scholarly journals Approximate Membership Function Shapes of Solutions to Intuitionistic Fuzzy Transportation Problems

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Bogdana Stanojevic ◽  
Milan Stanojević
Keyword(s):  
Membership Function ◽  
Transportation Problems ◽  
Solution Approach ◽  
Constraint System ◽  
Intuitionistic Fuzzy ◽  
Decision Variables ◽  
Optimal Values ◽  
Fuzzy Parameters ◽  
Fuzzy Solutions ◽  
The Membership Function

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.

scholarly journals Formulation of the membership function and determination of the input of fuzzy loads in the structural fuzzy analyzing problem

2007 ◽  
Vol 29 (2) ◽  
pp. 117-126
Author(s):  
Nguyen Van Pho
Keyword(s):  
Membership Function ◽  
Input Parameter ◽  
Design Standards ◽  
Input Parameters ◽  
Triangular Membership Function ◽  
Probabilistic Density Function ◽  
Fuzzy Parameters ◽  
Selection Of ◽  
The Membership Function

The fuzzy analyzing process consists of different steps. In this paper, the author considers only the method for formulation of the membership function of fuzzy loads acting on the structure. Based on the membership function of fuzzy loads, the combinations of deterministic of the regression analyzing process will be determined. The membership function of fuzzy loads is selected by the triangular membership function. It is in conformity with the concept on selection of loads in the design standards. The combination of inputs for the analyzing process will be determined, based on the number of present times of the value of input parameters (including the deterministic parameters, fuzzy parameters and the random ones) in the schema of analysis. The number of present times of input parameters is either proportional to value of the corresponding membership function or to the value of the probabilistic density function. A method for determining the appropriate combination of deterministic inputs so that each input parameter will present only one time in each combination is proposed. To illustrate the proposed method, an example on the determination of input combinations of tornado's velocity in Vietnam is presented.

scholarly journals OPERATOR ⊞A and ⊠A ON INTUITIONISTIC FUZZY RING

2020 ◽  
Vol 12 (1) ◽  
pp. 35
Author(s):  
Dian Pratama
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Ring Theory ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ring ◽  
The Membership Function

Intuitionistic fuzzy sets is a sets that are characterized by membership and non-membership function which  sum is less than one. When applied to ring theory, it will called intuitionistic fuzzy rings. The fuzzy set operator is a mapping between the membership function and the interval [0,1]. In this study, we will describe properties of operator  and  in intuitionistic fuzzy rings. The characteristics that will be studied include the structure of  and  if A is an intuitive and fuzzy ring and vice versa.

scholarly journals Circular intuitionistic fuzzy TOPSIS method with vague membership functions: Supplier selection application context

2021 ◽  
Vol 27 (1) ◽  
pp. 24-52
Author(s):  
Cengiz Kahraman ◽  
◽  
Nurşah Alkan ◽  
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Supplier Selection ◽  
Three Dimensional ◽  
Fuzzy Topsis ◽  
Intuitionistic Fuzzy Sets ◽  
Topsis Method ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Topsis ◽  
The Membership Function

The membership function of a general type-2 fuzzy set is three-dimensional in order to incorporate its vagueness through the third dimension. Similarly, Circular intuitionistic fuzzy sets (CIFSs) have been recently introduced by Atanassov (2020) as a new extension of intuitionistic fuzzy sets, which are represented by a circle representing the vagueness of the membership function. CIFSs allow decision-makers to express their judgments including this vagueness. In this study, the TOPSIS method, which is one of the most used multi-criteria decision-making methods is extended to its CIF version. The proposed CIF-TOPSIS methodology is applied to the supplier selection problem. Then, a sensitivity analysis based on criteria weights is conducted to check the robustness of the proposed approach. A comparative analysis with single-valued intuitionistic fuzzy TOPSIS method is also performed to verify the developed approach and to demonstrate its effectiveness

scholarly journals Rationale for the type of the membership function of fuzzy parameters of locomotive intelligent control systems

2015 ◽  
Vol 1 (3(73)) ◽  
pp. 4 ◽  
Author(s):  
Тетяна Василівна Бутько ◽  
Олександр Борисович Бабанін ◽  
Олександр Миколайович Горобченко
Keyword(s):  
Control Systems ◽  
Membership Function ◽  
Intelligent Control ◽  
Intelligent Control Systems ◽  
Fuzzy Parameters ◽  
The Membership Function

A METHOD FOR FINDING CRITICAL PATH WITH SYMMETRIC OCTAGONAL INTUITIONISTIC FUZZY NUMBERS

2020 ◽  
Vol 9 (11) ◽  
pp. 9273-9286
Author(s):  
N. Rameshan ◽  
D.S. Dinagar
Keyword(s):  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Membership Functions ◽  
Intuitionistic Fuzzy Number ◽  
Lower And Upper Bounds ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Membership Function

