scholarly journals Graphical representations of membership functions of maximum and minimum of two fuzzy numbers using computer program

2012 ◽  
Vol 31 ◽  
pp. 105-115 ◽  
Author(s):  
Shapla Shirin ◽  
Goutam Saha
Keyword(s):  
Computer Program ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Graphical Representations ◽  
Fuzzy Logics ◽  
Triangular Fuzzy Numbers ◽  
Different Types ◽  
Analytic Expressions ◽  
Short Time

The set of real numbers R is linearly ordered, but in the fuzzy set theory, this relation is true only for some set of fuzzy numbers where the sets of fuzzy numbers are expressed as the linguistic variables. Different types of Fuzzy machines based on fuzzy logic have been invented where fuzzy logics are described by fuzzy numbers and the fuzzy numbers are needed to compare. Besides these, many techniques are available to assist decision-makers to compare different fuzzy numbers. For these reasons, it is necessary to compute the maximum and the minimum of fuzzy numbers. Till now many researchers introduced different methods for computation, which are done by hand calculation, but these are very disgusting and time consuming to us. In this paper, we presents an algorithm to compute the maximum and the minimum of any two triangular fuzzy numbers, so that one can compare two fuzzy numbers easily in a short time and visualize the analytic expressions and the graphical representations of the maximum and the minimum of any two triangular fuzzy numbers. By using CAS (MATHEMATICA 7.0), the algorithm is implemented in a computer program in order to do these. This algorithm can easily be extended to apply for any type of fuzzy numbers which are comparable. Even it is able to compare more than two fuzzy numbers by comparing the maximum fuzzy number or minimum fuzzy number with another new fuzzy number.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10313GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 105-115

scholarly journals Communicating earthquake risk: mapped parameters and cartographic representation

2011 ◽  
Vol 11 (2) ◽  
pp. 359-366 ◽  
Author(s):  
J. M. Gaspar-Escribano ◽  
T. Iturrioz
Keyword(s):  
Risk Assessment ◽  
Seismic Risk ◽  
Risk Information ◽  
Decision Makers ◽  
Earthquake Risk ◽  
Graphical Representations ◽  
Related Risk ◽  
Different Types ◽  
Earthquake Effects ◽  
Earthquake Risk Assessment

Abstract. Earthquake risk assessment is probably the most effective tool for reducing adverse earthquake effects and for developing pre- and post-event planning actions. The related risk information (data and results) is of interest for persons with different backgrounds and interests, including scientists, emergency planners, decision makers and other stakeholders. Hence, it is important to ensure that this information is properly transferred to all persons involved in seismic risk, considering the nature of the information and the particular circumstances of the source and of the receiver of the information. Some experience-based recommendations about the parameters and the graphical representations that can be used to portray earthquake risk information to different types of audiences are presented in this work.

Ranking of Fuzzy Numbers by using Scaling Method

2019 ◽  
Vol 3 (2) ◽  
pp. 137-143
Author(s):  
Ayad Mohammed Ramadan
Keyword(s):  
Multidimensional Scaling ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Scaling Method ◽  
Ranking Of Fuzzy Numbers ◽  
First Time

In this paper, we presented for the first time a multidimensional scaling approach to find the scaling as well as the ranking of triangular fuzzy numbers. Each fuzzy number was represented by a row in a matrix, and then found the configuration points (scale points) which represent the fuzzy numbers in . Since these points are not uniquely determined, then we presented different techniques to reconfigure the points to compare them with other methods. The results showed the ability of ranking fuzzy numbers

scholarly journals New Similarity of Triangular Fuzzy Number and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xixiang Zhang ◽  
Weimin Ma ◽  
Liping Chen
Keyword(s):  
Collaborative Filtering ◽  
Fuzzy Number ◽  
Recommendation System ◽  
Fuzzy Numbers ◽  
Comprehensive Evaluation ◽  
Cloud Model ◽  
Triangular Fuzzy Number ◽  
New Method ◽  
Triangular Fuzzy Numbers

The similarity of triangular fuzzy numbers is an important metric for application of it. There exist several approaches to measure similarity of triangular fuzzy numbers. However, some of them are opt to be large. To make the similarity well distributed, a new method SIAM (Shape’s Indifferent Area and Midpoint) to measure triangular fuzzy number is put forward, which takes the shape’s indifferent area and midpoint of two triangular fuzzy numbers into consideration. Comparison with other similarity measurements shows the effectiveness of the proposed method. Then, it is applied to collaborative filtering recommendation to measure users’ similarity. A collaborative filtering case is used to illustrate users’ similarity based on cloud model and triangular fuzzy number; the result indicates that users’ similarity based on triangular fuzzy number can obtain better discrimination. Finally, a simulated collaborative filtering recommendation system is developed which uses cloud model and triangular fuzzy number to express users’ comprehensive evaluation on items, and result shows that the accuracy of collaborative filtering recommendation based on triangular fuzzy number is higher.

