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This article discusses the impact of Malaysia's formation on September 16, 1963. The establishment of Malaysia involves Malaya, Sabah, Sarawak and Singapore. Planning at the early stage includes Brunei but the State withdrew at the end of Malaysia's formation. Singapore also dropped out from the Malaysia Formation two years later in 1965. The formation of Malaysia has affected Malaysia to this day. The objective of the study is to discuss the benefits of politics, socialization and racial relations in Malaysia. Among the things discussed in this article are the benefits of the platform of socialisation and racial relations in Malaysia as well as the political aspects. Both of these were examined using historical approaches and library research. The findings show that Malaysia's establishment has made Malaysia a unique nation with racial diversity. This includes the establishment of many political parties based on their respective race or tribe, especially in Sabah and Sarawak. All Malaysians enjoy the benefits of Malaysia’s establishment for harmony and peace.

Soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. Soft multiset and fuzzy soft multiset are generalization concepts obtained from soft set theory. As a generlazation of fuzzy soft multiset we introduce the definition of intuitionistic fuzzy soft multiset and its operations and study some of their properties. Finally, we give an application in decision making problems.

In this paper, the authors propose the concept of expert complex fuzzy soft sets as an extension to the classical complex fuzzy set model. Instead of being concerned with the study of the basic set theoretic operations for this model, which are essentially generalizations of the corresponding operations of the complex fuzzy set model, we extend the study of this model through the establishment of the mappings on classes of expert complex fuzzy soft sets. Through these mappings, we introduce the image and inverse image of an expert complex fuzzy soft set, which have immense applications in real-life applications. In addition to presenting the properties of the images and inverse images of this model, we present two numerical examples to demonstrate the utility of these concepts.

In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh and Salleh (2011) define the concept of soft expert sets where the user can know the opinion of all experts in one model and give an application of this concept in decision making problem. So in this paper, we generalize the concept of a soft expert set to fuzzy soft expert set, which will be more effective and useful. We also define its basic operations, namely complement, union, intersection, AND and OR. We give an application of this concept in decision making problem. Finally, we study a mapping on fuzzy soft expert classes and its properties.

Type-2 fuzzy sets allow us to incorporate the uncertainties about the membership functions into fuzzy sets, thereby overcoming a problem that is inherent in type-1 fuzzy sets, which does not allow for any uncertainty in assigning values to the membership functions. Complex fuzzy sets are type-1 fuzzy sets with complex-valued grades of membership and are characterized by an additional phase term which enables it to better represent and capture the time-periodic and seasonal aspects of fuzziness that are prevalent in many real world problems and time-series applications. However, similar to type-1 fuzzy sets, the membership functions of complex fuzzy sets are difficult to enumerate, as they are subject to individual preferences and bias. To overcome this problem, we propose the concept of interval-valued complex fuzzy soft sets which combines complex fuzzy sets with type-2 fuzzy sets and soft sets. This adaption of complex fuzzy sets assigns an interval-based membership to each element and adequate paramete...

Complex fuzzy sets and its accompanying theory although at its infancy, has proven to be superior to classical type-1 fuzzy sets, due its ability in representing time-periodic problem parameters and capturing the seasonality of the fuzziness that exists in the elements of a set. These are important characteristics that are pervasive in most real world problems. However, there are two major problems that are inherent in complex fuzzy sets: it lacks a sufficient parameterization tool and it does not have a mechanism to validate the values assigned to the membership functions of the elements in a set. To overcome these problems, we propose the notion of complex fuzzy soft expert sets which is a hybrid model of complex fuzzy sets and soft expert sets. This model incorporates the advantages of complex fuzzy sets and soft sets, besides having the added advantage of allowing the users to know the opinion of all the experts in a single model without the need for any additional cumbersome operations. As such, this...

The aim of this study is to define and elaborate the concept of a complex fuzzy hypergroup, which is based on the concept of a complex fuzzy space.

This study was conducted to ascertain teaching Science and Mathematics in English will enhance English proficiency amongst the science stream students in UKM. The study found that the students agreed that the teaching of Science and Mathematics in English can improve their English proficiency. The results showed that teaching Science and Mathematics in English is capable of being a driven force in mastering basic English language and communication, and also in improving the explanation of the concept of Science and Mathematics in English.

In this paper we introduce the concept of possibility fuzzy soft expert set .We also define its basic operations, namely complement, union, intersection, AND and OR, and study some of their properties. Finally, we give an application of this theory in solving a decision making problem.

