In this work, we propose an approach for computing the compromised solution of an LR fuzzy linear system by using of a ranking function when the coefficient matrix is a crisp m´n matrix. To do this, we use expected interval to find an LR fuzzy vector, X~, such that the vector Â(AX~) has the least distance from Â(b~) in 1-norm and the 1-cut of X~ satisfies the crisp linear system AX=b. Then, we solve the constrained LP-problem by using LINGO 11 software package and obtain optimal fuzzy number solution. Finally, we illustrate the proposed method by solving two numerical examples.

Background and objective: In recent decades, universities have been investing more in collecting and reproducing knowledge. Competition for achieving such a situation has created new systems for ranking and evaluating universities. The main purpose of this research is to provide a good model for ranking universities and higher education institutions throughout the country. Methods and Materials: In this research, the results of theoretical research were first analyzed and then the data from semi-structured interviews were analyzed through the method of analysis. The encoding of strong relationships between concepts was accomplished by revising the text of the interview and reviewing the code, and ultimately the final components were extracted. At the end of this stage, the selected components were matched according to the model obtained from the theoretical framework and the background and, finally, the final values of ranking of universities and higher education centers were obtained. Results: The indexes obtained in this research for the ranking of universities and higher education institutions included: educational function, research performance, university magnitude, job creation and entrepreneurship, and academic rank and scientific and international reputation Conclusion: Based on the results, the calculated fit of the proposed model for ranking universities is suitable with experimental data and has favorable conditions.

Transport industry is one of the important and economic elements of each region. Because، in addition to that it is considered as an important and fundamental part، it affects many other activities of the societies and provides the possibility of appropriate productivity of potential capacity of the country. It is important that which province has more capacities in this industry and may help the managers in making better decisions to allocate resources and facilities and develop planning. Despite the importance of this industry، there has been little study about ranking the provinces in this industry. The aim of this research is to evaluate and rank the provinces in the field of transport. For this purpose، firstly، transport industry is divided to four parts of air transport، sea transport، freight transport، and passenger transport. For each part، appropriate indexes have been determined according to the library studies and interview with experts، and data are derived from valid statistical references. Then، indexes weights have been calculated by using Shannon Entropy in each part and then، with regard to the operation in each of the four parts، the provinces were ranked by using Taguchi Loss Function. This research is a descriptive analytical one، research domain is all provinces of the country، and the time period is the year 2012. According the results، in passenger transport، Semnan Province received the first rank and Yazd Province received the last rank. In freight and air transports، Tehran Province won the first rank and Golestan and Esfahan Provinces respectively had the last rank in these two parts. In sea transport، Hormozgan Province was in the first rank and Khuzestan Province in the last one.

Jaccard index similarity measure, which applies the extension principle approach to obtain fuzzy maximum and fuzzy minimum, has been proposed in ranking fuzzy numbers. However, the extension principle used is only applicable to normal fuzzy numbers and, therefore, fails to rank non-normal ones. Apart from that, the extension principle does not preserve the type of membership function of fuzzy numbers and also involves laborious mathematical operations. In this paper, a simple vertex fuzzy arithmetic operation, namely the function principle is applied. This paper also proposes the degree of optimism concept in aggregating the fuzzy evidence. The method is capable to rank both normal and non-normal fuzzy numbers in a simpler manner from all decision makers’ perspectives.

Jahanshahloo has suggested a method for the solving linear programming problems with zero-one variables. In this paper we formulate fully fuzzy linear programming problems with zero-one variables and a method for solving these problems is presented using the ranking function and also the branch and bound method along with an example is presented.