Abstract
The arithmetic operations on fuzzy number are basic content in fuzzy mathematics. But still the operations of fuzzy arithmetic operations are not established. There are some arithmetic operations for computing fuzzy number. Certain are analytical methods and further are approximation methods. In this paper we, compare the multiplication operation on triangular fuzzy number between α-cut method and standard approximation method and give some examples.
Highlights
Fuzzy sets have been introduced by Lotfi.A.Zadeh(1965)
When operating with fuzzy numbers, the result of our calculations strongly depend on the shape of the membership functions of these numbers
In many situations this problem is solved by approximation multiplication by a triangular or trapezoidal fuzzy number
Summary
Fuzzy sets have been introduced by Lotfi.A.Zadeh(1965). Since its inception 50 years ago, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. In many situations this problem is solved by approximation multiplication by a triangular or trapezoidal fuzzy number. Definition 2.5 Triangular Fuzzy Number It is a fuzzy number represented with three points as follows: A “ pa[1], a2, a3q. This representation is interpreted as membership functions and holds the following conditions (i) a1 and a2 is increasing function. Definition 2.9 Partial Negative triangular fuzzy number A Partial Negative triangular fuzzy number Ais denoted as A “ pa[1], a2, a3q , where at least one ai is negative for all i “ 1, 2, 3
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