This paper first improves Chen and Hsieh’ s definition of GENERALIZED FUZZY NUMBERS, which makes it the generalization of definition of FUZZY NUMBERS. Secondly, in terms of the GENERALIZED FUZZY NUMBERS set, we introduce two different kinds of orders and arithmetic operations and metrics based on the -cutting sets or GENERALIZED -cutting sets, so that the GENERALIZED FUZZY NUMBERS are integrated into a partial ordering set, a semi-ring and a complete non-separable metric space. Again, through two isomorphism theorem, the relationship between GENERALIZED FUZZY number space and FUZZY number space is established. Finally, as an application of GENERALIZED FUZZY NUMBERS, the concept of continuous GENERALIZED FUZZY number-valued functions is introduced. And it is pointed out that many results of trapezoidal GENERALIZED FUZZY NUMBERS can also be extended to GENERALIZED FUZZY NUMBERS.

The objective of this paper is to develop arithmetic operations between GENERALIZED trapezoidal (triangular) FUZZY NUMBERS so that the drawbacks of the existing works are overcome. In this respect, the extension principle has been used to calculate different arithmetic operations.

Because of the suitability of FUZZY NUMBERS in representing uncertain values, ranking the FUZZY NUMBERS has widely applications in different sciences. Many models are presented in field of ranking the FUZZY NUMBERS that each one rank based on special criteria and features. The purpose of this paper is presenting a new method for ranking GENERALIZED FUZZY NUMBERS based on some parameters such as membership degree, mean, standard deviation and parametric form of membership function. This paper introduce existing ranking models, comparing them the proposed model is presented .Considering special sets of FUZZY NUMBERS, the advantages of proposed model is expressed. The main purpose of this paper is to present a reliable ranking method for GENERALIZED FUZZY NUMBERS.

Ranking GENERALIZED FUZZY NUMBERS plays an important role in many applied models and, in particular, decision-making procedures. In ranking process of two GENERALIZED FUZZY NUMBERS, it is natural to compare the sets of values in support of two generalised FUZZY NUMBERS. Accordingly, the comparison of a real number and a generalised FUZZY number as well as two generalised FUZZY NUMBERS have to be considered. On the other hand, it is seen that a definitive process of comparison of a real number and a generalised FUZZY number, as well as two generalised FUZZY NUMBERS, is not possible. So in this study, a method for comparing a real number and a generalised FUZZY number with a degree of accuracy (between a zero and one) is defined and then the method is GENERALIZED to compare two generalised FUZZY NUMBERS. In general, an index to rank a real number and generalised FUZZY number is constructed. Eventually, this index is extended to rank two generalised FUZZY NUMBERS based on the concept of accuracy of comparison. The advantage of our method is that it can compare two generalised FUZZY NUMBERS with an accuracy of comparison. Also, a definition is introduced to make a definitive comparison. Finally, the proposed method is illustrated by some numerical examples.

The purpose of this paper is to introduce the concepts of lacunary stronglyDm-summable andlacunary Dm -statistically convergent of GENERALIZED difference sequences of FUZZY NUMBERS. Some results are obtained related to these concepts.

FUZZY risk analysis, as a powerful tool to address uncertain information, can provide an appropriate method for risk analysis. However, the previous FUZZY risk analysis methods still have some weaknesses. To overcome the weaknesses of existing FUZZY risk analysis methods, a novel method for ranking GENERALIZED FUZZY NUMBERS is proposed for addressing FUZZY risk analysis problems. In the proposed method, a new value of ranking score is obtained based on ordered weighted averaging (OWA) operator. The proposed method takes into consideration of the different importance of the three scoring factors defuzzified value, height and spread. Comparing to some existing methods, the new method can get more reasonable results in some situations.