In this paper we share our experience of conducting a mathematics camp to a group of 16-years-old school students. This camp is special since throughout their learning history, the students, like most school students in Malaysia, are only exposed to the academic side of mathematics. By this we mean the emphasis given by the school is only on academic achievement measured by the string of A's in the examination results. Of course in order to achieve this, the preferred mode of teaching and learning is geared towards drill and practice. None of the students from this group have experienced “outdoor” mathematics as to be given in this camp. The camp which consisted of several hands-on activities and done in small groups was conducted outdoors in a very relaxed and light-hearted atmosphere. The activities aimed at introducing several areas of mathematics such as group theory and number theory and their relevance to our everyday live. One niche activity which is considered as ethno-centric was also conducted. Indeed it exposed to the students the mathematical elements in the Malay culture. At the end of the camp questionnaires were distributed to the students to gauge their reaction to this mode of learning. A chi-squared test conducted showed that there was no relationship between student's understanding on the mathematics camp's module with their streams, hence the modules are applicable to both pure science and social science stream. In all, students were satisfied with the overall conduct of the mathematics camp, where they felt that this camp was very useful and helped improve their mathematical skills and knowledge.

In this paper, numerical algorithm is applied for solving fuzzy differential equations based on generalized Hukuhara differentiability. In order to enhance the order of accuracy of the solutions, a developed fourth order Runge-Kutta method is apply for solving fuzzy differential equations. The purpose of this study is to explore the explicit methods which we believe that most of the explicit methods can be improved and modified to cater and solve fuzzy differential equations. This paper is divided into six sections. In the first section, some basic definitions and theorem are reviewed. The numerical examples are given to illustrate the efficiency of the method and the comparison with the existing method is discussed.

In this paper we present a new formulation of complex intuitionistic fuzzy rings based on the notion of complex intuitionistic fuzzy space.

This work deals with an adjustable approach for ranking objects based on fuzzy soft models. We first generate two preorder relations, thus, two equivalence relations based on the fuzzy soft topology. Then, a method for data ranking is designed according to these binary relations. The connection between Separation axioms and such data ranking method is also studied. Finally, an example is provided to illustrate this method for problem of data ranking.

The paper we present a new formulation of complex fuzzy ring. We give some examples and related results.

We propose the theory of possibility intuitionistic fuzzy soft expert theory and define some related concepts pertaining to this notion as well as the basic operations on this concept, namely, the complement, union, intersection, AND, and OR. The basic properties and relevant laws pertaining to this concept such as De Morgan’s laws are proved. Lastly, a generalized algorithm is introduced and applied to the concept of possibility intuitionistic fuzzy soft expert sets in hypothetical decision making problem.

In this paper, we continue the study of complex fuzzy groups by introducing the notion of complex fuzzy normal subgroup based on complex fuzzy space as a generalisation of fuzzy normal subgroup in the sense of Dib.

The present paper, introduces a complex vague relation (CVR) as a generalization of a vague relation by extending the range of truth-membership and false-membership functions from the closed unit interval [0, 1] to the unit circle in the complex plane. Then we introduce the basic operations on CVRs, namely complement, union and intersection. Some examples are given.

This paper deals with the orienteering problem (OP) which is a combination of two well-known problems (i.e., travelling salesman problem and the knapsack problem). OP is an NP-hard problem and is useful in appropriately modeling several challenging applications. As the parameters involved in these applications cannot be measured precisely, depicting them using crisp numbers is unrealistic. Further, the decision maker may be satisfied with graded satisfaction levels of solutions, which cannot be formulated using a crisp program. To deal with the above-stated two issues, we formulate thefuzzyorienteering problem (FOP) and provide a method to solve it. Here we state the two necessary conditions of OP of maximizing the total collected score and minimizing the time taken to traverse a path (within the specified time bound) as fuzzy goals and the remaining necessary conditions as crisp constraints. Using the max-min formulation of the fuzzy sets obtained from the fuzzy goals, we calculate the fuzzy decision sets (ZandZ∗) that contain the feasible paths and the desirable paths, respectively, along with the degrees to which they are acceptable. To efficiently solve large instances of FOP, we also present a parallel algorithm on CREW PRAM model.

This paper conceptually defines and studies the complex fuzzy hyperring, which relies on the notion that complex fuzzy spaces are a direct generalization of fuzzy hyperring.

In this paper a three stage Runge Kutta method based Contraharmonic Mean is applied for solving fuzzy differential equations based on generalized Hukuhara differentiability. This study intends to explore an explicit method which can be improved and modified to solve fuzzy differential equations. Some definitions and theorem are reviewed as a basis in solving fuzzy differential equations. A numerical example is given to illustrate the accuracy of the method. The comparison with the existing method is also discussed. The proposed method gives better numerical results and suitable for solving fuzzy differential equations.

In this paper we combine two definitions, namely fuzzy soft multiset and complex fuzzy set to construct the definition of a complex fuzzy soft multiset and study its properties. In other words, we study the extension of a fuzzy soft multiset from real numbers to complex numbers. We also introduce its basic operations, namely complement, union and intersection. Some examples are given.