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With the continuous improvement and development of various decision-making methods, it has led to the widespread use of fuzzy sets and fuzzy numbers. At the same time, the application of decision-making methods in different fuzzy environments has been very effective in addressing the deficiencies in existing research. At present, triangular fuzzy numbers have been widely used in the evaluation aspects of various decision making methods, and the proposed R-number effectively solve the uncertainty involving problems related to future events, but the existing research based on the TOPSIS method in the R-number environment has not yet been clearly applied to the triangular fuzzy number environment, and the indifference threshold-based attribute ratio analysis (ITARA) method in the fuzzy environment has yet to be extended. Therefore, this paper proposes a fuzzy indifference threshold-based attribute ratio analysis (FITARA) method based on triangular fuzzy numbers for solving the problem of determining attribute weights in the multi-attribute decision-making process. Secondly, the various risks of the decision environment and the impact on future events are considered and R-number are used to solve this puzzle. In addition, the incorporation of risk perception factors in the context of the existing RTOPSIS method considering multiple risk factors and the use of Manhattan distances to optimize the large number of operations in the process of the method resulted in the development of the FITARA-RTOPSIS model. Finally, the proposed FITARA-RTOPSIS method is applied to the problem of siting emergency supplies storage depots, and the effectiveness of the proposed method is verified through comparative analysis. [ABSTRACT FROM AUTHOR]

The recruitment of university researchers can be considered a multi-attribute group decision-making (MAGDM) problem. MAGDM is a familiar issue with uncertainty and fuzziness in the decision-making field. Generalized hesitation fuzzy numbers (GHFNs) as a new expanded form of hesitation fuzzy numbers (HFNs) can better express the uncertain information in MAGDM. The TODIM is a very classical and widely used method to deal with the MAGDM issue. In this paper, we integrate cumulative prospect theory (CPT) into TODIM to consider not only decision makers' subjective risk preferences but also their confidence level to obtain more reasonable choices under risk conditions. Therefore, we propose the GHF CPT-TODIM approach to tackle the MAGDM issue. Meanwhile, in the GHF environment, it is proposed to use the volatility of attribute information (entropy weighting method) to obtain the importance of attributes, obtain the unknown attribute weight, and enhance the rationality of weight information. Finally, the validity and usefulness of the technique are verified by applying the GHF CPT-TODIM technique to the recruitment of university researchers and comparing it with the existing GHF MAGDM method, which offers a new way to solve the MAGDM problem with GHFNs. [ABSTRACT FROM AUTHOR]

This paper is concerned with the solution mechanism to solve the transportation problem under unpredictability by using interval valued intuitionistic fuzzy parameters. The parameters are chosen as intervals in which costs are modeled by intuitionistic fuzzy numbers, whereas source and destination are taken as crisp values. Various methods of transportation problem like VAM, Monalisha's Approximation method, Zero point method are used to illustrate the cost in interval numbers by using the interval arithmetic operations. For each method, a solution is derived without converting into crisp expression followed by a graphical representation. [ABSTRACT FROM AUTHOR]

Uncertainty has long been explored as an objective and inalienable reality, and then modeled via different theories such as probability theory, fuzzy sets (FSs) theory, vague sets, etc. Hesitant fuzzy sets (HFSs) as a generalization of FSs, because of their flexibility and capability, extended and applied in many practical problems very soon. However, the above theories cannot meet all the scientific needs of researchers. For example, in some decision-making problems we encounter predetermined definite data, which have inductive uncertainties. In other words, the numbers themselves are crisp in nature, but are associated with varying degrees of satisfaction or fairness from the perspective of each decision-maker/judge. To this end, in this article, hesitant fuzzy numbers as a generalization of hesitant fuzzy sets will be introduced. Some concepts such as the operation laws, the arithmetic operations, the score function, the variance of hesitant fuzzy numbers, and a way to compare hesitant fuzzy numbers will be proposed. Mean-based aggregation operators of hesitant fuzzy numbers, i.e. hesitant fuzzy weighted arithmetic averaging (HWAA), hesitant fuzzy weighted geometric averaging (HWGA), hesitant fuzzy ordered weighted arithmetic averaging (HOWAA), and hesitant fuzzy ordered weighted geometric averaging (HOWGA) operators have been discussed in this paper, too. These new concepts will be used to model, and solve an uncertain multi-attribute group decision making (MAGDM) problem. The proposed method will be illustrated by a numerical example and the validity of the obtained solution will be checked by test criteria. [ABSTRACT FROM AUTHOR]

