Search

To the best of author's knowledge, only three approaches are proposed in the literature to solve fully fuzzy linear fractional transportation problems. (Linear fractional transportation problems in which each known parameter is represented by a fuzzy number.) In this paper, it is pointed out that it is inappropriate to use any of these existing approaches as some mathematical incorrect assumptions are considered in these existing approaches. Also, a new approach (named as Mehar approach) is proposed to solve fully fuzzy linear fractional transportation problems. Furthermore, an exact fuzzy optimal solution of an existing fully fuzzy linear fractional transportation problem is obtained by the proposed Mehar approach. [ABSTRACT FROM AUTHOR]

Khatter (Soft Comput 24:6847–16,867, 2020) pointed out that although several approaches are proposed in the literature to solve single-valued neutrosophic linear programming problems (SVNLPPS) (linear programming problems in which all the parameters except decision variables are either represented by single-valued triangular neutrosophic numbers (SVTNNS) or single-valued trapezoidal neutrosophic numbers (SVTrNNS)). However, all the methods for comparing single-valued neutrosophic numbers (SVNNS), used in existing approaches, are independent from the attitude of the decision-maker towards the risk. To fill this gap, Khatter (2020), firstly, proposed a method for comparing two SVNNS by considering the attitude of the decision-maker towards the risk. Then, using the proposed comparing method, Khatter (2020) proposed an approach to solve SVNLPPS. In this paper, it is pointed out that a mathematical incorrect result is considered in Khatter's approach. Hence, it is inappropriate to use Khatter's approach. Also, it is pointed out that some mathematical incorrect results are considered in other existing approaches for solving SVNLPPS. Hence, it is inappropriate to use other existing approaches for solving SVNLPPS. Furthermore, to resolve the inappropriateness of Khatter's approach and other existing approaches, a new approach (named as Mehar approach) is proposed to solve SVNLPPS. Finally, correct optimal solution of some existing SVNLPPS is obtained by the proposed Mehar approach. [ABSTRACT FROM AUTHOR]

In this research work, a novel approach is proposed by introducing numerous scaling factors in the original equilibrium optimization technique which can be named as modified equilibrium optimization (MEO) algorithm and is utilized for the load frequency control (LFC) of two-area hybrid distributed power system. The introduced MEO meta-heuristic algorithm is compared with a standard EO algorithm and other meta-heuristic algorithms for different standard benchmark test functions. Furthermore, the genuine utilization of the MEO algorithm is tried by designing a multi-stage PID (MS-PID) controller for frequency regulation of the power system with distributed energy sources including renewable sources. The supremacy of the reinforced MEO methodology-based MS-PID controller for enhanced frequency regulation is presented and its outcomes are compared with the EO-tuned PID and MS-PID. From the performance comparison, it is recognized that the MEO-based MS-PID controller is more efficacious. [ABSTRACT FROM AUTHOR]

Mahmoodirad et al. (Soft Comput, 2018. 10.1007/s00500-018-3115-z) proposed an approach for solving fully intuitionistic fuzzy transportation problems (FIFTPs) (transportation problems in which each parameter is represented as a triangular intuitionistic fuzzy number). In this approach, firstly, an unbalanced fully intuitionistic fuzzy transportation problem (FIFTP) is transformed into a balanced FIFTP, and then the intuitionistic fuzzy (IF) optimal solution of the transformed balanced FIFTP is obtained. In this paper, it is shown that Mahmoodirad et al.'s approach fails to transform an unbalanced FIFTP and hence, Mahmoodirad et al.'s approach fails to find the IF optimal solution of unbalanced FIFTPs. It is obvious that to overcome this limitation of Mahmoodirad et al.'s approach, there is need to propose a method to transform an unbalanced FIFTP into a balanced FIFTP. Therefore, in this paper, a new method (named as JMD method) is proposed to transform an unbalanced FIFTP into a balanced FIFTP. [ABSTRACT FROM AUTHOR]

To the best of our knowledge, only the existing approach (Rabiei et al. in Soft Comput 18(10), 2043–2059, 2014) has been proposed to construct a full interval-valued fuzzy linear regression model [a regression model when the observation of the response, independent variables as well as the regression coefficients are triangular interval-valued fuzzy numbers (TIVFNs)]. However, after a deep study, it is observed that a mathematical incorrect assumption has been considered in this approach. Furthermore, it is observed that to resolve this mathematical incorrect assumption, there is a need to propose the multiplication of an unrestricted TIVFN (regression coefficient) with a restricted TIVFN [observed values of independent variable(s)]. Keeping the same in mind, in this paper, the same type of multiplication is proposed, and with the help of proposed multiplication, a modified approach is proposed to construct a full interval-valued fuzzy regression model. Also, the modified results of some existing real-life problems are obtained with the help of the modified approach. [ABSTRACT FROM AUTHOR]

