A necessary condition for comparing and ranking of triangular fuzzy numbers on the basis of height-independent ranking techniques

2021 ◽  
Vol 24 (4) ◽  
pp. 269-277
Author(s):  
Alireza Sotoudeh-Anvari
Keyword(s):  
Fuzzy Sets ◽  
Open Problem ◽  
Fuzzy Numbers ◽  
Necessary Condition ◽  
Triangular Fuzzy Numbers ◽  
Ranking Methods ◽  
Effect Analysis ◽  
Suggested Approach ◽  
Signed Distance ◽  
Total Integral

The open problem of comparing fuzzy numbers as one of the most important issues in fuzzy sets has been studied by many researchers. However, this problem has not been solved up to now and perhaps it will never be fully answered. This work proposes a necessary condition for ranking of triangular fuzzy numbers on the basis of some efficient height-independent ranking methods such as centroids, total integral value, signed distance and defuzzification. To the best of our knowledge, this paper provides the first use of a necessary condition in ranking methods. Fortunately, suggested approach is very straightforward, fast and efficient to use in the real problems. To evaluate the suggested approach with the result of existing methods, six examples are presented. Finally, we apply this necessary condition for ranking fuzzy numbers to a fuzzy failure mode and effect analysis (FMEA) problem. The results show that our approach is practical and has reasonable outcome.

scholarly journals Inventory Model with Demand Dependant on Unit Cost- Input Parameters as Triangular Fuzzy Numbers

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
R. Kasthuri, Et. al.
Keyword(s):  
Fuzzy Numbers ◽  
Unit Cost ◽  
Inventory Model ◽  
Average Total Cost ◽  
Triangular Fuzzy Numbers ◽  
Lot Size ◽  
Distance Method ◽  
Total Cost ◽  
Signed Distance ◽  
Fuzzy Environment

This paper considers an inventory model in which the shortages are backlogged and the demand is dependent on unit cost. An optimum value for average total cost is calculated by considering various input costs, lot size and maximum inventory under fuzzy environment. The process of defuzzification is done by using the signed distance method. Numerical example and sensitivity analysis is given for calculating both crisp and fuzzy values of the total cost.

Planning of a Project with Imprecise Activity Time

2016 ◽  
pp. 505-515
Author(s):  
Sk. Md. Abu Nayeem ◽  
Madhumangal Pal
Keyword(s):  
Fuzzy Numbers ◽  
Critical Path ◽  
Project Evaluation ◽  
Triangular Fuzzy Numbers ◽  
Activity Time ◽  
Ranking Methods ◽  
Mathematical Techniques ◽  
Activity Times

A project where activity times are characterized by intervals or triangular fuzzy numbers is considered in this chapter. Classical project evaluation and review technique (PERT) cannot be directly applied to such projects. Comparison of two intervals or two triangular fuzzy numbers plays an important role in this problem. Ranking methods based on some fuzzy mathematical techniques are discussed and two algorithms for finding the critical path for such a project are given. An illustrative example is also provided.

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

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Handan Akyar
Keyword(s):  
Risk Analysis ◽  
Fuzzy Numbers ◽  
New Method ◽  
Economic Systems ◽  
Triangular Fuzzy Numbers ◽  
Ranking Methods ◽  
Analysis Problem ◽  
Centroid Point ◽  
Fuzzy Risk Analysis ◽  
Fuzzy Ranking

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.

scholarly journals Application Of Rating Scale Model In Conversion Of Rating Scales' Points To The Form Of Triangular Fuzzy Numbers

2014 ◽  
Vol 14 (2) ◽  
pp. 7-18
Author(s):  
Bartłomiej Jefmański
Keyword(s):  
Rating Scales ◽  
Fuzzy Numbers ◽  
Rating Scale ◽  
Transformation Method ◽  
Economic Research ◽  
Scale Model ◽  
Triangular Fuzzy Numbers ◽  
Measurement Scales ◽  
Suggested Approach ◽  
Rating Scale Model

Abstract A new application of fuzzy sets theory in social and economic research is a fuzzy measurement of respondents' opinions. In the subject literature fuzzy rating scales or fuzzy conversion scales are being applied. In this second case, a key stage is a choice of such parameters' values of fuzzy numbers which will best illustrate the perception of linguistic values constituting points of measurement scales. In the construction of fuzzy conversion scales the item response theory models can find an application. The transformation method of verbal categories to the form of triangular fuzzy numbers with the application of rating scale model was proposed in this article. Usefulness of a suggested approach was introduced on the basis of the analysis of selected research results on inhabitants' quality of life in one of the Lower Silesian Voivodship districts. The analysis results showed big ambiguity of particular verbal categories and, in consequence, the validity of fuzzy conversion scales application.

