The importance of fuzzy numbers to express uncertainty in certain applications, concerned with decision making, is observed in a large number of problems of different kinds. In Decision making problems, the best of available alternatives is chosen to the possible extent. In the process of ordering the alternatives, ranking of fuzzy numbers plays a key role. A large volume of ranking methods, based on different features, have been available in this domain. Owing to the complicated nature of fuzzy numbers, the so far introduced methods suffered setbacks or posed difficulties or showed drawbacks in one context or other. In addition, some methods are lengthy and complicated to apply on concerned problems. In this article, a new ranking procedure based on defuzzification, stemmed from the concepts of geometric mean and height of a fuzzy number, is proposed. Finally, numerical comparisons are made with other existing procedures for testing and validation of proposed method with the support of some standard numerical examples.

Abstract. In this paper, the general solution of the homogeneous matrix difference system is constructed in terms of two fundamental matrix solutions. The general solution of the inhomogeneous matrix difference system is established by the variation of parameters formula. A unique solution of the twopoint boundary value problem associated with the matrix difference system is constructed by applying the QR-algorithm and the Bartels-Stewart algorithm.

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Ternary semihyperring is an algebraic structure with one binary hyper operation and ternary multiplication. In this paper, we give some properties of hyperideals in ternary semihyperring. We introduce the notion of simple, (0-)simple ternary semihyperring and characterize the minimality and maximality of hyperideals in ternary semihyperring. The relationship between them is investigated in ternary semihyperring extending and generalizing the analogous results for ternary semirings.

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