Mashallah Matinfar - Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
Somayeh Ezadi - Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran

Many practical applications, under the definitive evolutionary state of the nature, the consequences of the decisions, mental states of a decision maker are required. Thus the need for a new concept for decision analysis under the Z-number is proposed by the mentioned concept. A Z-number has two components (?A ̃,?B ̃ ). Initialy, ? ̃ , is a value constraint with a real-valued uncertain variable, X, is allowed to take. The second component, B ̃ , is a measure of reliability (certainty) which belongs the first component. Because the concept is relatively new Z-number in fuzzy sets, hence, its basic theoretical aspects are yet undetermined. This paper presented a method for rating and ranking Z-numbers for a setof Z-numbers. hence, we propose a new method for ranking fuzzy numbers based on that of Hyperbolic tangent function, the mean. Afterwards the proposed method is capable of rankings properties. Then, using the same technique we propose a method for ranking Z-numbers. Next, by the same technique we propose a method for ranking Z-numbers. This method consists three layers. The first layer is the gravitycenter in Part ? ̃ of the Z-numbers obtains. The second layer, applies the mean in Part ?A ̃ of the Z-numbers obtained. And the third one implies the Hyperbolic tangent function and the values obtained from the two mentioned layers rank which determines the Z-numbers. Our proposed method for ranking Znumbers compared to some existing methods.

Z-numbers, Fuzzy numbers; Ranking of fuzzy numbers; Ranking of Z-numbers; Standard deviation; convex combination; Hyperbolic tangent function; Score method