In many cases, complex problems cannot be accurately described by precise numerical values. Fuzzy theory provides a suitable tool for solving these problems. However, if decision makers cannot reach an agreement on the method for defining linguistic variables based on fuzzy sets, TIVFNs (triangular interval-valued fuzzy numbers) can provide more accurate modeling. Therefore, solving fuzzy MCGDM (multiple criteria group decision-making) problem with an unknown expert weight and criterion weight in TIVFNs has become an important research direction. In this paper, TIVF-VIKOR (triangular interval-valued fuzzy VIKOR) method, which is suitable for the environment of TIVFNs, is proposed to solve the problem of fuzzy MCGDM. To achieve this goal, the TIVF-VIKOR method is innovatively adopted similarity and coefficient of variation are combined to calculate expert weight, and deviation maximization method based on divergence matrix is used to calculate criterion weight. VIKOR method is used to find the compromise solutions, which are converted into the form of binary connection number, and the optimal compromise solution is obtained after ranking. The proposed method is applied to the problem of machine fault detection, and the validity and feasibility of the method are illustrated. Compared with the TOPSIS∖ELECTRE method, the ranking results of the three methods are equivalent, and the fluctuation of the TIVF-VIKOR method is more distinct. [ABSTRACT FROM AUTHOR]

Regional bus scheduling is necessary to urban public transport that is complicated by the necessity of assigning trips that belong to several routes to buses located at different depots while reducing fleet size and operating costs. Considering the reality of emergencies that may interfere with the ability of vehicles to complete trips on time, it is reasonable to use fuzzy numbers to express uncertain delay times. Based on this idea, this paper proposes a chance-constrained programming model of regional bus scheduling that will reflect additional constraints such as the capacities of related depots and fueling needs. The objective of this paper is to maximize utilization of fleet vehicles. To overcome the defect of premature convergence in the particle swarm optimization algorithm (PSO), an improved PSO is proposed by using an organic fusion with group search optimization. Finally, an example demonstrates the correctness and effectiveness of the model and algorithm. [ABSTRACT FROM AUTHOR]

This paper is to deal with a kind of fuzzy multi-objective linear programming (FMOLP) problem with symmetric trapezoidal fuzzy numbers. Several methods has been proposed in order to obtain fuzzy efficient solution to FMOLP problem. In this paper, we change FMOLP problem into the complete stratified fuzzy linear programming problem, then use the stratified simplex method to obtain the fuzzy optimal solution directly without converting them to crisp linear programming problem. We then prove that this fuzzy optimal solution is the fuzzy efficient solution of the original FMOLP problem. A numerical example is given to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a new method for ranking fuzzy numbers named as possibility-based comparison relation. The method is based on cut sets and comparison relation on interval values. Three parts are involved in the paper. Firstly, a new formula of cut sets of interval values is introduced. Then with the help of the formula, a new comparison relation on interval values is presented, and applied to the issue of ranking fuzzy numbers using fuzzy attitude functions. Secondly, some numerical examples are used not only to demonstrate the procedure of the proposed method but also to compare with previous methods. Finally, by use of the ranking method, a fuzzy attitude-based decision model is introduced to solve fuzzy decision making problems. Some examples are given for illustration. The achievements in the presented work will provide an effective ranking method with good results for decision making problems. [ABSTRACT FROM AUTHOR]

In this paper the generalized symmetric fuzzy numbers are brought into the knowledge and a new ranking function was proposed for it. Using this ranking function, any kind of fuzzy linear programming problem can be solved. The proposed ranking function is illustrated by the numerical example. Moreover, Comparison of optimal solution of proposed and existing methods are discussed. The proposed method is posing no difficulty to understand and execute the fuzzy optimal solution of a symmetric fuzzy linear programming problem in real world situations. [ABSTRACT FROM AUTHOR]

Dhanasekar et al. (International Journal of Fuzzy Systems 19 (2017) 1479-1491) proposed a fuzzy Hungarian MODI algorithm to solve fully fuzzy transportation problems. Dhanasekar et al. have used the standard multiplication of trapezoidal fuzzy numbers in their proposed method. In this paper, it is pointed out that the method, proposed by Dhanasekar et al., is not valid for standard multiplication of trapezoidal fuzzy numbers and is valid only if a special type of multiplication of fuzzy numbers is used. [ABSTRACT FROM AUTHOR]

