A New Method for Solving Generalized Trapezoidal Fuzzy Inventory Model with Shortage Under Space Constraint

In this paper, an EOQ(economic order quantity) model with shortage and space constraint has been analyzed in a fuzzy environment. The costs namely holding cost, shortage cost, setup cost, the ware house capacity and the objective are usually deterministic in nature. In this paper these have been considered to be generalized trapezoidal fuzzy numbers which are more realistic in nature. The ranking method proposed by Amit Kumar [1,2] has been used for ranking the fuzzy numbers. The fuzzy inventory problem has been transformed in to crisp inventory problem. For this EOQ and minimum total cost have been calculated. This method has been illustrated by means of numerical example

A multidimensional approach to rank fuzzy numbers based on the concept of magnitude

Ranking fuzzy numbers have become of growing importance in recent years, especially as decision-making is increasingly performed under greater uncertainty. In this paper, we extend the concept of magnitude to rank fuzzy numbers to a more general definition to increase in flexibility and generality. More precisely, we propose a multidimensional approach to rank fuzzy numbers considering alternative magnitude definitions with three novel features: multidimensionality, normalization, and a ranking based on a parametric distance function. A multidimensional magnitude definition allows us to consider multiple attributes to represent and rank fuzzy numbers. Normalization prevents meaningless comparison among attributes due to scaling problems, and the use of the parametric Minkowski distance function becomes a more general and flexible ranking approach. The main contribution of our multidimensional approach is the representation of a fuzzy number as a point in a $n$-dimensional normalized space of attributes in which the distance to the origin is the magnitude value. We illustrate our methodology and provide further insights into different normalization approaches and parameters through several numerical examples. Finally, we describe an application of our ranking approach to a multicriteria decision-making problem within an economic context in which the main goal is to rank a set of credit applicants considering different financial ratios used as evaluation criteria

An improvised similarity measure for generalized fuzzy numbers

Similarity measure between two fuzzy sets is an important tool for comparing various characteristics of the fuzzy sets. It is a preferred approach as compared to distance methods as the defuzzification process in obtaining the distance between fuzzy sets will incur loss of information. Many similarity measures have been introduced but most of them are not capable to discriminate certain type of fuzzy numbers. In this paper, an improvised similarity measure for generalized fuzzy numbers that incorporate several essential features is proposed. The features under consideration are geometric mean averaging, Hausdorff distance, distance between elements, distance between center of gravity and the Jaccard index. The new similarity measure is validated using some benchmark sample sets. The proposed similarity measure is found to be consistent with other existing methods with an advantage of able to solve some discriminant problems that other methods cannot. Analysis of the advantages of the improvised similarity measure is presented and discussed. The proposed similarity measure can be incorporated in decision making procedure with fuzzy environment for ranking purposes

Momentum Ranking Function of Z-Numbers and its Application to Game Theory

بعد أن قدم زاده مفهوم ارقام - z أبدى العلماء في مختلف المجالات اهتماما كبيرا بتطبيق هذا المفهوم على مختلف التطبيقات. في تطبيقات أرقام - z ، لمقارنة رقمين z ، يعد إجراء الترتيب ضروريا. في حين تم بالفعل اقتراح عدد قليل من وظائف الترتيب في الأدبيات ، هناك حاجة لتطوير بعض وظائف الترتيب الجيدة. في هذه الورقة ، تم اقتراح دالة ترتيب جديدة لأرقام - z  "وظيفة ترتيب الزخم" (MRF). أيضا ، تم النظر في المشكلات النظرية للعبة حيث تكون عناصر مصفوفة العائد هي أرقام - z وتم توضيح تطبيق وظيفة ترتيب الزخم في مثل هذه المشكلات.After Zadeh introduced the concept of z-number scientists in various fields have shown keen interest in applying this concept in various applications. In applications of z-numbers, to compare two z-numbers, a ranking procedure is essential.  While a few ranking functions have been already proposed in the literature there is a need to evolve some more good ranking functions.  In this paper, a novel ranking function for z-numbers is proposed- "the Momentum Ranking Function"(MRF). Also, game theoretic problems where the payoff matrix elements are z-numbers are considered and the application of the momentum ranking function in such problems is demonstrated