A Mathematical Study of Fuzzy Logic Techniques in Software Engineering

Estimation models in software engineering are used to predict some important attributes of future entities such as software development effort, software reliability and programmer productivity. Estimation by fuzzy logic techniques is one of the most attractive techniques in software effort estimation field. In this paper I propose a new approach based on reasoning by fuzzy logic to estimate effort . Keywords-fuzzy logic, productivity I. INTRODUCTION Fuzzy Logic In 1948, Alan Truing wrote a paper, which marked the beginning of a new era, the era of the intelligent machine. To allow computers to mimic the way humans think, the theories of fuzzy sets and fuzzy logic was created. Classical logic deals with crisp knowledge where statements can only be either true or false, while fuzzy logic deals with vaguely formulated or uncertain knowledge. Dr. Lotfi Asker Zedeh first used the term fuzzy in the engineering journal, Proceedings of the IRE in 1962. Fuzzy sets were introduced by Zadeh (ZADE65) as an extension of the classical nation of the set. Fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets generalize classical sets, since the indicator functions of classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values O or 1. In fuzzy set theory, classical sets are usually known as crisp sets. Fuzzy logic is a methodology, based on fuzzy set theory, classical sets are usually known as crisp sets. Fuzzy logic is a methodology, based on fuzzy set theory to solve problems, which are too complex, to be understood quantitatively (ZADE65). Fuzzy logic is a superset of conventional logic that has been extended to handle the concept of partial truth. Fuzzy logic can be thought of as the application side of fuzzy set theory. It is an effective technique to solve uncertainties due to imprecise data. Fuzzy Number A fuzzy number is a quantity whose value is imprecise, rather than exact as in the case of ordinary single valued numbers. A fuzzy number is represented by a membership function, whose domain is a fuzzy set. The membership function associates a real number (0, 1) with each point in the fuzzy set, called degree of uncertainty or grade of membership. The membership μ A (x) of an element x of a classical set A, as subset of the universe x, is defined by :