In order to make the comprehensive decision-making results more consistent with the actual situation, a fuzzy comprehensive decision-making model with fuzzy combined weighting is developed in this paper. The fuzzy combined weighting method (FCWM) is proposed in the model to determine the weights of decision factors (indexes). The subjective weight and objective weight are combined in the FCWM to reduce the decision error caused by either using subjective weight or objective weight alone. In addition, the fuzziness of combined weights is taken into account in FCWM to make the decision-making results more realistic. The fuzzy structured element is used to express fuzzy numbers in the model. The analysis algorithm of fuzzy comprehensive decision based on the expression of fuzzy structured element is given to solve the problem of complex operations among fuzzy numbers. The decision model was applied to the order of metal mine gob management. It provides guidance for gob management reasonably and orderly. The research results also provide a new idea for the determination of weights in other fuzzy analysis models. [ABSTRACT FROM AUTHOR]

In this paper, the concept of lacunary strongly p-Cesàro summable sequences of weight g for fuzzy numbers is introduced by using ideal. In addition to this concept, inclusion theorems are also presented. The study leaves some interesting open problems. [ABSTRACT FROM AUTHOR]

This paper addresses a selective maintenance optimization problem for a fuzzy multi-state system composed of fuzzy multi-state elements. Due to insufficient data and unpredictable external working conditions, both the performance capacity and states transition intensities of multi-state elements cannot be known precisely, but are represented by fuzzy numbers. Additionally, both the durations of a break and a succeeding mission are also treated as fuzzy values. To maximize the fuzzy probability of a system successfully completing a succeeding mission, a selective maintenance model is proposed to identify an optimal subset of maintenance activities to be performed on some elements in the system. A solution algorithm containing three rules to eliminate inferior solutions and narrowdown elements' states combinations is proposed to resolve the new selective maintenance model in a computationally efficient manner. An illustrative example of an archibald is presented to demonstrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Since linguistic intuitionistic fuzzy numbers (LIFNs) can more easily express the fuzzy information in a qualitative setting, it is necessary to extend their operational rules and develop the decision making method based on the LIFNs. In this paper, we propose some new operational laws such as the subtraction and division, score function and accuracy function for (LIFNs), and we develop the linguistic intuitionistic fuzzy entropy, which can measure not only the fuzziness but also the intuitionism. Then we propose a method for determining the objective weight of attributes by the proposed entropy. In addition, because the VIKOR(from Serbian: VIseKriterijumska Optimizacija IKompromisno Resenje) method is an effective decision making tool which can select the optimal alternative by the maximizing "group utility" and minimizing "individual regret", we extended the VIKOR method to process the linguistic intuitionistic fuzzy information (LIFI) based on the new operational laws, and proposed an extended VIKOR method for the multiple attribute decision making (MADM) problems with LIFI. An illustrative example shows the effectiveness and advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

Compared to fuzzy numbers, intuitionistic fuzzy numbers provide greater opportunities for solving complex decision-making problems, especially when they are related to ambiguities, uncertainties and vagueness. However, their use is more complex, especially when it comes to ordinary users. Therefore, in this paper an approach adopted for evaluating alternatives on the basis of a smaller number of some more complex evaluation criteria is proposed. The approach is based on the use of linguistic variables, triangular intuitionistic fuzzy numbers, and the Hamming distance. At the end, a case study of hotels' websites evaluation is given to demonstrate the practicality and effectiveness of the proposed approach, together with its limitations and weaknesses. Additionally, a new procedure for ranking intuitionistic fuzzy numbers is proposed and its use is verified. [ABSTRACT FROM AUTHOR]

In this paper, with respect to how to express the complex fuzzy information, we proposed the concept of interval-valued linguistic intuitionistic fuzzy numbers (IVLIFNs), whose membership and non-membership are represented by interval-valued linguistic terms, then the Hamming distance is defined, further, we also proposed the interval-valued linguistic intuitionistic fuzzy entropy. Considering that the VIKOR method can achieve the maximum "group utility" and minimum of "individual regret", we extended the VIKOR method to process the interval-valued linguistic intuitionistic fuzzy information (IVLIFI), and proposed an extended VIKOR method for the multiple attribute decision making (MADM) problems with IVLIFI. And an illustrative example shows the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to develop a new ranking methodology for solving matrix games with intuitionistic fuzzy payoffs in terms of a value and ambiguity of triangular intuitionistic fuzzy numbers (TIFNs). In order to obtain an equilibrium solution of this matrix game, we construct two auxiliary TIFN programming models that are transformed into bi-objective linear programming models which are solved by a lexicographic methodology. The validity and applicability of the proposed methodology in this paper are illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

