Ahmad Termimi Ab Ghani

The Use of Interval Type-2 Fuzzy TOPSIS in Supplier Selection

Supplier selection is one of the most important activities in supply chain management. However, the method of selecting appropriate supplier is not straightforward as it involves number of potential suppliers with diverse criteria. This paper aims to select the best supplier using interval type-2 fuzzy Technique for Order Preference by Similarity to Ideal Solution (IT2FTOPSIS) method. The method is used to a case study of computer components supplier selection. Of the four candidate suppliers, it is found that the supplier S3 is the best candidate. It indicates that the IT2FTOPSIS method offers a feasible solution to supplier selection problem.

A DEMATEL method with single valued neutrosophic set (SVNS) in identifying the key contribution factors of Setiu Wetland’s coastal erosion

This study intends to employ the decision-making trial and evaluation laboratory (DEMATEL) method to identify the influential factors contributed towards coastal erosion. This investigation specifically studies the coastal erosion in Setiu Wetlands coastal areas which located in Terengganu, Malaysia. The single valued neutrosophic set (SVNS) is used into the DEMATEL instead of crisp numbers. Twelve factors of coastal erosion with three dimensions were identified from literature review and consultation with group of experts. By considering the interrelationships among factors, DEMATEL is applied to acquire the importance and cause-effect relationships among the influential factors of coastal erosion. Obtained result reveals that coastal development gives a significant influence in contributing coastal erosion. The result from this study offers an insight for stakeholders to understand cause-effect relationships among coastal erosion factors in which can provide a precautious short or long term strategies. Keywords: Coastal erosion, DEMATEL, Neutrosophic INTRODUCTION A decision-making trial and evaluation laboratory (DEMATEL) method is a well-known method for clarifying the interrelationship among the factors of multi-criteria decision making (MCDM) problem. The main feature of DEMATEL is its ability to provide a cause-effect relationship diagram which splitted factors into either causal or effect group. The DEMATEL method has been applied in various case studies such as in implementation of successful green supply chain management (GSCM) [1], GSCM adoption in a food packaging company [2] and auto components manufacturing sector [3], prioritizing investment projects [4] and many more. The traditional DEMATEL that uses crisp numbers of integer from 0 to 4 cannot handle the fuzziness and uncertainty elements. Therefore, many reseachers have worked on the extended DEMATEL method using fuzzy numbers [5-7]. Although fuzzy numbers are successfully employed in DEMATEL method, they are unable to deal with any indeterminate and inconsistent information that exists in real world. Therefore, Smarandache [8] has proposed the concept of neutrosophic set (NS) to tackle that issue. The neutrosophic set generalizes the concepts of the classic set, fuzzy set (FS), intuitionistic fuzzy set (IFS), interval-valued intuitionistic fuzzy set (IVIFS) and etc. [8]. In the neutrosophic Proceeding of the 25th National Symposium on Mathematical Sciences (SKSM25) AIP Conf. Proc. 1974, 020011-1–020011-8; https://doi.org/10.1063/1.5041542 Published by AIP Publishing. 978-0-7354-1681-9/

Global weights of coastal erosion risk factors using AHP method: A case study of Setiu Wetlands

