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.

In spite numerous researches on ranking method based on intuitionistic fuzzy numbers, there has not been any study on preference degree based on intuitionistic fuzzy numbers. This paper extends a preference criterion for ranking intuitionistic fuzzy numbers inspire by a well known method of ranking fuzzy numbers. The main properties of the extended preference degree will be also studied into the space of intuitionistic fuzzy numbers. In addition, the feasibility and effectiveness of the proposed ranking method is examined via an applied example related to the multi-criteria group decision-making based on intuitionistic fuzzy linguistic terms. The proposed method also compared with some common methods of ranking intuitionistic fuzzy numbers. Through specific theoretical and numerical results, it is shown that the proposed preference criterion provide us with a useful and valuable way to handle intuitionistic fuzzy numbers in many practical applications of decision making such as multiple attributes group decision-making based on linguistic variables.

In this paper, we deal with a linear programming problem with non-symmetric trapezoidal intuitionistic fuzzy numbers. In recent years, many authors have studied the symmetric trapezoidal intuitionistic fuzzy numbers. After defining a ranking function and arithmetic operations on these numbers, they solved the intuitionistic fuzzy linear programming problem.But the main problem with their method was that only available for symmetric trapezoidal intuitionistic fuzzy numbers. Now in order to overcome this limitation, in this paper, we present a new arithmetic and a new ordering for non-symmetric trapezoidal intuitionistic fuzzy numbers. Then, we present the general model of an intuitionistic fuzzy linear programming problems and prove a number of important theorems for solving it. Then we present the intuitionistic fuzzy simplex algorithm and finally, by presenting two examples, we will show the application of this new approach and show its superiority over the fuzzy mode.

For many decision problems with uncertainty, triangular intuitionistic fuzzy number is a useful tool in expressing ill-known quantities. This paper develops a novel decision method based on zero-sum game for multiple attribute decision making problems where the attribute values take the form of triangular intuitionistic fuzzy numbers and the attribute weights are unknown. First, a new value index is defined for triangular intuitionistic fuzzy numbers on the basis of the centroid. Thereby, a new ranking approach is presented for comparing triangular intuitionistic fuzzy numbers. We formulate a multiple attribute decision making problem as a two-person zero-sum game with payoffs of triangular intuitionistic fuzzy numbers. Then, following the new ranking approach, the fuzzy matrix game is converted as a pair of crisp linear programming models, and the optimal strategies are objectively derived by solving such models. Therefore, the ranking order of alternatives is determined by the expected scores of alternatives. An example of video monitoring system selection is demonstrated to illustrate the effectiveness of the proposed methodology.

In the present paper, the acceptance single sampling plan is developed by the generalized intuitionistic fuzzy numbers. The $\alpha_1$-cut and $\alpha_2$-cut sets of the generalized intuitionistic fuzzy numbers are applied to construct the acceptance single sampling plan. We also investigate the operating characteristic curve, where the parameter is considered the generalized intuitionistic fuzzy number. The $(\alpha_1,\alpha_2)$-cut set of generalized intuitionistic fuzzy operating characteristics is constructed. The bands are represented with upper and lower bounds instead of curves for operating characteristics and evaluated in detail. Finally, the numerical example is given to illustrate the proposed approach.

The present work concentrates on vagueness in the lifetime parameter and the generalized intuitionistic fuzzy set are extended to reliability characteristics. In order to satisfy this purpose, generalized intuitionistic fuzzy numbers are applied to evaluate the reliability of dif- ferent systems. The reliability characteristics of systems using Pareto lifetime distribution are investigated where the lifetime scale parameter is assumed to be a generalized intuitionistic fuzzy number. In general, the generalized intuitionistic fuzzy reliability function, generalized intu- itionistic fuzzy conditional reliability function, generalized intuitionistic fuzzy hazard function, generalized intuitionistic fuzzy mean time to fail- ure and their cut sets are discussed. The whole mentioned reliability functions are discussed for generalized intuitionistic fuzzy Pareto life- time systems. Furthermore, reliability analysis of the series and parallel systems are performed and numerical example is illustrated based on the proposed approach.

The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws. Furthermore, based on these operators, an approach to multi-criteria decision-making, in which assessments are in the form of TIT2 intuitionistic fuzzy numbers has been developed. A practical example to illustrate the decision-making process has been presented and compared their results with the existing operator results.

In practical problems where imprecise components are an inseparable part of them, using fuzzy sets to check their features and measure their efficiency solves some of the current limitations. In this article, we examine the problem of linear regression in an intuitionistic fuzzy environment. Here, we consider the input and output data as intuitionistic fuzzy numbers and assume that the coefficients of the model are crisp numbers. Since to correctly determine the coefficients, we need to calculate the distance between the output of the model and the output data, we present a new parametric distance to calculate the distance between intuitionistic fuzzy numbers. The salient point in this article is that the researcher can estimate the parameter values of the model based on different decision-making levels. To show the efficiency and test the proposed method, several examples are presented at the end of the article. The results are calculated and compared based on the values of different levels of decision-making.

In this paper, the intuitionistic fuzzy set and the triangular intuitionistic fuzzy number were displayed, as well as the intuitionistic fuzzy semi-parametric logistic regression model when the parameters and the dependent variable are fuzzy and the independent variables are crisp. Two methods were used to estimate the model on fuzzy data representing Coronavirus data, which are the suggested method and {The Wang et al method}, through the mean square error and the measure of goodness-of-fit, the suggested estimation method was the best.

In many optimization problems, all decision-makers are not on the same level, but decision-makers may be placed in a hierarchical structure.‏ ‎Also, it is possible that the parameters of the problem are not stated crisp, but are presented in different types of fuzzy or interval. ‎In this study‎, ‎we considered ‎two‎ ‎‎‎state of the bilevel linear programming problems with ambiguity uncertainty.‎‏‎ In one of the problems, ‎all‎ the parameters were trapezoidal intuitionistic fuzzy numbers, and in the other, ‎all‎ the parameters were triangular intuitionistic fuzzy numbers. By using the proposed ranking method, we obtain the ‎‎‎bilevel linear programming problem corresponding to each state, which is solved by the usual methods.