scholarly journals Inclusion of uncertainty with different types of fuzzy numbers into DEMATEL

2021 ◽  
Vol 16 (1) ◽  
pp. 49-59
Author(s):  
Tjaša Šmidovnik ◽  
Petra Grošelj
Keyword(s):  
Complex System ◽  
Decision Making ◽  
Fuzzy Sets ◽  
Construction Projects ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Different Types

Nowadays the multi-criteria decision making is very complicated due to uncertainty, vagueness, limited sources, knowledge and time. The Decision-making Trial and Evaluation Laboratory (DEMATEL) method is a widely used multi-criteria decision-making method to analyze the structure of a complex system. It is useful in analysing the cause and effect relationships between the components of the system. Fuzzy sets can be used to include uncertainty in multi-criteria decision making. Linguistic assessments of decision makers can be translated into fuzzy numbers. In this study, fuzzy numbers, intuitionistic fuzzy numbers and neutrosophic fuzzy numbers were used for the decision makers evaluations in the DEMATEL method. The aim of this study was to evaluate how different types of fuzzy numbers affect the final results. An application of risk in construction projects was selected from the literature, where seven experts used a linguistic scale to evaluate different criteria. The results showed that there are only slight differences between the weights of the criteria with regard to the type of fuzzy numbers.

Application of interval-valued triangular fuzzy numbers and their functional to the healthcare problems

Dependability ◽  
2021 ◽  
Vol 21 (1) ◽  
pp. 23-33
Author(s):  
Kapil Naithani ◽  
Rajesh Dangwal
Keyword(s):  
Failure Probability ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Fault Tree Analysis ◽  
Triangular Fuzzy Number ◽  
Triangular Fuzzy Numbers ◽  
Index Method ◽  
Estimate Reliability ◽  
Failure Tree ◽  
Interval Valued

Aim. In healthcare field there exist different types of uncertainty due to medical error generated by human and technologies. In general the crisp value generate loss of precision and inaccuracy about result and therefore the available data is not sufficient to assessed clinical process up to desired degree of accuracy. Therefore fuzzy set theory play as an important and advance role in accuracy of results in healthcare related problems. Methods. Here for more accuracy of result, we use functional fuzzy numbers in this paper. This study uses a new fuzzy fault tree analysis for patient safety risk modelling in healthcare. In this paper we will use level (λ, ρ) interval-valued triangular fuzzy number, their functional, t-norm operation and centre of gravity defuzzification method to evaluate fuzzy failure probability and estimate reliability of system. The effectiveness of these methods is illustrated by an example related to healthcare problems and then we analyse the result obtained with the other existing techniques. Tanaka et al.’s approach has been used to give the rank of basic events of the considered problems. Also, we use functional of fuzzy numbers to analyse the change in fuzzy failure probability. Results. The paper examines the application of the failure tree, t-norm and functional fuzzy numbers in the context of interval-valued triangular fuzzy numbers. The research examined two types of healthcare-specific problems and the corresponding defuzzification techniques for the purpose of reliability analysis using the existing methods. The authors concluded that t-norm is not associated with significant accumulation and identified how a functional fuzzy number affects reliability. Similarly, using the V index method, the least critical events were found for each system.

scholarly journals A Direct Method to Compare Bipolar LR Fuzzy Numbers

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Reza Ghanbari ◽  
Khatere Ghorbani-Moghadam ◽  
Nezam Mahdavi-Amiri
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Direct Method ◽  
Optimization Algorithms ◽  
Real Life ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Real Life Problem ◽  
A Direct Method

We propose a new method for ordering bipolar fuzzy numbers. In this method, for comparison of bipolar LR fuzzy numbers, we use an extension of Kerre’s method being used in ordering of unipolar fuzzy numbers. We give a direct formula to compare two bipolar triangular fuzzy numbers in O(1) operations, making the process useful for many optimization algorithms. Also, we present an application of bipolar fuzzy number in a real life problem.

