers Types 1, 2 and 3 have been selected. The procedure to obtain the evidences in pointwise form involved four phases, which are determining the fuzzy maximum and minimum, fuzzy intersection and union, fuzzy evidences and simplification using Maple software. The results show that the values of evidences can be directly determined from the point of the fuzzy numbers.

Academic Poster Evaluation by Mamdani-Type Fuzzy Inference System

The evaluation of poster presentation involves decision-making based on multiple criteria that are mostly subjective in nature. A detailed rubric assessment tool is usually used to facilitate the decision-making process. However, this process can be challenging due to the factors of imprecision and vagueness in human judgement. Therefore, there is a need to develop a new evaluation method that can overcome this problem. Fuzzy Inference System (FIS) has been successfully applied in many fields such as automatic control, data classification, expert systems and management science. This study proposed an FIS model for the evaluation process of students’ academic poster. The development of the model involved four inputs and one output with 256 rules has been created. The Mamdani inference with trapezoidal fuzzy numbers and centroid defuzzification are implemented in this development process via MATLAB software. Comparison between the FIS method and the conventional method yields different ranking results. Also, the poster rating obtained from the FIS method is thought to be aligned with human reasoning. Conclusively, this model demonstrates that it is more flexible, reliable, and provides ease of use to decision-makers.

Fuzzy time series forecasting model with natural partitioning length approach for predicting the unemployment rate under different degree of confidence

Fuzzy time series forecasting model has been proposed since 1993 to cater for data in linguistic values. Many improvement and modification have been made to the model such as enhancement on the length of interval and types of fuzzy logical relation. However, most of the improvement models represent the linguistic term in the form of discrete fuzzy sets. In this paper, fuzzy time series model with data in the form of trapezoidal fuzzy numbers and natural partitioning length approach is introduced for predicting the unemployment rate. Two types of fuzzy relations are used in this study which are first order and second order fuzzy relation. This proposed model can produce the forecasted values under different degree of confidence.

Dice Index with Algebraic Product and Minimum t-Norm for Ranking Fuzzy Numbers

In fuzzy environments, the ranking of fuzzy numbers (RFNs) is important for solving decision-making problems. Many ranking methods have been developed based on various techniques but no method can provide satisfactory solution to every situation and case. Some methods lack in certain aspects such as inconsistency with human intuition, non-discriminating results and difficulty of interpretation. In this paper, fuzzy preference relation ranking methods based on Dice index with algebraic product and minimum t-norm are proposed. The procedure of the ranking methods involves six steps which are determining fuzzy maximum and fuzzy minimum, intersection and union of fuzzy numbers (FNs), scalar cardinality of FNs, fuzzy evidences and total fuzzy evidences. The findings show that the type of t-norm used affects the ranking results of some FNs.