Nor Hanimah Kamis

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...

Optimization of the parking spaces: A case study of Dataran Mawar, UiTM Shah Alam

Recently, the numbers of cars have been increased collateral with the economic growth and the needs of living. Parking problem is one of the crucial problems that we have to face in the overcrowding area. Campus area faced the same problem where the parking spaces are very limited to the staff, students and visitors. Therefore, we proposed a basic mathematical model to make an improvement on the number of parking spaces as maximum as possible. We considered three types of parking designs which are perpendicular parking, parallel parking and diagonal (angle) parking where each design proposed a basic mathematical algorithm respectively. By comparing these three different designs, the most suitable design for certain area at Dataran Mawar, UiTM Shah Alam is identified and the maximum numbers of parking spaces are obtained when the selected designs are combined. These algorithms can be used as an alternative model in optimizing the parking spaces in other congested area.

An integrated fuzzy approach to solving multi-criteria decision making problems

This paper proposed an integrated fuzzy approach based on Consistent Fuzzy Preference Relations (CFPR) and Generalized TOPSIS. The procedure of CFPR are improved by adapting Centroid-Index as defuzzification operator, in order to represent the whole set of fuzzy numbers correctly. The CFPR requires only (n-1) pair-wise comparisons for n given criteria, where this situation prove that the increasing number of criteria will not exponentially increased the number of pair-wise comparisons in criteria weights determination process. The evaluation of alternative towards criteria is carried out and the ranking can be obtained by using Generalized TOPSIS method. This method introduced Up and Lo operators for the purpose of determining ideal and negative ideal solutions, that are adequate under fuzzy environment and satisfied the partial ordering relations. The implementation of this integrated approach is presented in the selection of best notebook for students, which involved two decision makers, four criteria and four alternatives. The proposed method can be used as an alternative procedure in solving multi-criteria decision making (MCDM) problems.

Centroid method in fuzzy LinPrera: A case study of UiTM, Shah Alam

This paper proposed a modified procedure of fuzzy LinPrera by adapting the Centroid method to defuzzify the final results into crisp values that best represents the whole set of fuzzy numbers. It is known that average is not suitable to use as a defuzzification method because it cannot represent the whole set of the fuzzy numbers and not consider the height of the membership function. By utilization of Centroid method, the defuzzification of fuzzy numbers can be done efficiently and the ranking process can be easily carried out. This modified procedure is adapted to the selection of best study mode offered by Universiti Teknologi MARA (UiTM) for working people in order to demonstrate the calculations and obtain the final results. This study reveals that the Centroid method in Fuzzy LinPrera procedure is effective and suitable to use as an alternative tool in solving MCDM problems.

Portfolio insurance of a portfolio reflected by FTSE Bursa Malaysia KLCI

A good investment portfolio is a properly selected group of investment products such as stocks, bonds and cash equivalents. On top of grouping a brilliant portfolio, an excellent portfolio manager will consider the risk of downturn in financial performance as an important event that need to be taken care of at it best. This paper focuses on managing this risk of a well-diversified investment portfolio. The focus is to be narrowed down into finding the assurance value of the risk. This assurance value will be evaluated under specific strategy of buying traded European put option. The most celebrated Black-Scholes model to option pricing will be used in determining the values of these portfolio insurance strategies. General input parameters such as volatility and dividend yields of the portfolio will be taken from the performance of FTSE Bursa Malaysia KLCI (FTSEBMKL) as the portfolio is reflected by the performance on the index. The value results will be then viewed as numerical evaluation of some well-diversified portfolio examples, which will vary in term of specific input parameters of certain cases. This study provides straightforward insurance strategies a portfolio manager would have done in managing risk of downturn in the financial market. This strategy structure could be further enhanced by considering various other financial tools that are available or to be made available in the financial world.

