Fully Fuzzy Time-Cost Trade-Off in a Project Network - A New Approach

In this paper, we propose a new approach to Fuzzy network crashing in a project network whose activity times are uncertain. The uncertain parameters in the project network are represented by triangular fuzzy numbers. By using a new type of fuzzy arithmetic and a fuzzy ranking method we propose a method for finding an optimal duration by crashing the fuzzy activities of a project network without converting the fuzzy activity times to classical numbers. A numerical example is provided to illustrate the proposed method. Keywords: Triangular fuzzy number, fuzzy ranking, fuzzy project network, Critical path, crashing

Fuzzy Risk Analysis for a Production System Based on the Nagel Point of a Triangle

Ordering and ranking fuzzy numbers and their comparisons play a significant role in decision-making problems such as social and economic systems, forecasting, optimization, and risk analysis problems. In this paper, a new method for ordering triangular fuzzy numbers using the Nagel point of a triangle is presented. With the aid of the proposed method, reasonable properties of ordering fuzzy numbers are verified. Certain comparative examples are given to illustrate the advantages of the new method. Many papers have been devoted to studies on fuzzy ranking methods, but some of these studies have certain shortcomings. The proposed method overcomes the drawbacks of the existing methods in the literature. The suggested method can order triangular fuzzy numbers as well as crisp numbers and fuzzy numbers with the same centroid point. An application to the fuzzy risk analysis problem is given, based on the suggested ordering approach

A New Ranking Function of Triangular Fuzzy Numbers for Solving Fuzzy Linear Programming Problems with Big -M Method

The objective of this paper is to introduce a new ranking function of Triangular Fuzzy Numbers for solving fuzzy linear programming problems in objective function and find the optimal solution of it by Big -M Method. A numerical example is given to illustrate the proposed method

Selection method by fuzzy set theory and preference matrix

In fuzzy decision making problems, fuzzy ranking is one of the most preferred aeras. The aim of this paper to develop a new ranking method which is reliable and doesnot need tremendous arithmetic calculations. Also it can be used for all type of fuzzy numbers which are represented as crisp form or in linguistic form. Fuzzy multi criteria decision making commonly employs methods such as ordering method,Fuzzy Analytic Hierarchy Process [FAHP], Fuzzy Technique for Order Preference by Similarity to Ideal Solution [FTOPSIS]and hybrid method. The FAHP commonly uses triangular fuzzy numbers and trapezoidal fuzzy numbers while the FTOPSIS method identifies the best alternative as the one that is nearest to the positive ideal solution and farthest to the negative ideal solution. Although both these methods have been widely used, they have their drawbacks. The accuracy of these methods decreases as the number of alternative increases i.e. the more complex the problem, less the accuracy and all the methods have many computations. In order to overcome this problem, we propose a method which is a combination of method of Blin and Whinston(1973) and method of Shimura(1973). This way the advantages of both the methods may be utilized to arrive at a decision that involves vague data. In this  paper, we use the concept of preference matrix to find the membership grades and calculate the ranking. Keywords: Fuzzy set, preference matrix, multi person decision making, multi criteria decision making(MCDM), relativity function matrix

Refractured Well Selection for Multicriteria Group Decision Making by Integrating Fuzzy AHP with Fuzzy TOPSIS Based on Interval-Typed Fuzzy Numbers

Multicriteria group decision making (MCGDM) research has rapidly been developed and become a hot topic for solving complex decision problems. Because of incomplete or non-obtainable information, the refractured well-selection problem often exists in complex and vague conditions that the relative importance of the criteria and the impacts of the alternatives on these criteria are difficult to determine precisely. This paper presents a new model for MCGDM by integrating fuzzy analytic hierarchy process (AHP) with fuzzy TOPSIS based on interval-typed fuzzy numbers, to help group decision makers for well-selection during refracturing treatment. The fuzzy AHP is used to analyze the structure of the selection problem and to determine weights of the criteria with triangular fuzzy numbers, and fuzzy TOPSIS with interval-typed triangular fuzzy numbers is proposed to determine final ranking for all the alternatives. Furthermore, the algorithm allows finding the best alternatives. The feasibility of the proposed methodology is also demonstrated by the application of refractured well-selection problem and the method will provide a more effective decision-making tool for MCGDM problems

A Fuzzy Delphi Consensus Methodology Based on a Fuzzy Ranking

Delphi multi-round survey is a procedure that has been widely and successfully used to aggregate experts’ opinions about some previously established statements or questions. Such opinions are usually expressed as real numbers and some commentaries. The evolution of the consensus can be shown by an increase in the agreement percentages, and a decrease in the number of comments made. A consensus is reached when this percentage exceeds a certain previously set threshold. If this threshold has not been reached, the moderator modifies the questionnaire according to the comments he/she has collected, and the following round begins. In this paper, a new fuzzy Delphi method is introduced. On the one hand, the experts’ subjective judgments are collected as fuzzy numbers, enriching the approach. On the other hand, such opinions are collected through a computerized application that is able to interpret the experts’ opinions as fuzzy numbers. Finally, we employ a recently introduced fuzzy ranking methodology, satisfying many properties according to human intuition, in order to determine whether the expert’s fuzzy opinion is favorable enough (comparing with a fixed fuzzy number that indicates Agree or Strongly Agree). A cross-cultural validation was performed to illustrate the applicability of the proposed method. The proposed approach is simple for two reasons: it does not need a defuzzification step of the experts’ answers, and it can consider a wide range of fuzzy numbers not only triangular or trapezoidal fuzzy numbers

An implementation of the Dilkstra algorithm for fuzzy costs (Technical report 2018)

This report presents an implementation the Dijkstra algorithm applied to a type V fuzz graph. This new algorithm can find the shortest path in a graph with edge costs are defined as positive triangular fuzzy number