In some cases of using multi-criteria decision making methods for solving real-world problems ratings of alternatives cannot be determined precisely, and that is why they are expressed in the form of intervals. Therefore, the aim of this paper is to extend the MOORA method for solving decision making problems with interval data. By extending the ratio system part of MOORA method, an algorithm to determine the most preferable alternative among all possible alternatives, when performance ratings are given as intervals, is presented. Finally, an example is shown to highlight the proposed procedure, at the end of this paper. [ABSTRACT FROM AUTHOR]

There are several papers in the literature in which generalized fuzzy numbers are used for solving real life problems but to the best of our knowledge, till now no one has used generalized fuzzy numbers for solving the maximal flow problems. In this paper, the existing algorithm is modified to find fuzzy maximal flow between source and sink by representing all the parameters as generalized triangular fuzzy numbers. To illustrate the modified algorithm a numerical example is solved and the obtained results are compared with the existing results. If there is no uncertainty about the flow between source and sink then the proposed algorithm gives the same result as in crisp maximal flow problems. [ABSTRACT FROM AUTHOR]

In some practical situations the decision maker is interested in setting multi aspiration levels for objectives that may not be expressed in a specific manner. So in this paper, Atanassov's intuitionistic fuzzy transportation problem with multi-item, multi-objective function assuming multiple choices is considered. We have modeled multi-objective multi-choice multi-item Atanassov's intuitionistic fuzzy transportation problem (MMMIFTP), and its several special cases. Possibility, necessity and credibility measures for Atanassov's intuitionistic fuzzy numbers for the first time have been developed here. Solution methodology of those models using chance operator has been discussed. A real life example is presented to illustrate proposed models numerically and the results are compared. The optimal results are obtained by using three different soft computing techniques (i) Interactive satisfied method, (ii) Global criteria method and (iii) Goal programming method. [ABSTRACT FROM AUTHOR]

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, and the ranking of IFNs is a very difficult problem. In this paper ranking of triangular intuitionistic fuzzy numbers (TIFNs) is made by means of magnitude and applied to solve intuitionistic fuzzy linear programming problem. Numerical examples are examined to demonstrate the implementation of ranking method. [ABSTRACT FROM AUTHOR]

The paper proposes the concepts of an interval neutrosophic linguistic set (INLS) and an interval neutrosophic linguistic number (INLN) as a further generalization of the concepts of an intuitionistic linguistic set (ILS) and an intuitionistic linguistic fuzzy number (ILFN). Then, we introduce basic operational rules of INLNs and define the score function, accuracy function, and certainty function of an INLN. Furthermore, we propose an interval neutrosophic linguistic weighted arithmetic average (INLWAA) operator and an interval neutrosophic linguistic weighted geometric average (INLWGA) operator and investigate their properties, and then establish a decision-making method based on the INLWAA and INLWGA operators to handle multiple attribute decision-making problems with interval neutrosophic linguistic information. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach. [ABSTRACT FROM AUTHOR]

There are several methods in the literature to deal with the sensitivity analysis of fuzzy linear programming (FLP) problems. In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, a new method is proposed to handle the sensitivity analysis of that kind of FLP problems in which the elements of the coefficient matrix of the constraints are represented by real numbers, and the remaining parameters are represented by symmetric trapezoidal fuzzy numbers. To the best of our knowledge, till now there is no method in the literature to deal with the sensitivity analysis of such FLP problems without converting them to the crisp linear programming problems. The advantages of the proposed method over existing methods are discussed. To illustrate the approach a numerical example is examined by using the proposed method and the obtained results are discussed. The method is easy to understand and to apply for dealing with the sensitivity analysis of the same problems occurring in real life situations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making (MADM) problems for selecting the construction project in which attribute values take the form of interval-valued intuitionistic fuzzy information. Firstly, some operational laws of interval-valued intuitionistic fuzzy numbers and score function and accuracy function of interval-valued intuitionistic fuzzy numbers are introduced. Then, we utilize Einstein operations to develop the interval-valued intuitionistic fuzzy Einstein correlated averaging (IVIFECA) operator. The prominent characteristic of this operator is that they can not only consider the importance of the elements or their ordered positions, but also reflect the interactions phenomena among the decision making attributes or their ordered positions. We have applied the IVIFECA operator to multiple attribute decision making problems for selecting the construction project with interval-valued intuitionistic fuzzy information. Finally an illustrative example for involving a construction project selection has been given to show the developed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following problems: 1. 'Let à is a fuzzy number and x a real number. Then, what do we say about whether x is greater (smaller) than or equal to �'. 2. 'Let à and $\tilde{B}$ are two fuzzy numbers. Then, what do we say about whether $\tilde{B}$ is greater (smaller) than or equal to �'. [ABSTRACT FROM AUTHOR]