30.00 020011-1 set, there are three elements called truth-membership, indeterminacy-membership, and falsity-membership which represented independently. Since each element of NSs are nonstandard unit interval of ] [ + − 1 , 0 , it is hard to apply to real scientific problems. Therefore, Wang et al. [9-10] introduced two subclass sets of NSs which are single valued neutrosophic set (SVNS) and interval neutrosophic set (INS). In recent years, the researches on NSs have been developed and were applied to solve various MCDM problems. Das et al. [11] proposed an algorithm approach using neutrosophic soft matrix with employing the combination of the neutrosophic set (NS) and soft set (SS). Ali et al. [12] proposed neutrosophic recommender system based on algebraic neutrosophic measures and applied it for medical diagnosis decision making problem. Besides that, Ye [13] introduced new exponential operational laws of INSs which based on crisp values and the exponents are interval neutrosophic numbers (INNs). Deli et al. [14] introduced bipolar neutrosophic set and a few of its operations. Liu and Luo [15] developed some power aggregation operators on simplified neutrosophic set (SNS). Şahin and Küçük [16] proposed the concept of neutrosophic subsethood based on distance measure for SVNSs. Neutrosophic sets have been successfully applied and literally enhance the fuzzy theories in overall. To fill the gaps and also to get reap of the capability of neutrosophic set in handling inderminate situations, this paper proposes the single valued neutrosophic sets (SVNSs) into DEMATEL procedure. To demonstrate the applicability of the proposed method, we applied it in coastal erosion problem which is can be considered as an MCDM problem. The rest of the paper is as follows. Second section introduces some basic concepts of neutrosophic set. Third section explains the proposed neutrosophic DEMATEL method. Fourth section provides an illustrative example where the proposed methodology is tested out. Then the last section will be a conclusion. PRELIMINARIES In this section, some basic concepts of neutrosophic sets are given. Definition 1 ([10]) Let X be a space of points (objects) with generic elements in X denoted by x. An SVNS A in X is characterized by truth-membership function ( ) x TA , indeterminacy-membership function ( ) x I A , and falsity membership function ( ) x FA . Then, an SVNS A can be denoted by ( ) ( ) ( ) { } X x x F x I x T x A A A A ∈ = , , , , where ( ) ( ) ( ) [ ] 1 , 0 , , ∈ x F x I x T A A A for each point x in X. Therefore, the sum of ( ) ( ) ( ) x F x I x T A A A and , satisfies the condition ( ) ( ) ( ) 3 0 ≤ + + ≤ x F x I x T A A A . Decision making normally involves human language or commonly referred as linguistic variables. A linguistic variable simply represents words or terms used in human language. Therefore, this linguistic variable approach is a convenient way for decision makers to express their assessments. Ratings of criteria can be expressed by using linguistic variables such as very important (VI), important (I), low important (LI), not important (NI), etc. Linguistic variables can be transformed into SVNSs as shown in the Table 1. TABLE 1. Linguistic variable and Single Valued Neutrosophic Numbers (SVNNs) [17] Integer Linguistic variable SVNNs 0 No influence/ Not important 9 . 0 , 8 . 0 , 1 . 0 1 Low influence/important 7 . 0 , 6 . 0 , 35 . 0 2 Medium influence/important 45 . 0 , 4 . 0 , 5 . 0 3 High influence/important 15 . 0 , 2 . 0 , 8 . 0 4 Very high influence/important 1 . 0 , 1 . 0 , 9 . 0 The group of decision makers have their own decision weights based on their experience and knowledge in the decision problem. Thus, the weight of each decision maker may not be equal to each other. The weight of each decision maker is considered with linguistic variables and conveyed in SVNNs.

Solutions of interval type-2 fuzzy polynomials using a new ranking method

Coastal erosion is one of the global problems which also one of the national’s environmental major concerns. The coastal erosion can be easily happened if the sea level rises along with the frequent and huge storms. There are various risk factors that can be related with coastal erosion such as tidal range, storm surge, wave height and etc. However, the relative weights for these risk factors are still inconclusive. Thus, this paper aims to determine the relative global weights of risk factors that contribute to coastal erosion using the Analytic Hierarchy Process (AHP) method. Three decision makers were invited to provide judgments for pair-wise comparison matrices of the method. The global weights were obtained using the concept of group decision making environment. The result shows that the most influencing risk factor is shoreline evolution with the highest weightage (20.74%) compared to the other factors.Coastal erosion is one of the global problems which also one of the national’s environmental major concerns. The coastal erosion can be easily happened if the sea level rises along with the frequent and huge storms. There are various risk factors that can be related with coastal erosion such as tidal range, storm surge, wave height and etc. However, the relative weights for these risk factors are still inconclusive. Thus, this paper aims to determine the relative global weights of risk factors that contribute to coastal erosion using the Analytic Hierarchy Process (AHP) method. Three decision makers were invited to provide judgments for pair-wise comparison matrices of the method. The global weights were obtained using the concept of group decision making environment. The result shows that the most influencing risk factor is shoreline evolution with the highest weightage (20.74%) compared to the other factors.

On Values of Games

A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples in...

Horner-Muller’s Method for Solving Interval Type-2 Fuzzy Polynomials

In this paper, we present some recent results of infinite games played on a finite graph. We mainly work with generalized reachability games and Buchi games. These games are two-player concurrent games in which each player chooses simultaneously their moves at each step. We concern here with a description of winning strategies and payoff functions over infinite plays. Each play and the outcome of a game are completely determined by strategies of the players. We classify strategies regarding their use of history. Our goal is to give simple expressions of values for each game. Moreover, we are interested in the question of what type of optimal (e-optimal) strategy exists for both players depending on the type of games.