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Kumar and Garg (Applied Intelligence, 2017, ) pointed out the limitations of some existing methods for solving intuitionistic fuzzy multi-attribute decision-making (MADM) problems. Also, to overcome the limitations, Kumar and Garg proposed a connection number (CN) based method for solving intuitionistic fuzzy MADM problems. In this paper, it is shown that the ranking method, used in Step 5 of Kumar and Garg's method for comparing connection numbers (CNs), fails to compare two distinct CNs. Hence, Kumar and Garg's method fails to rank the alternatives of intuitionistic fuzzy MADM problems. Furthermore, to overcome the limitation of Kumar and Garg's method, a new ranking method (named as Mehar ranking method) is proposed for comparing CNs. [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]

To the best of our knowledge, there is only one approach for solving neutrosophic cost minimization transportation problems. Since neutrosophic transportation problems are a new area of research, other researchers may be attracted to extend this approach for solving other types of neutrosophic transportation problems like neutrosophic solid transportation problems, neutrosophic time minimization transportation problems, neutrosophic transshipment problems, and so on. However, after a deep study of the existing approach, it is noticed that a mathematical incorrect assumption has been used in these existing approaches; therefore there is a need to modify these existing approaches. Keeping the same in mind, in this paper, the existing approach is modified. Furthermore, the exact results of some existing transportation problems are obtained by the modified approach. [ABSTRACT FROM AUTHOR]

Several authors have proposed different methods for solving fuzzy minimum cost flow (MCF) problems. In this paper, some single and multi-objective fuzzy MCF problems are chosen which cannot be solved by using any of the existing methods and a new method is proposed for solving such type of problems. The main advantage of the proposed method over existing methods is that the fuzzy MCF problems which can be solved by using the existing methods can also be solved by the proposed method. But, there exist several fuzzy MCF problems which can be solved only by using the proposed method i.e., it is not possible to solve these problems by using the existing methods. To illustrate the proposed method and also to show the advantages of the proposed method over existing methods some single and multi-objective fuzzy MCF problems which cannot be solved by using the existing methods are solved by using the proposed method and the obtained results are discussed. [ABSTRACT FROM AUTHOR]

Chen and Tsai [Eur J Oper Res 212:386-397, ] proposed a method to find the lower and upper bound of α-cut of the minimum total fuzzy crash cost and optimal fuzzy activity times of the project networks in fuzzy environments and used the values of lower and upper bounds, corresponding to different values of α, to obtain the minimum total fuzzy crash cost and the optimal fuzzy activity times. In this paper, it is pointed out that in the α-cut of optimal fuzzy activity times, obtained by using the existing method, the lower bound is not necessarily less than the upper bound. Also, some modifications in the existing method are suggested so that in the α-cut of optimal fuzzy activity time, the lower bound is always less than or equal to upper bound. [ABSTRACT FROM AUTHOR]

In the literatures, the sensitivity analysis of fuzzy transportation problems has not been explored like other mathematical programming problems. In this paper, a new method is proposed for the same. To illustrate the proposed method a numerical example is solved by using the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: To the best of our knowledge, there is no method in literature for solving such fully fuzzy linear programming (FLP) problems in which some or all the parameters are represented by unrestricted L-R flat fuzzy numbers. Also, to propose such a method, there is need to find the product of unrestricted L-R flat fuzzy numbers. However, there is no method in the literature to find the product of unrestricted L-R flat fuzzy numbers. In this paper, firstly the product of unrestricted L-R flat fuzzy numbers is proposed and then with the help of proposed product, a new method (named as Mehar’s method) is proposed for solving fully FLP problems. It is also shown that the fully FLP problems which can be solved by the existing methods can also be solved by the Mehar’s method. However, such fully FLP problems in which some or all the parameters are represented by unrestricted L-R flat fuzzy numbers can be solved by Mehar’s method but can not be solved by any of the existing methods. [Copyright &y& Elsevier]

Abstract: Ghatee and Hashemi [M. Ghatee, S.M. Hashemi, Ranking function-based solutions of fully fuzzified minimal cost flow problem, Inform. Sci. 177 (2007) 4271–4294] transformed the fuzzy linear programming formulation of fully fuzzy minimal cost flow (FFMCF) problems into crisp linear programming formulation and used it to find the fuzzy optimal solution of balanced FFMCF problems. In this paper, it is pointed out that the method for transforming the fuzzy linear programming formulation into crisp linear programming formulation, used by Ghatee and Hashemi, is not appropriate and a new method is proposed to find the fuzzy optimal solution of multi-objective FFMCF problems. The proposed method can also be used to find the fuzzy optimal solution of single-objective FFMCF problems. To show the application of proposed method in real life problems an existing real life FFMCF problem is solved. [Copyright &y& Elsevier]

