The new concept of a Z – number has been recently introduced in decision making analysis. This concept is capable of effectively dealing with uncertainty in information about a decision. As this concept is relatively new in fuzzy sets, its underlying theoretical aspects have not been established yet. In this paper, a multi-layer methodology for ranking Z – numbers is proposed for the first time...

in a previous work, we introduced particular fuzzy numbers anddiscussed some of their properties. in this paper we use the comparison methodintroduced by dorohonceanu and marin[5] to compare between these fuzzynumbers.

In this work, a new concept of upper dense sequence in interval (0,1] is introduced. There are infinitely many upper dense sequences in interval (0,1]. Using any upper dense sequence, a new decomposition theorem for fuzzy sets is established and proved. Then, using a chosen upper dense sequence as one of the necessary reference systems, infinitely many total orderings on the set of all fuzzy nu...

Dubois and Prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions. In this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval-valued possibilistic mean and investigate its relationship to the interval-valued probabilistic mean. W...

the importance as well as the diculty of the problem of ranking fuzzy numbers is pointed out. here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its signal/noise ratios, where the signal and the noise are de ned as the middle-point and the spread of each a-cut of a fuzzy number, respectively. we use the value of a ...

In this paper, a new hypothesis of fuzzy number has been proposed which is more precise and direct. This approach considered as an equivalence class on set real numbers R with its algebraic structure properties along theoretical study computational results. Newly defined provides well-structured summary that offers both deeper knowledge about the theory extensive view algebra. We field newly op...

This paper is on the solutions of fuzzy initial value problems for fourth-order fuzzy differential equations with positive and negative fuzzy coefficients by fuzzy Laplace transform. Examples are solved. Conclusions are given.

Ranking of fuzzy numbers plays a very important role in linguistic decision making and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques has been shown to produce nonintuitive results in certain cases. In this paper, some new approaches for ranking of trapezoidal fuzzy numbers are introduced. Keywords— Magnitude of...

A novel formalism is presented, which enables the processing of heterogeneous data including numeric-, interval-valued-, or fuzzydata. The data in question are represented herein as interval-supported fuzzy sets with suitable membership functions. The term Fuzzy Interval Number (FIN) denotes one of the aforementioned types of data. A FIN can have either a positive or a negative membership funct...