 # Introduction to Fuzzy Logic and Fuzzy Linear Programming

Pandian Vasant (University of Technology Petronas, Malaysia) and Hrishikesh S. Kale (K.K.Wagh Institute of Engineering Education & Research, India)
DOI: 10.4018/978-1-59904-843-7.ch061
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## Abstract

Fuzzy logic (FL) is a mathematical technique for dealing with imprecise data and problems that have many solutions rather than one. Although it is implemented in digital computers which ultimately make only yesno decisions, FL works with ranges of values, solving problems in a way that more resembles human logic. FL is a multi-valued (as opposed to binary) logic developed to deal with imprecise or vague data. Classical logic holds that everything can be expressed in binary terms: 0 and 1, black and white, yes or no; in terms of Boolean algebra, everything is in one set or another but not in both. FL allows for partial membership in asset values between 0 and 1, shades of gray, and introduces the concept of the “fuzzy set.” When the approximate reasoning of FL (Zadeh, 1965) is used with an expert system, logical inferences can be drawn from imprecise relationships. FL theory was developed by Lofti A. Zadeh at the University of California in the mid 1960s. However, it was not applied commercially until 1987 when the Matsushita Industrial Electric Co. used it to automatically optimize the wash cycle of a washing machine by sensing the load size, fabric mix, and quantity of detergent and has applications in the control of passenger elevators, household applications, and so forth.

## Key Terms in this Chapter

Fuzzy Linear Programming (FLP): FLP deals with the optimization (maximization or minimization) of a function of variables known as fuzzy objective function, subject to a set of fuzzy linear equations and/or inequality known as restrictions or fuzzy constraints.

Fuzzy Band: The fuzzy groups also can be called a fuzzy band.

Membership Function (MF): An MF is a curve that defines how each point in the input space is mapped to a membership value (or degree of membership) between 0 and 1.

MATLAB®: MATLAB® is a very highly sophisticated technical computing tool box for solving FLP problems.

Fuzzy Set: A fuzzy set on a classical set ? is defined as follows: The MF µA(x) quantifies the grade of membership of the elements x to the fundamental set ?.

Degree of Satisfaction: The degree of satisfaction is the level of satisfaction with respect to vagueness in the fuzzy parameter, and it is measured between 0 and 1.

Fuzzy Logic: Fuzzy logic is a mathematical technique for dealing with imprecise data and problems that have many solutions rather than one.

Linear Programming (LP): LP deals with the optimization (maximization or minimization) of a function of variables known as objective function, subject to a set of linear equations and/or inequality known as restrictions or constraints.

Satisfactory/Compromise Solution: Satisfactory/compromise solution is a fuzzy optimization solution that will be provided to the decision makers for the implementation purpose.

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