Abstract We define $$2n+1$$ 2 n + 1 and 2 n fuzzy numbers, which generalize triangular trapezoidal respectively. Then, we extend the preference relation relative to rank numbers. When data is representable in terms of number, FMCDM (fuz...

In this paper, we propose a novel approach for constructing a preference fuzzy distance measure. For this purpose, we propose a new and effective preference ordering based on the Abbasbandy and Hajjari’s approach [2].

We studied here on some simple examples the interaction between valuation family, parameters and ranking result. The ranking method studied is based upon the idea of associating with a fuzzy number a scalar value, its valuation, and using this valuation to compare and order fuzzy numbers. The valuation method considered was introduced initially by the Yager and Filev. This valuation consists in...

In this study the author discusses the problem of defuzzification by minimizing the weighted distance between two fuzzy quantities. Also, this study obtains the nearest point with respect to a fuzzy number and shows that this point is unique relative to the weighted distance. By utilizing this point, a method is presented for effectively ranking fuzzy numbers and their images to overcome the de...

This chapter describes different methods for comparing and ordering fuzzy numbers. Theoretically, fuzzy numbers can only be partially ordered, and hence cannot be compared. However, in practical applications, such as decision making, scheduling, market analysis or optimisation with fuzzy uncertainties, the comparison of fuzzy numbers becomes crucial. Theoretically, fuzzy numbers can only be par...

This paper presents a new approach to compare fuzzy numbers using α-distance. Initially, the metric distance on the interval numbers based on the convex hull of the endpoints is proposed and it is extended to fuzzy numbers. All the properties of the α-distance are proved in details. Finally, the ranking of fuzzy numbers by the α-distance is discussed. In addition, the proposed method is compare...

The purpose of this research paper was to propose a method which can be utilized to determine the different types of performance measures on the basis of the crisp values for the fuzzy queuing model which has an unreliable server and where the rate of arrival, the rate of service, the rate of breakdown and the rate of repair are all expressed as the fuzzy numbers. In this case the inter arrival...

The critical path problem is a classical and important network optimization problem appearing in many applications, especially in planning and controlling the complex projects. However the result of classical critical path method computation cannot properly match the real-world problem. This gives rise to fuzzy environment and hence we have fuzzy critical path method. In this paper, two differe...

Abstract. In this paper, a new procedure for project scheduling called 'fuzzy cash flow weight' and 'fuzzy discounted cash flow weight' is studied with the aid of generalized trapezoidal fuzzy numbers. A new ranking procedure namely 'SD of PILOT' (Shortest Distance of the Point of Intersection of Legs of Trapezium) is proposed to find out the output of the above said notion. Relevant arithmetic...