The prioritization of failures within the automotive industry: The two-step failure mode and effect analysis integrated approach

2020 ◽  
Vol 234 (12) ◽  
pp. 1559-1570
Author(s):  
Nikola Banduka ◽  
Aleksandar Aleksić ◽  
Nikola Komatina ◽  
Amanda Aljinović ◽  
Danijela Tadić
Keyword(s):  
Failure Mode ◽  
Automotive Industry ◽  
Fuzzy Numbers ◽  
Fuzzy Classification ◽  
Product Choice ◽  
Triangular Fuzzy Numbers ◽  
Effect Analysis ◽  
Process Failure ◽  
Interval Type

Traditionally, in the automotive industry, the risk posed by failures in manufacturing is based on the conventional process failure mode and effect analysis. The market changes, as well as limited financial resources dedicated to business improvement, induce the need for employment of advanced management tools. The rating of failures is derived from the research using the suggested fuzzy classification method based on the Pareto analysis. It is assumed that the classification criterion should be determined as the product of the overall product choice and the risk priority numbers given by applying the traditional process failure mode and effect analysis. All the uncertainties that exist in the problem under consideration are represented by linguistic expressions that are modeled on the interval type-2 triangular fuzzy numbers. The overall product choice is based on a fuzzy analytical hierarchy process with interval type-2 triangular fuzzy numbers. The execution of management initiatives based on the priority of failures can result in the improvement of the manufacturing process and overall business efficiency. The proposed model is tested using real-life data from a single vehicle manufacturer operating in the Western Balkans and representing a part of a global automotive supply chain.

scholarly journals Inventory Model with Demand Dependant on Unit Cost- Input Parameters as Triangular Fuzzy Numbers

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
R. Kasthuria
Keyword(s):  
Fuzzy Numbers ◽  
Unit Cost ◽  
Inventory Model ◽  
Average Total Cost ◽  
Triangular Fuzzy Numbers ◽  
Lot Size ◽  
Distance Method ◽  
Total Cost ◽  
Signed Distance ◽  
Fuzzy Environment

This paper considers an inventory model in which the shortages are backlogged and the demand is dependent on unit cost. An optimum value for average total cost is calculated by considering various input costs, lot size and maximum inventory under fuzzy environment. The process of defuzzification is done by using the signed distance method. Numerical example and sensitivity analysis is given for calculating both crisp and fuzzy values of the total cost.

scholarly journals Real-Time Fuzzy Data Processing Based on a Computational Library of Analytic Models

Data ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 59
Author(s):  
Yuriy Kondratenko ◽  
Nina Kondratenko
Keyword(s):  
Data Processing ◽  
Fuzzy Sets ◽  
Real Time ◽  
Fuzzy Numbers ◽  
Fuzzy Arithmetic ◽  
Fuzzy Data ◽  
Triangular Fuzzy Numbers ◽  
Arithmetic Operations ◽  
Automatic Mode ◽  
Analytic Models

This work focuses on fuzzy data processing in control and decision-making systems based on the transformation of real-timeseries and high-frequency data to fuzzy sets with further implementation of diverse fuzzy arithmetic operations. Special attention was paid to the synthesis of the computational library of horizontal and vertical analytic models for fuzzy sets as the results of fuzzy arithmetic operations. The usage of the developed computational library allows increasing the operating speed and accuracy of fuzzy data processing in real time. A computational library was formed for computing of such fuzzy arithmetic operations as fuzzy-maximum. Fuzzy sets as components of fuzzy data processing were chosen as triangular fuzzy numbers. The analytic models were developed based on the analysis of the intersection points between left and right branches of considered triangular fuzzy numbers with different relations between their parameters. Our study introduces the mask for the evaluation of the relations between corresponding parameters of fuzzy numbers that allows to determine the appropriate model from the computational library in automatic mode. The simulation results confirm the efficiency of the proposed computational library for different applications.

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