# IN CONVERSATION with Prof Babington Bonginkosi Makamba - C-rated Researcher and Maths Prof

Professor Babington Bonginkosi Makamba is a C-rated Researcher and Mathematics Professor in the Mathematics Department, Faculty of Science and Agriculture. He was born in Tsitsikama, Humansdorp and currently resides in Fort Beaufort.

Prof Makamba holds the following post school qualifications:

- Higher Primary Teachers Certificate (Lovedale College)
- BSc majoring in Applied Mathematics (distinction), Mathematics (distinction) and Applied Computer Science (UFH 1981)
- BSc Hons in Mathematics (UFH 1982)
- MSc Mathematics (Rhodes University 1983). Dissertation:
*Representation of the Symmetric Group S*_{n } - PhD Mathematics (Rhodes University 1993). Thesis:
*Studies in Fuzzy Subgroups*

**Career Progression:**

Prof Makamba started his career as a Mathematics and Physics Teacher between 1972 and 1977 at Somerset East Secondary School. In 1981 he was appointed as a Graduate Assistant in Mathematics at the University of Fort Hare. A year later he joined Rhodes University as a Tutor in the Academic Support Programme.

He rejoined UFH as a Maths Lecturer in 1983. Over the years, he has occupied several senior positions at Fort Hare. These include the roles of Senior Lecturer, HoD for the Mathematics Department, Deputy Dean in the Faculty of Science and Associate Professor. He became a full Professor of Mathematics in 2012.

**Please share some information about your research field:**

My research area is Fuzzy Subgroups and I specialise in the classification of fuzzy subgroups. I have published more than 30 papers in this area in peer-reviewed journals, most of which are co-authored with my current co-researcher Prof Venkat Murali at Rhodes University. Other papers are co-authored with my students and colleagues in the Department of Mathematics.

**What is Fuzzy Mathematics?**

Fuzzy Mathematics is mathematics of imprecision. A fuzzy set is a set in which objects or elements belong to it to a certain degree. We usually use the interval [0,1] as a membership scale, such that if an element m belongs to set A to a degree 0, then m does not belong to A, and if an element n belongs to set A to a degree 1, then n belongs to A (fully).

However, some elements may belong to set A to a degree x where x is a proper fraction, hence the imprecision of belonging. This fuzzy mathematics has now moved into all areas of classical mathematics. Unlike in ordinary sets, a fuzzy group has infinitely many fuzzy subgroups.

Even a finite group has infinitely many fuzzy subgroups. That is the reason why I started to work towards some form of ``a finite group that has a finite number of fuzzy subgroups’’. This involved classification of fuzzy subgroups. In this classification, we group together all the fuzzy subgroups with similar properties and count them as one ``fuzzy subgroup’’. In this way, we do have that a finite group has a finite number of fuzzy subgroups. This research also involves generating formulae for the numbers of distinct fuzzy subgroups of finite groups, particularly cyclic groups and abelian groups of ranks 2 and 3.

I have also used special groups such as dihedral and symmetric groups in the classification of fuzzy subgroups. The current classification technique was proposed by me while I was still doing my PhD at Rhodes University. Since then it has been used in research by many scholars in fuzzy mathematics. My area of research still provides a lot of scope for further research.

I have successfully supervised and examined the following fuzzy groups theses:

**Masters:** External Examiner (x3) and Supervisor (x4)

**PhDs **: External Examiner (x4) and Supervisor (x3)

** **

**What do you think are your most significant research accomplishments?**

- Having my papers published in accredited journals.
- Seeing international scholars using my concept of equivalent fuzzy subgroups in their research.
- And also seeing students at other universities writing theses based on my work.

**How do you ensure your research is well communicated, digested, and acted upon?**

I publish my research outputs in peer-reviewed international journals. There is simply no better communication.

**What has been the greatest impact of your work?**

The citation of many of my papers in research internationally, and seeing students at both alma maters (UFH and Rhodes) writing theses and graduating using my notion of equivalence.

**What advice would you give to young researchers out there?**

**Critique**your paper before submitting it to a peer-reviewed journal. This will help you to identify topics that still need further research. This then widens your area of research.**Involve**colleagues and/or students in your research in order to lighten your load and avoid frustration. This also helps to critique your work.- Ensure that your paper
**arouses interest**to those reading it. So enjoy what you are doing. - When doing research,
**focus on quality more than quantity**. This will assist you to publish in highly rated journals. - Give research
**quality time**. Avoid doing your research when your mind is tired. - Lastly,
**use simple language**and avoid ambiguity.