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]

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]

Shakeel et al. (Soft Comput 24: 1585–1597, 2020) proposed the concept of a Pythagorean uncertain linguistic hesitant fuzzy set (PULHFS), some arithmetic operations of Pythagorean uncertain linguistic hesitant fuzzy sets (PULHFSs), an approach for comparing PULHFSs and a Pythagorean uncertain linguistic hesitant fuzzy weighted averaging (PULHFWA) operator as well as it extensions. Also, using the proposed comparing approach and the proposed aggregation operators, Shakeel et al. proposed a method for solving multi-attribute group decision making (MAGDM) problems. In future other researchers may use Shakeel et al.'s work in their research work. However, it is observed that the approach for comparing PULHFSs and aggregation operators, proposed by Shakeel et al. (Soft Comput 24: 1585–1597, 2020), are not appropriate. Hence, the method for solving MAGDM problems, proposed by Shakeel et al., is also not appropriate. The aim of this note is to make the researchers aware of the inappropriateness of Shakeel et al. work. Furthermore, point out that to resolve the inappropriateness of Shakeel et al. work (Soft Comput 24: 1585–1597, 2020) is a challenging open research problem. [ABSTRACT FROM AUTHOR]

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = ( V , E ) , a cost function c : V → Z + , a partition P 1 , … , P r of the edge set E , and a parameter k i for each partition P i . The objective is to find a minimum cost set of vertices which cover at least k i edges from the partition P i . We call this the Partition-VC problem. In this paper, we give matching upper and lower bound on the approximability of this problem. Our algorithm is based on a novel LP relaxation for this problem. This LP relaxation is obtained by adding knapsack cover inequalities to a natural LP relaxation of the problem. We show that this LP has integrality gap of O ( log ⁡ r ) , where r is the number of sets in the partition of the edge set. We also extend our result to more general settings. For example we consider a problem where additionally edges have profits, and we would like to pick a minimum cost set of vertices which cover edges of total profit at least Π i for each partition P i . We call this the Knapsack Partition Vertex Cover problem. We give an O ( log ⁡ r ) approximation algorithm for this problem as well. [ABSTRACT FROM AUTHOR]

In this paper, we consider the fully fuzzy unbalanced transportation problem in which the total availability/production is more than the total demand and propose a method to solve it. Such problems are usually solved by adding a dummy destination. Since the dummy destination has no existence in reality, the excess availability is not transported at all and is held back at one or more origins. The method proposed in this paper gives the additional information that to which of the destination(s) the excess availability be transported for future demand at minimum cost. The advantage of the proposed method over the existing method is that the fuzzy optimal solution obtained does not involve the dummy destination. The method has been illustrated with the help of an example. [ABSTRACT FROM AUTHOR]

Simultaneous visualization and concentration quantification of molecules in biological tissue is an important though challenging goal. The advantages of fluorescence lifetime imaging microscopy (FLIM) for visualization, and electron paramagnetic resonance (EPR) spectroscopy for quantification are complementary. Their combination in a multiplexed approach promises a successful but ambitious strategy because of spin label‐mediated fluorescence quenching. Here, we solved this problem and present the molecular design of a dual label (DL) compound comprising a highly fluorescent dye together with an EPR spin probe, which also renders the fluorescence lifetime to be concentration sensitive. The DL can easily be coupled to the biomolecule of choice, enabling in vivo and in vitro applications. This novel approach paves the way for elegant studies ranging from fundamental biological investigations to preclinical drug research, as shown in proof‐of‐principle penetration experiments in human skin ex vivo. [ABSTRACT FROM AUTHOR]

Simultaneous visualization and concentration quantification of molecules in biological tissue is an important though challenging goal. The advantages of fluorescence lifetime imaging microscopy (FLIM) for visualization, and electron paramagnetic resonance (EPR) spectroscopy for quantification are complementary. Their combination in a multiplexed approach promises a successful but ambitious strategy because of spin label‐mediated fluorescence quenching. Here, we solved this problem and present the molecular design of a dual label (DL) compound comprising a highly fluorescent dye together with an EPR spin probe, which also renders the fluorescence lifetime to be concentration sensitive. The DL can easily be coupled to the biomolecule of choice, enabling in vivo and in vitro applications. This novel approach paves the way for elegant studies ranging from fundamental biological investigations to preclinical drug research, as shown in proof‐of‐principle penetration experiments in human skin ex vivo. [ABSTRACT FROM AUTHOR]