In this paper, we introduce a new method to solve Interval-Valued Transportation Problem (IVTP) to deal with those problems of transportation wherein the information available is imprecise. First, a newly proposed fuzzification method is used to convert the IVTP to octagonal fuzzy transportation problem and then with the help of ranking function proposed in this paper, the fuzzy transportation problem is converted into crisp transportation problem. Lastly, Initial Basic Feasible Solution (IBFS) of this problem is obtained using Vogel’s Approximation Method and the solution is improved using Modified Distribution (MODI) method. A numerical example with interval data is solved using the proposed algorithm to make comparison of the solution with some other methods. Also, a numerical example with parameters in the form of octagonal fuzzy numbers is illustrated to compare the effectiveness of the proposed ranking technique. The proposed fuzzification and ranking technique can be used in the other fields of decision making dealing with the data in the same form as considered in this paper.

In real world, we come across transportation problems, wherein the associated data involves some sort of uncertainty, which at times can be most appropriately represented in the form of interval numbers. Since ordering of intervals involves complexity, hence, we have used fuzzy concept to solve Interval-Valued Transportation Problems (IVTPs). We have proposed new fuzzification methods for conversion of interval number to trapezoidal, pentagonal, hexagonal and heptagonal fuzzy numbers, thereby converting IVTP to Fuzzy Transportation Problem (FTP). Further, we have proposed new ranking functions for conversion of these fuzzy numbers to crisp numbers, which can also be used in other fields of decision making. The crisp-valued transportation problem is then solved using Vogel’s Approximation Method followed by Modified Distribution method. Numerical illustration for the proposed algorithm is given in a later section. The solutions obtained for these examples are used to approximate the solutions for octagonal, nonagonal and decagonal FTPs corresponding to IVTP, using Newton’s Polynomial. On the basis of these solutions, ordering of effectiveness of various types of fuzzy numbers in solving IVTP is done. Lastly, comparison is made between the optimal solutions obtained by various methods. The proposed method can be applied to industrial transportation problems in which the difference between the actual and the proposed demand and supply is quite significant.

Due to information transmission mistakes as well as arisen errors while processing data in surveying and monitoring state information of any system, uncertain and incomplete information may be produced. Based on these points, present paper extends our study for the development of a vague scheme for fault tree analysis of any general system. The functioning of the developed vague scheme is demonstrated for diagnosis of cannula fault in power transformers using vague fault tree analysis (VFTA) and beta distribution for failure possibility estimation. By using these techniques we have proposed herein, the extension of Pandey et al., in 2011 to define the continuous attribute values transformed into the vague numbers to give a realistic estimate of failure possibility of a basic event in VFTA. Further, it explains a new approach based on Euclidean distance between vague numbers, to rank the basic events in accordance with their Vague Importance Index (VII). 852 M. K. Sharma et al.

In this article, we propose a method based on a new ranking technique to find optimal solution for a pentagonal fuzzy transportation problem. Firstly, the proposed ranking method which is based on the centroid concept is applied. This transforms the pentagonal fuzzy transportation problem to crisp transportation problem and then the proposed algorithm is applied to find optimal solution of the problem in crisp form. Also, a new method to find initial basic feasible solution (IBFS) of crisp valued transportation problems is introduced in the paper. Further, we give two numerical illustrations for the newly proposed algorithm and compare the solution obtained with the solutions of existing methods. The proposed method can easily be understood and applied to real life transportation problems. Moreover, the proposed ranking method can be used to solve various other fuzzy problems of operations research.

World is full of uncertainties. In decision-making problems, uncertainty occurs in many forms such as fuzzy, rough, interval, soft and researchers use data in one of these forms for presenting uncontrollable factors. This paper aims to develop an effective method for solving bi-matrix game problem with interval payoffs assuming that the players know the upper and lower bounds on payoffs. First, bi-matrix game model with interval payoffs is considered. This model is then transformed to another model with fuzzy payoffs. Finally, ranking approach is used to convert the model to crisp-valued bi-matrix game model. Further, due to correspondence between games and programming problem, the Nash equilibrium of interval bimatrix game is obtained by solving a deterministic nonlinear programming problem with nonlinear objective and linear constraints. Finally, a real-life problem of marketing management is solved to validate, approve and illustrate the effectiveness of the proposed model and its solution method. The results derived are compared with some previously defined methods and conclusions are drawn further.