The concept of this paper represents finding fuzzy critical path using octagonal fuzzy number. In project scheduling, a new method has been approached to identify the critical path by using Symmetric Octagonal Intuitionistic Fuzzy Number (SYMOCINTFN). For getting a better solution, we use the fuzzy octagonal number rather than other fuzzy numbers. The membership functions of the earliest and latest times of events are by calculating lower and upper bounds of the earliest and latest times considering octagonal fuzzy duration. The resulting conditions omit the negative and infeasible solution. The membership function takes up an essential role in finding a new solution. Based on membership function, fuzzy number can be identified in different categories such as Triangular, Trapezoidal, pentagonal, hexagonal, octagonal, decagonal, hexa decagonal fuzzy numbers etc.

scholarly journals ALGORITMA FUZZY GOAL PROGRAMMING UNTUK MASALAH PEMROGRAMAN BILEVEL MULTIOBJEKTIF

2018 ◽  
Vol 10 (1) ◽  
pp. 1
Author(s):  
Syarifah Inayati
Keyword(s):  
Membership Function ◽  
Goal Programming ◽  
Fuzzy Goal Programming ◽  
Hierarchical Organization ◽  
Decision Makers ◽  
Decision Variables ◽  
Fuzzy Goals ◽  
Fuzzy Goal ◽  
Upper Level ◽  
The Membership Function

Bilevel multiobjective programming problems are mathematical programming that solves the problem of planning with two decision makers (DM) in two level or hierarchical organization with the objective function of each organization can be more than one. In this paper, we discussed the special case of this problem with single decision maker at the upper level and multiple decision makers at the lower level. This problem can be solved using fuzzy goal programming (FGP) approach. In this approach, the membership function for the defined fuzzy goals of all objective functions of DMs at the two levels was developed first in the model formulation of the problem. Thus the membership function for vector of fuzzy goals of the decision variables controlled by the leader. Then FGP approach requires the leader to set goals for each objective that he/she wishes to attain. A preferred solution is then defined for minimizes the deviations from the set of goals. Numerical example is provided to illustrate the approach.

scholarly journals Least-looping stepping-stone-based ASM approach for transportation and triangular intuitionistic fuzzy transportation problems

2021 ◽  
Author(s):  
Kedar Nath Das ◽  
Rajeev Das ◽  
Debi Prasanna Acharjya
Keyword(s):  
Optimal Solution ◽  
Transportation Engineering ◽  
Key Factors ◽  
Solution Quality ◽  
Transportation Problems ◽  
Stepping Stone ◽  
Intuitionistic Fuzzy ◽  
Real World Problem ◽  
Statistical Results ◽  
Made In

AbstractTransportation problem (TP) is a popular branch of Linear Programming Problem in the field of Transportation engineering. Over the years, attempts have been made in finding improved approaches to solve the TPs. Recently, in Quddoos et al. (Int J Comput Sci Eng (IJCSE) 4(7): 1271–1274, 2012), an efficient approach, namely ASM, is proposed for solving crisp TPs. However, it is found that ASM fails to provide better optimal solution in some cases. Therefore, a new and efficient ASM appoach is proposed in this paper to enhance the inherent mechanism of the existing ASM method to solve both crisp TPs and Triangular Intuitionistic Fuzzy Transportation Problems (TIFTPs). A least-looping stepping-stone method has been employed as one of the key factors to improve the solution quality, which is an improved version of the existing stepping-stone method (Roy and Hossain in, Operation research Titus Publication, 2015). Unlike stepping stone method, least-looping stepping-stone method only deals with few selected non-basic cells under some prescribed conditions and hence minimizes the computational burden. Therefore, the framework of the proposed method (namely LS-ASM) is a combination of ASM (Quddoos et al. 2012) and least-looping stepping-stone approach. To validate the performance of LS-ASM, a set of six case studies and a real-world problem (those include both crisp TPs and TIFTPs) have been solved. The statistical results obtained by LS-ASM have been well compared with the existing popular modified distribution (MODI) method and the original ASM method, as well. The statistical results confirm the superiority of the LS-ASM over other compared algorithms with a less computationl effort.

scholarly journals Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems

2021 ◽  
Author(s):  
Firoz Ahmad
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Practical Implication ◽  
Real Life ◽  
Future Research ◽  
Programming Approach ◽  
Solution Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiobjective Optimization Problems

AbstractThis study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.

Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators

2020 ◽  
Vol 39 (3) ◽  
pp. 4427-4441
Author(s):  
Bin Xu
Keyword(s):  
Network Security ◽  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Computer Network ◽  
Information Aggregation ◽  
Security Evaluation ◽  
Uncertain Information ◽  
Intuitionistic Fuzzy ◽  
Computer Network Security

The concept of fuzzy number intuitionistic fuzzy sets (FNIFSs) is designed to effectively depict uncertain information in decision making problems which fundamental characteristic of the FNIFS is that the values of its membership function and non-membership function are depicted with triangular fuzzy numbers (TFNs). The dual Hamy mean (DHM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this paper, we used the dual Hamy mean (DHM) operator and dual weighted Hamy mean (WDHM) operator with fuzzy number intuitionistic fuzzy numbers (FNIFNs) to propose the fuzzy number intuitionistic fuzzy dual Hamy mean (FNIFDHM) operator and fuzzy number intuitionistic fuzzy weighted dual Hamy mean (FNIFWDHM) operator. Then the MADM methods are proposed along with these operators. In the end, we utilize an applicable example for computer network security evaluation to prove the proposed methods.

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