Many RANKING methods have been proposed so far. However, there is not any method which can always give a satisfactory solution for every situation. In this paper, we propose a method for RANKING FUZZY NUMBERS based on the distance method and compare the results with other RANKING methods in some examples.

RANKING FUZZY NUMBERS(FNs) was a critical issue in FUZZY computing field. Generally, triangular FNs, trapezoidal FNs, and even interval-valued FNs(IVFNs) were often expressed in RANKING. However, RANKING intuitionistic FNs(IFNs) were less mentioned due to the complicated components in membership functions. Herein, we will develop FUZZY binary relation that is an extended FUZZY preference relation(EFPR) to express the preference degree of two IFNs, and then the relation is improved to be a relative preference relation(RPR) used to rank a set of IFNs. Since EFPR on IFNs is a total ordering relation, RPR will be also a total ordering relation. Based on belonging and non-belonging components of membership functions in IFNs, using EFPR being also FUZZY preference relation(FPR) is suitable to compare FNs on pairwise, but time complexity on FUZZY operation of comparison computing is complicated. Hence, RPR is developed to avoid comparing on pairwise. Through yielding RPR values for a set of IFNs, IFNs are effectively and efficiently ranked to utilize related decision-making problems.

In this paper I will introduce the trapezoidal intuitionistic FUZZY NUMBERS (IF NUMBERS) and will prove some operations for them. Also I am going to propose a new ordering method for IF NUMBERS in which I will consider two characteristic values of membership and non-membership functions for an IF number. These values are defined by the integral of the inverse FUZZY membership and non-membership functions multiplied by the grade with powered parameter.

In this paper, a novel approach for RANKING FUZZY NUMBERS based on the angle measure is introduced. Several left and right spreads at each chosen a-levels of FUZZY NUMBERS is used to determine center of mass points (CMPs) and then, the angels between the CMPs and the horizontal axis is calculated. The total angle is determined by averaging the computed angles and finally, the novel method is compared with other methods by solving some numerical examples.

Dombi and Baczy nski presented a new approach to the problem of implication operation by introducing the preference implication, which has very advantageous properties. In this paper, it is presented how the preference implication is connected with soft inequalities and with sigmoid functions. Utilizing this connection the preference implication-based preference measure for two FUZZY NUMBERS is introduced and its key properties, including the reciprocity, are described. Then, the exact expression for computing the new preference measure for trapezoidal FUZZY NUMBERS is presented. Here, using the new preference measure, two crisp relations over trapezoidal FUZZY NUMBERS are introduced. It is shown that one of them is a strict (but not a total) order relation, and the other one is an equivalence relation. The strict order relation can be used to rank comparable FUZZY NUMBERS, while the equivalence relation, which we call the indifference relation, expresses that the order of some FUZZY NUMBERS is indifferent. These two crisp relations can be used to rank a collection of trapezoidal FUZZY NUMBERS. Lastly, the proposed RANKING method is compared with some well-known existing FUZZY number RANKING methods.

The importance as well as the difficulty 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 defined as the middle-point and the spread of each-cut of a FUZZY number, respectively. We use the value of a as the weight of the signal/noise ratio of each-cut of a FUZZY number to calculate the RANKING index of each FUZZY number. The proposed method can rank any kinds of FUZZY NUMBERS with different kinds of membership functions.

In this paper, we propose a new approach for RANKING all FUZZY NUMBERS based on revising the RANKING method proposed by Ezzati et al. [10].To this end, we present and investigate some properties of the proposed approach in details. Finally, to illustrate the advantage of the proposed method, it is applied to several groups of FUZZY NUMBERS and the results are compared with other related and familiar ones.

The concept of an intuitionistic FUZZY number (I F N) is of importance for representing an ill-known quantity. RANKING FUZZY NUMBERS plays a very important role in the decision process, data analysis and applications. The concept of an intuitionistic FUZZY number (IFN) is of importance for quantifying an ill-known quantity. RANKING of intuitionistic FUZZY NUMBERS plays a vital role in decision making and linear programming problems. Also, RANKING of intuitionistic FUZZY NUMBERS is a very difficult problem. In this paper, a new method for RANKING intuitionistic FUZZY number is developed by means of magnitude for different forms of intuitionistic FUZZY NUMBERS. In Particular RANKING is done for trapezoidal intuitionistic FUZZY NUMBERS, triangular intuitionistic FUZZY NUMBERS, symmetric trapezoidal intuitionistic FUZZY NUMBERS, and symmetric triangular intuitionistic FUZZY NUMBERS. Numerical examples are illustrated for all the defined different forms of intuitionistic FUZZY NUMBERS. Finally some comparative numerical examples are illustrated to express the advantage of the proposed method.

Since the inception of intuitionistic FUZZY sets in 1986, many authors have proposed different methods for RANKING intuitionistic FUZZY NUMBERS (IFNs). However, due to the complexity of the problem, a method which gives a satisfactory result to all situations is a challenging task. Most of them contained some shortcomings, such as requirement of complicated calculations, inconsistency with human intuition and indiscrimination and some produce different RANKINGs for the same situation and some methods cannot rank crisp NUMBERS. For overcoming the above problems, in this paper, a new parametric RANKING method for IFNs is proposed. It is developed based on the concept -cuts and -cuts and area on left side of IFNs. The proposed RANKING method is applied to solve partner selection problem in which the rating of partner on attributes are expressed by using triangular IFNs. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method.