On using &agr;-cuts to evaluate fuzzy equations
Fuzzy Sets and Systems
Solving linear and quadratic fuzzy equations
Fuzzy Sets and Systems
Solving systems of linear fuzzy equations
Fuzzy Sets and Systems
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
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Linear equation systems play a very important role in engineering, mathematics, statistics and other disciplines. Fuzzifying either parameters or variables or both in these systems has been one of the research areas in the fuzzy literature since these kinds of systems are encountered in many applications. These systems are generally called fuzzy linear equations. Various types of these models have been examined for a decade. The solution procedures of these systems depend on different methods such as extension principle and interval arithmetic. Also, the method which is often used in computing inverse of a matrix in real case could be extended to fuzzy case, which employs linear equation system and identity matrix. For this purpose, we propose a new method which includes some new definitions which are fuzzy zero number, fuzzy one number and fuzzy identity matrix. Based on these definitions, direct computation of fuzzy inverse matrix is done using fuzzy arithmetic and fuzzy equation system. Actually, this simply extends the notion used in real case to fuzzy case. Calculation is realized with two different settings. While the first one is called direct numerical solution, the other is obtained by choice of decision maker. It is noted that the uniqueness of the calculated fuzzy inverse matrix is not guaranteed.