Why is fuzzy logic

In particular, fuzzy logic is best suited for control-systems fields. For instance, fuzzy logic has been applied in areas such as breakdown prediction of nuclear reactors in Europe, earthquake forecasting in China, and subway control in Japan.

The control rules that describe an anti-lock braking system may consist of parameters such as the car's speed, the brake pressure, the brake temperature, the interval between applications of the brakes and the angle of the car's lateral motion to its forward motion.

The range of values of these parameters are all continuous, open to interpretation by a design engineer. One such rule in an anti-lock braking system could be: IF brake temperature is 'warm' AND speed is 'not very fast,' then brake pressure is 'slightly decreased. There are also many fuzzy logic chips processors that are built to do special tasks without using conventional computers. The outlook for fuzzy logic is therefore very promising. Jim Diederich, a professor of mathematics at the University of California at Davis, is working on the applications of fuzzy logic in biological systems.

He recently tried out fuzzy logic techniques on one specialized set of biological systems--his students--when he proposed the following rules for one of his courses Special Topics in Mathematics Math Fuzzy Sets, Numbers and Logic Course Information A midterm will be given around mid term.

The final will be given around final time. Homework will be assigned fairly regularly. The midterm and final each will normally count as a substantial part of the grade. The homework will not be insignificant in counting as part of the grade. An excellent final will result in a somewhat excellent grade. Solid work in two of the three areas, midterm, final and homework, will result in a solid grade. It refers to a family of many-valued logics , where the truth-values are interpreted as degrees of truth.

In other words, like in classical logic, one imposes truth-functionality. Fuzzy logic emerged in the context of the theory of fuzzy sets, introduced by Lotfi Zadeh Fuzzy logic arises by assigning degrees of truth to propositions.

In particular in engineering contexts fuzzy control, fuzzy classification, soft computing it is aimed at efficient computational methods tolerant to suboptimality and imprecision see, e. Mathematical fuzzy logic focuses on logics based on a truth-functional account of partial truth and studies them in the spirit of classical mathematical logic, investigating syntax, model theoretic semantics, proof systems, completeness, etc. A fundamental assumption of mainstream mathematical fuzzy logic is that connectives are to be interpreted truth-functionally over the set of degrees of truth.

These three truth-functions yield the original semantics of fuzzy logic proposed by Joseph Goguen , later studied formally by, e. Interestingly, each left-continuous t-norm determines a suitable choice for implication. In the general t-norm setting, the negation is interpreted using the residuum. This Hilbert-style system is a strongly complete finitary axiomatization of the logic MTL, i.

In terms of computational complexity, the validity problem for this logic is asymptotically not worse than in classical logic: it remains coNP-complete.

It is distinguished as the only t-norm based logic where the validity of a formula in a given evaluation does not depend on the specific values assigned to the propositional variables, but only on the relative order of these values.

There are also reasons to consider weaker fuzzy logics. Such interpretations of conjunctions are called uninorms. Finally, taking into account that fuzzy logics, unlike classical logic, are typically not functionally complete, one can increase their expressive power by adding new connectives.

A thorough overview of all the kinds of propositional fuzzy logics mentioned in this section and a general theory thereof can be found in the Handbook of Mathematical Fuzzy Logic 3 volumes, Cintula et al. The semantics is given by structures in which predicate symbols are interpreted as functions mapping tuples of domain elements into truth-values. There are two ways of introducing first-order counterparts for other propositional t-norm based fuzzy logics.

In this manner one obtains syntactic presentations of first-order variants of, e. Then, the natural question is whether, in each case, these two routes lead to the same logic as it happened for MTL. For soundness there is no problem, as the axiomatic systems are easily checked to be sound with respect to their corresponding classes of structures.

As for completeness, there is no general answer and the problem has to be considered case by case. One of the main tools in the study of fuzzy logic is that of algebraic semantics. The approach of FL imitates the way of decision making in humans that involves all intermediate possibilities between digital values YES and NO.

It can be implemented in systems with various sizes and capabilities ranging from small micro-controllers to large, networked, workstation-based control systems.

Membership functions allow you to quantify linguistic term and represent a fuzzy set graphically. Here, each element of X is mapped to a value between 0 and 1.

It is called membership value or degree of membership. It quantifies the degree of membership of the element in X to the fuzzy set A. Only 11 research papers were accepted.

Research papers were accepted from 22 researchers at 13 universities and research institutions in the USA, Canada, India, Japan, and Iran. This special issue describes many important research advancements in real-life applications of fuzzy logic.

Also, it creates awareness of real-life applications of fuzzy logic and thereby encourages others to do research and development in more real-life applications of fuzzy logic. There are numerous other applications of fuzzy logic that have to be researched and developed. Harpreet Singh Madan M. I am deeply appreciative of the dedication to me of this special issue, of the journal of Advances in Fuzzy Systems. Additionally, I appreciate very much being asked by the editors to contribute a brief foreword.

For me, the foreword is an opportunity to offer a comment on the theme of the special issue. First, a bit of history, my paper on fuzzy sets was motivated by my feeling that the then existing theories provided no means of dealing with a pervasive aspect of reality—unsharpness fuzziness of class boundaries. Without such means, realistic models of human-centered and biological systems are hard to construct.

My expectation was that fuzzy set theory would be welcomed by the scientific communities in these and related fields. Contrary to my expectation, in these fields, fuzzy set theory was met with skepticism and, in some instances, with hostility.

What I did not anticipate was that, for many years after the debut of fuzzy set theory, its main applications would be in the realms of engineering systems and consumer products. The first significant real-life applications of fuzzy set theory and fuzzy logic began to appear in the late seventies and early eighties. Among such applications were fuzzy logic-controlled cement kilns and production of steel. Soon, many others followed, among them home appliances, photographic equipment, and automobile transmissions.

The past two decades have witnessed a significant change in the nature of applications of fuzzy logic. Nonengineering applications have grown in number, visibility, and importance. Among such applications are applications in medicine, social sciences, policy sciences, fraud detection systems, assessment of credit-worthiness systems, and economics.

Particularly worthy of note is the path-breaking work of Professor Rafik Aliev on application of fuzzy logic to decision making in the realm of economics. Once his work is understood, it is certain to have a major impact on economic theories. Underlying real-life applications of fuzzy logic is a key idea. Almost all real-life applications of fuzzy logic involve the use of linguistic variables. A linguistic variable is a variable whose values are words rather than numbers.

The concept of a linguistic variable was introduced in my paper. In science, there is a deep-seated tradition of according much more respect for numbers than for words. In fact, scientific progress is commonly equated to progression from the use of words to the use of numbers.