Decision making models based on Consistent Fuzzy Preference Relations with different defuzzification methods

This paper focuses on improvising decision making models based on Consistent Fuzzy Preference Relations (CFPR). Fuzzy numbers are used as input values in the entries of decision matrices. Center of Gravity (COG), Radius of Gyration (ROG) and Centroid Index (CI) which are the formulae in the defuzzification process are utilized to transform these fuzzy numbers into crisp values. An improvised procedure in determining the criteria weights and ranking of alternatives based on CFPR with three different defuzzification methods are then proposed. Selection of best houses for residents in Shah Alam is considered in this study in order to demonstrate the calculation parts. The results show that the ranking orders of three different decision making models are the same. This reveals that these models give precise results while consistency is still preserved. Therefore, the models can be used as alternative tools in solving decision making problems.

RSA cryptosystem with fuzzy set theory for encryption and decryption

In the communication area, user is more focus on communication instead of security of the data communication. Many cryptosystems have been improvised to achieved the effectiveness in communication. RSA cryptosystem is one of well-known cryptosystem used to secure the information and protect the communication by providing a difficulty to the attackers specifically in encryption and decryption. As need arises for guarantee the security of the cryptosystem while the communication must be ensured, we propose a new RSA cryptosystem which is based on fuzzy set theory whereby the plaintext and the ciphertext are in terms of Triangular Fuzzy Number (TFN). Decryption result shows that the message obtained is the same as the original plaintext. This study reveals that the fuzzy set theory is suitable to be used as an alternative tool in securing other cryptosystem.

Ordering of Z-numbers

The concept of Z-number which was introduced by Zadeh in 2010 has captured attention by many due to its enormous applications in the area of Computing with Words (CWW). A Z-number is an ordered pair of fuzzy numbers, (A, R), where A essentially plays the role of fuzzy restriction which is a real-valued uncertain variable and R is a measure of reliability of the first component. Besides its theoretical development, Z-numbers have been successfully applied to decision making problems under uncertain environment. In any decision making evaluation using Z-number, ideally the final outcome of the calculation should also be in Z-number. A question will arise: how do we order the Z-numbers so that the preference of the alternatives can be ranked appropriately? In this paper, we propose a method of ordering the Z-number via the transformation of the Z-numbers to fuzzy numbers. The Z-number will then be ranked using a ranking fuzzy number method. The proposed method will be tested in several combinations of Z-numb...

Strategic planning decision making using fuzzy SWOT-TOPSIS with reliability factor

Strategic planning is a process of decision making and action for long-term activities in an organization. The Strengths, Weaknesses, Opportunities and Threats (SWOT) analysis has been commonly used to help organizations in strategizing their future direction by analyzing internal and external environment. However, SWOT analysis has some limitations as it is unable to prioritize appropriately the multiple alternative strategic decisions. Some efforts have been made to solve this problem by incorporating Multi Criteria Decision Making (MCDM) methods. Nevertheless, another important aspect has raised concerns on obtaining the decision that is the reliability of the information. Decision makers evaluate differently depending on their level of confidence or sureness in the evaluation. This study proposes a decision making procedure for strategic planning using SWOT-TOPSIS method by incorporating the reliability factor of the evaluation based on Z-number. An example using a local authority in the east coast of...

Consistent linguistic fuzzy preference relations method with ranking fuzzy numbers

Multi-Criteria Decision Making (MCDM) methods have been developed to help decision makers in selecting the best criteria or alternatives from the options given. One of the well known methods in MCDM is the Consistent Fuzzy Preference Relation (CFPR) method, essentially utilizes a pairwise comparison approach. This method was later improved to cater subjectivity in the data by using fuzzy set, known as the Consistent Linguistic Fuzzy Preference Relations (CLFPR). The CLFPR method uses the additive transitivity property in the evaluation of pairwise comparison matrices. However, the calculation involved is lengthy and cumbersome. To overcome this problem, a method of defuzzification was introduced by researchers. Nevertheless, the defuzzification process has a major setback where some information may lose due to the simplification process. In this paper, we propose a method of CLFPR that preserves the fuzzy numbers form throughout the process. In obtaining the desired ordering result, a method of ranking fu...