Approximate Membership Function Shapes of Solutions to Intuitionistic Fuzzy Transportation Problems

In this paper, proposing a mathematical model with disjunctive constraint system, and providing approximate membership function shapes to the optimal values of the decision variables, we improve the solution approach to transportation problems with trapezoidal fuzzy parameters. We further extend the approach to solving transportation problems with intuitionistic fuzzy parameters; and compare the membership function shapes of the fuzzy solutions obtained by our approach to the fuzzy solutions to full fuzzy transportation problems yielded by approaches found in the literature

NEUTROSOPHIC MULTI-OBJECTIVE LINEAR PROGRAMMING

For modeling imprecise and indeterminate data for multi-objective decision making, two different methods: neutrosophic multi-objective linear/non-linear programming neutrosophic goal programming, which have been very recently proposed in the literatuire. In many economic problems, the well-known probabilities or fuzzy solutions procedures are not suitable because they cannot deal the situation when indeterminacy inherently involves in the problem. In this case we propose a new concept in optimization problem under uncertainty and indeterminacy. It is an extension of fuzzy and intuitionistic fuzzy optimization in which the degrees of indeterminacy and falsity (rejection) of objectives and constraints are simultaneously considered together with the degrees of truth membership (satisfaction/acceptance). The drawbacks of the existing neutrosophic optimization models have been presented and new framework of multi-objective optimization in neutrosophic environment has been proposed. The essence of the proposed approach is that it is capable of dealing with indeterminacy and falsity simultaneously

An Efficient Algorithm for Fuzzy Linear Fractional Programming Problems via Ranking Function

في العديد من التطبيقات مثل الإنتاج ، يعد التخطيط لصانع القرار أمرًا مهمًا في تحسين دالة الهدف الضبابية للمسالة  حيث تحتوي على نسبة دالتين ضبابيتين ، والتي يمكن ان تسلم باستخدام تقنية مسالة البرمجة الكسرية الضبابية  . يتم النظر في فئة خاصة من تقنية التحسين تسمى مسالة البرمجة الكسرية الضبابية في هذا العمل عندما تكون معاملات دالة الهدف للمسالة ضبابية. تم اقتراح دالة الترتيب الجديدة واستخدامها لتحويل بيانات مسالة البرمجة الكسرية الضبابية من رقم غامض إلى رقم واضح بحيث يمكن تجنب العيب عند معالجة المسالة الضبابية الأصلية. هنا يتم اعتماد نهج وظيفة الترتيب الجديدة للأرقام الضبابية العادية لترتيب الأرقام الضبابية المثلثية مع حسابات أبسط وأسهل بالإضافة إلى تقصيرها في الإجراءات. يتم تقليل مشكلة البرمجة الكسرية الضبابية أولاً إلى مشكلة البرمجة الكسرية ثم حلها باستخدام التقنية للحصول على الحل الأمثل. لديها القدرة على إعطاء أفضل حل لدعم نظرية الحل المقترحة في هذا العمل ، يتم تضمين بعض مسائل البرمجة الكسرية الضبابية لضمان ميزة وكفاءة ودقة الخوارزمية المقترحة. بالإضافة إلى ذلك ، تصف هذه الورقة البحثية مقارنة بين حلولنا المثالية مع الحلول الأخرى القائمة لعدم المساواة للقيود في مسائل البرمجة الكسرية الضبابية.In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler and easier calculations as well as shortening in the procedures. The fuzzy fractional programming problem is the first reduced to a fractional programming problem and then solved with the technique to obtain the optimal solution. It has a power to give a best solution for supporting the solution theory proposed in this work, some numerical fuzzy fractional programming problem are included to ensure the advantage, efficiency and accuracy of the suggested algorithm. In addition, this research paper describes a comparison between our optimal solutions with other existing solutions for inequalities constrains fuzzy fractional program

An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel Programming

The aim of this paper is to develop a new ranking technique for intuitionistic fuzzy numbers using the method of defuzzification based on probability density function of the corresponding membership function, as well as the complement of nonmembership function. Using the proposed ranking technique a methodology for solving linear bilevel fuzzy stochastic programming problem involving normal intuitionistic fuzzy numbers is developed. In the solution process each objective is solved independently to set the individual goal value of the objectives of the decision makers and thereby constructing fuzzy membership goal of the objectives of each decision maker. Finally, a fuzzy goal programming approach is considered to achieve the highest membership degree to the extent possible of each of the membership goals of the decision makers in the decision making context. Illustrative numerical examples are provided to demonstrate the applicability of the proposed methodology and the achieved results are compared with existing techniques