# Fuzzy, Neutrosophic Sets, Vital to Technological Advancement - Don

A Don in the Department of Mathematics, College of Physical Sciences (COLPHYS), Professor Adesina Agboola, has highlighted the benefits of Fuzzy and Neutrosophic Sets to technological advancement, saying that while Fuzzy Set was first introduced by Professor Lotfi Zadeh in 1965, as an extension and generalisation of the Classical Set Theory, Professor Florentin Smarandache introduced the Neutrosophic Set in 1995, as a generalisation and extension of the Fuzzy Set. According to him, Fuzzy and Neutrosophic Sets have practical real life applications in Robotics, Computer Science, Artificial Intelligence, Control Systems, Engineering, Quantum Theory, Languages, Information Technology, Economics, Finance, Psychology, Law, Politics and Medicine. He went further to state that thermostats in the modern day air-conditioners and refrigerators are controlled by Fuzzy Logic. Professor Agboola, whose major area is Pure Mathematics (Algebra), which he noted, was different from Applied Mathematics, added that when a Pure Mathematician, George Boole, was working on the Boolean Algebra and Binary Numbers, little did he know that such an innovation could be the basis for the development of Computer Science and Information Technology. A Pure Mathematician usually concentrates on the establishing logical statements and proofs in his/her area of specialisation, without having to bother about their applications. Professor Agboola stressed that Fuzzy Set permits the gradual assessment of the membership of elements in a set, which is characterized with the aid of a membership function, valued in the real unit interval [0, 1]. “So, what I have been doing for over 15 years or more is the Pure Mathematics. We have been studying and developing Algebraic Structures, Algebraic Hyperstructures, Fuzzy Algebraic Structures, Neutrosophic Algebraic Structures and Neutrosophic Algebraic Hyperstructures”, he stated.

Speaking further, Professor Agboola said that, “If you go to secondary schools today, the students learn only about the Classical Set, and even up to the university level, students are being taught only the Classical Set Theory. wherein an element either belongs to a set, or does not. Citing an example, the mathematician stated that, “Suppose we were considering a set of students in FUNAAB, if I pick somebody, the person must have the identity of being a FUNAAB student before he/she can belong to the set. But, if I pick someone else, who has nothing doing with FUNAAB, that person cannot be in that set. So, that is what the Classical Set (Theory) is all about. It’s either you are a member or you are not a member. But, in the real sense of it, that kind of a set or that kind of Mathematics, is not suitable for modeling the real life, full of uncertainties, vagueness and indeterminacies. Hence the need for the creation of Fuzzy and Neutrosophic Sets".

Expatiating further on the Fuzzy Set, Professor Agboola noted that, “If we are considering a set of brilliant students in Mathematics in this University, only the students with As or Bs can belong to the set and not the students with Cs, Ds, Es and even Fs under the Classical Set. However, under the concept of Fuzzy Set, all the students can belong to the set but with varying degrees of membership. Those with As may be graded 0.9, Bs with 0.8, Cs with 0.5, Ds with 0.4, Es with 0.1 and Fs with 0.01. In this way, all the students will be considered to be brilliant with various degrees of brilliance and they can all belong to the set. When all the factors present in an environment are considered in the modeling of the environment, the result obtained will be closer to the reality, when compared with the results obtained when some factors are neglected by assumptions."

Citing another example, Professor Agboola said that, “In our daily activities, we usually make use of expressions like: hot tea, very hot water, cold water, very cold water, hot sun, fresh apple, tall boy, very tall girl, short tree, long train, beautiful car, big television, small radio, bright star, etc. The imprecise (vague) terms like hot, very cold, fresh, tall, long, very short, very big, etc, have no place in the Classical Set Theory, but are well accommodated in the Theory of Fuzzy Set.

The Don stated further that, as powerful as the Theory of Fuzzy Set is, it cannot be used to model situations involving indeterminacies. Hence, the need for the creation of the Theory of Neutrosophic Set by Smarandache.The Fuzzy Set Theory presents only the true values and the false values. However, in the Neutrosophic Set, we have the true values, the false values and the indeterminant values.

Giving more examples, the Don said that “Suppose we consider the proposition ‘Tomorrow it will be raining’, the proposition cannot have a fixed-valued component structure. At time t1, it may be 40 percent true, 45 percent false and 50 percent indeterminate; but at time t2, it may change to have 50 percent true, 30 percent false and 49 percent indeterminate, depending on the new evidences, sources, etc. Also, that a known good football club will win a match may be 65 percent true, 25 percent false and 30 percent indeterminate and that a known brilliant student in Mathematics will make a First Class Degree in Mathematics at the end of his/her course may be 70 percent true, 10 percent false and 15 percent indeterminate.” All these possible situations can only be accommodated in the Neutrosophic Set Theory. If the truth value, falsehood value and indeterminacy value can be factored in the modeling of a situation, the result will be closer to the reality, than when compared to using only the truth value and falsehood value as stipulated in the Fuzzy Set Theory.

Due to their importance and wide range of applications, Professor Agboola recommended the inclusion of Fuzzy and Neutrosophic Sets in the curricula of higher levels of undergraduate and postgraduate programmes in Mathematics, Computer Science, Statistics, Physics and Engineering in all Nigerian universities.

Professor Agboola identified the challenges facing research in Mathematics and other disciplines in the country to include inadequate funding as well as apathy and non-conducive working environment. He advised upcoming researchers in Nigeria not to give up, but be encouraged to forge ahead, by working hard to publish good research papers, to become ever relevant in today’s academic world.

Professor Agboola, a recipient of the 2015 Distinguished Achievement Award in Paradoxism by the International Association of Paradoxism, a vanguard movement in the arts and sciences, was recognised for his outstanding contributions in the areas of Neutrosophic Theory and the development of New Neutrosophic Algebraic Structures and Neutrosophic Algebraic Hyperstructures, among others.