Appraisement and benchmarking of supply chain performance extent

2015 ◽  
Vol 5 (1) ◽  
pp. 2-30 ◽  
Author(s):  
Santosh Kumar Sahu ◽  
Saurav Datta ◽  
Siba Sankar Mahapatra
Keyword(s):  
Decision Making ◽  
Supply Chain ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Supply Chain Performance ◽  
Triangular Fuzzy Numbers ◽  
Subjective Judgment ◽  
Content Type ◽  
Grey Relation ◽  
Evaluation Information

Purpose – Supply chain performance (SCP) extent can be attributed as a function of multiple criteria/attributes. Most of the criterions/attributes being intangible in nature; SCP appraisement relies on the subjective judgment of the decision makers. Moreover, quantitative appraisement of SCP appears to be very difficult due to involvement of ill-defined (vague) performance measures as well as metrics. The purpose of this paper is to develop an efficient decision support system (DSS) to facilitate SCP appraisement, benchmarking and related decision making. Design/methodology/approach – This study explores the concept of fuzzy logic in order to tackle incomplete and inconsistent subjective judgment of the decision makers’ whilst evaluating supply chain’s overall performance. Grey relational analysis has been adopted in the later stage to derive appropriate ranking of alternative companies/enterprises (in the same industry) in view of ongoing SCP extent. Findings – In this work, a performance appraisement index system has been postulated to gather evaluation information (weights and ratings) in relation to SCP measures and metrics. Combining the concepts of fuzzy set theory, entropy, ideal and grey relation analysis, a fuzzy grey relation method for SCP benchmarking problem has been presented. First, triangular fuzzy numbers and linguistic evaluation information characterized by triangular fuzzy numbers have been used to evaluate the importance weights of all criteria and the superiority of all alternatives vs various criteria above the alternative level. Then, the concept of entropy has been utilized to solve the adjusted integration weight of all objective criteria above the alternative level. Moreover, using the concept of the grey ration grades, various alternatives have been ranked accordingly. Originality/value – Finally, an empirical example of selecting most appropriate company has been used to demonstrate the ease of applicability of the aforesaid approach. The study results showed that this method appears to be an effective means for tackling multi-criteria decision-making problems in uncertain environments. Empirical data have been analysed and results obtained thereof, have been reported to exhibit application potential of the said fuzzy grey relation based DSS in appropriate situation.

A New Point of View for Fuzzy Numbers and Their Defuzzification

2015 ◽  
Vol 23 (06) ◽  
pp. 909-926 ◽  
Author(s):  
Romà Adillon ◽  
Lambert Jorba
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Graphical Representation ◽  
Point Of View ◽  
Geometrical Approach ◽  
Triangular Fuzzy Numbers ◽  
Trapezoidal Fuzzy Numbers

In this paper we develop a new graphical representation of fuzzy numbers, which we then employ to propose a geometrical approach to their defuzzification. The calculations involved in the proposed method and the resultant representation use Moore's semiplane for intervals and therefore are far simpler than those involved in other approaches. We start by representing triangular and trapezoidal fuzzy numbers in Moore's semiplane. Then we extend this work to any fuzzy number. Although this extension has to be undertaken in [Formula: see text], it preserves all the properties we study for trapezoidal and triangular fuzzy numbers in Moore's semiplane.

scholarly journals Multi-Criteria Decision-Making for Airport Operation Performance Using Triangular Fuzzy Numbers

2019 ◽  
Vol 3 (3) ◽  
pp. 01-15
Author(s):  
Adeel Ahmad ◽  
Sana Akram ◽  
Muhammad Farhan Tabassum ◽  
Alia Kausar ◽  
Nousheen Ilyas
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Triangular Fuzzy Numbers ◽  
Operation Performance ◽  
Linguistic Form ◽  
Fuzzy Environment ◽  
Simple Additive Weighting

This paper advocates Multi-Criteria Decision-Making (MCDM) which evaluates the operation performance of airports using Fuzzy Simple Additive Weighting (FSAW) method. Assigned weights by decision- makers were in a linguistic form. These linguistic forms were converted into triangular fuzzy numbers. We chose three airports designated as A1, A2 and A3 and examined by four decision makers D1, D2, D3 and D4 under a fuzzy environment for performance against the chosen criteria. FSAW method gives similar decision results which shows that this method is effective, relevant and reliable for this kind of MCDM.

scholarly journals Computing Cluster Centers of Triangular Fuzzy Numbers using Innovative Metric Distance

2019 ◽  
Vol 8 (11) ◽  
pp. 3378-3381
Keyword(s):  
Fuzzy Number ◽  
Clustering Algorithm ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy C Means ◽  
Fuzzy C Means Clustering ◽  
Metric Distance ◽  
Matlab Programming ◽  
Computing Cluster

In this paper we compute cluster centers of triangular fuzzy numbers through fuzzy c means clustering algorithm and kernel based fuzzy c means clustering algorithm. An innovative distance between the triangular fuzzy numbers is used and the distance is complete metric on triangular fuzzy numbers. The set of triangular fuzzy numbers and an another set with the same triangular fuzzy numbers by including an outlier or noisy point as an additional triangular fuzzy number are taken to find the cluster centers using MATLAB programming. An example is given to show the effectiveness between the algorithms.

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