Seikh and Dutta (Soft Comput 26: 921–936, 2022) claimed that there does not exist any approach to solve single-valued trapezoidal neutrosophic (SVTrN) matrix games (matrix games in which each payoff is represented by a SVTrN number). To fill this gap, Seikh and Dutta, firstly, proposed SVTrN non-linear programming problems (NLPPs) corresponding to Player-I and Player-II. Then, Seikh and Dutta proposed two different approaches to transform the proposed SVTrN NLPPs into crisp linear programming problems (CLPPs). Finally, Seikh and Dutta claimed that an optimal solution of the transformed CLPPs also represents an optimal solution of SVTrN NLPPs. Brikaa (Soft Comput 26: 9137–9139, 2022) pointed out that a mathematically incorrect result is considered in Seikh and Dutta's first approach to transform SVTrN NLPPs into CLPPs. Therefore, the transformed CLPPs are not equivalent to SVTrN NLPPs. Hence, it is mathematically incorrect to assume that an optimal solution of the transformed CLPPs also represents an optimal solution of SVTrN NLPPs. Brikaa also proposed an approach to transform the SVTrN NLPPs into CLPPs. In this paper, it is pointed out that on solving the CLPPs, obtained by Brikaa's approach corresponding to SVTrN NLPPs of Player-I and Player-II, different optimal value is obtained. Also, it is pointed out that on solving the CLPPs, obtained by Seikh and Dutta's second approach corresponding to SVTrN NLPPs of Player-I and Player-II, a different optimal value is obtained. However, in the actual case, the obtained optimal value should be the same as in the literature; it is proved that the CLPPs corresponding to Player-I and Player-II represent a primal–dual pair. This indicates that neither the CLPPs, obtained by Brikaa's approach nor the CLPPs, obtained by Seikh and Dutta's second approach, are equivalent to the SVTrN NLPPs of Player-I and Player-II. Hence, it is inappropriate to use the CLPPs, obtained by Brikaa's approach as well as Seikh and Dutta's second approach to find an optimal solution for the SVTrN NLPPs of Player-I and Player-II. Also, Brikaa's approach as well as Seikh and Dutta's second approach is modified to transform SVTrN NLPPs into their equivalent CLPPs. Furthermore, it is proved that the CLPPs corresponding to SVTrN NLPPs of Player-I and Player-II, obtained by the proposed modified approaches, represent a primal–dual pair. Finally, the correct result of a SVTrN matrix game, considered by Seikh and Dutta to illustrate their approaches, is obtained by the proposed modified approaches. [ABSTRACT FROM AUTHOR]

In this paper, we discuss some new numerical methods to solve a fully fuzzy linear system (FFLS) with triangular fuzzy numbers of the form $$ ( {m,\alpha ,\beta }) $$. Almost every existing method that intends to solve a FFLS confines the coefficient matrix and the solutions to be non-negative fuzzy numbers. The main intent of the proposed methods is to remove these restrictions and widen the scope of fuzzy linear systems in scientific applications. The methods are illustrated with the help of numerical examples and are conceptually easy to understand and apply in real life situations. [ABSTRACT FROM AUTHOR]

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Syst Appl 36:6833-6842, ) is incorrect. The main aim of this paper is to propose a new approach for the ranking of L- R type generalized fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as RM approach. The main advantage of the proposed approach is that it provides the correct ordering of generalized and normal fuzzy numbers and it is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets Syst 118:375-385, ). [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]

Amin et al. (Soft Comput 23:5353–5366, 2019), firstly, proposed a trapezoidal cubic hesitant fuzzy weighted geometric (TrCHFWG) aggregation operator for aggregating trapezoidal cubic hesitant fuzzy sets (TrCHFSs). Then, using the proposed aggregation operator, Amin et al. proposed TOPSIS (Technique for order preference by similarity to ideal solution) method for solving multi-attribute group decision making problems under TrCHFS environment. In this note, it is pointed out that Amin et al.'s aggregation operator is not valid as the monotonicity property is not satisfied for Amin et al.'s TrCHFWG aggregation operator. Hence, it is inappropriate to use Amin et al.'s TOPSIS method. Also, it is pointed out that to resolve the inappropriateness of Amin et al.'s TrCHFWG aggregation operator as well as Amin et al.'s TOPSIS method is an open challenging research problem. [ABSTRACT FROM AUTHOR]