In todays advanced world, transportation and the movement of travelers and goods are very importance. In the present decade, with increases in the number of commuters and vehicles and also with the limitations on today's roads connectivity, implementing new technology in the field of traffic intelligence management has become mandatory. This paper attempts to solve the traffic congestion problem by presenting a mathematical model for controlling the time steps of traffic lights on crossings one of the major characteristics of this method is its universality. The proposed model describes a four-way intersection which uses eight traffic lights (the maximum number possible on such an intersection); these lights can be removed based on the intersection type to create a simpler or special-case model from the original one. Next with respect to the limitations of giving precise and constant values to parameters such as the arrival and departure ratio in the intersection, the maximum and minimum period the light stays green, the congestion on the roads and..., fuzzy models are used because of their tolerance of divergence from the expected constraints and using them our model more closely resembles real life situations and therefore is more practical. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for finding positive solution of fully fuzzy polynomial equations systems employing Gröbner bases benefits. First, the system of fully fuzzy polynomial equations is converted to an equivalent crisp polynomial equations system. Then, using Gröbner basis properties a criteria for determining existence and finding positive fuzzy solutions of original system is introduced. The big advantage of the proposed method lies in the fact that it attains all positive fuzzy solutions of problem at a time. Finally, some applied numerical examples are illustrated to demonstrate the proficiency of the given approach. [ABSTRACT FROM AUTHOR]

Linear programming (LP) is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency. Although conventional LP models require precise data, managers and decision makers dealing with real-world optimization problems often do not have access to exact values. Fuzzy sets have been used in the fuzzy LP (FLP) problems to deal with the imprecise data in the decision variables, objective function and/or the constraints. The imprecisions in the FLP problems could be related to (1) the decision variables; (2) the coefficients of the decision variables in the objective function; (3) the coefficients of the decision variables in the constraints; (4) the right-hand-side of the constraints; or (5) all of these parameters. In this paper, we develop a new stepwise FLP model where fuzzy numbers are considered for the coefficients of the decision variables in the objective function, the coefficients of the decision variables in the constraints and the right-hand-side of the constraints. In the first step, we use the possibility and necessity relations for fuzzy constraints without considering the fuzzy objective function. In the subsequent step, we extend our method to the fuzzy objective function. We use two numerical examples from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and the computational efficiency of the procedures and algorithms. [ABSTRACT FROM AUTHOR]

This paper proposed a new and simple solution approach to solve a general fuzzy system of linear equations. In the original system, the coefficient matrix is considered as real crisp whereas the unknown variable vector and right hand side vector are considered as fuzzy. Here, three different types of fuzzy numbers viz. triangular, trapezoidal and Gaussian fuzzy numbers are taken into consideration. First the system is solved in term of fuzzy centre then this solution is used with width to get the final solution of the original system. Solution theorems are stated and proved related to the proposed method. The method is also used to solve some known example problems found in the references and the results are compared to show the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the bounded dual simplex algorithm for solving minimum cost flow problem with fuzzy cost, which its aim is to find the least fuzzy cost of a commodity through a capacitated network in order to satisfy demands at certain nodes using available supplies at other nodes. This algorithm begins with dual feasibility and iterates between dual and primal problems until optimality is achieved. Here, we use the linear ranking functions to compare fuzzy numbers. By using the proposed method the optimal solution of minimum cost flow problems with fuzzy costs can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed. [ABSTRACT FROM AUTHOR]

To the best of our knowledge, there is no method in the literature for solving such fuzzy transportation problems in which the different cost parameters are represented by different type of LR flat fuzzy numbers. In this paper, a new method is proposed for solving similar type of fuzzy transportation problems. To illustrate the proposed method and also to show the advantages of the proposed method some fuzzy transportation problems which can not be solved by using any of the existing method are solved. Also, it is shown that the fuzzy transportation problems which can be solved by the existing methods can also be solved by using the proposed method and the same results are obtained. [ABSTRACT FROM AUTHOR]