Possibility mean and variation coefficient based ranking methods for type-1 fuzzy numbers and interval type-2 fuzzy numbers

2016 ◽  
Vol 30 (4) ◽  
pp. 2157-2168 ◽  
Author(s):  
Xiuzhi Sang ◽  
Xinwang Liu
Keyword(s):  
Fuzzy Numbers ◽  
Variation Coefficient ◽  
Ranking Methods ◽  
Interval Type

Multi-criteria decision-making method based on type-2 fuzzy sets

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 431-450 ◽  
Author(s):  
Jing Wang ◽  
Qing-Hui Chen ◽  
Hong-Yu Zhang ◽  
Xiao-Hong Chen ◽  
Jian-Qiang Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Computational Models ◽  
Fuzzy Numbers ◽  
Multi Criteria Decision Making ◽  
Interval Numbers ◽  
Interval Type ◽  
Uncertainty Information

Type-2 fuzzy sets (T2FSs) are the extension of type-1 fuzzy sets (T1FSs), which can convey more uncertainty information in solving multi-criteria decision-making (MCDM) problems. Motivated by the extension from interval numbers to triangular fuzzy numbers, three-trapezoidal-fuzzy-number-bounded type-2 fuzzy numbers (TT2FNs) are defined on the basis of interval type-2 trapezoidal fuzzy numbers (IT2TFNs), and they can convey more uncertainty information than T1FSs and IT2FSs. Moreover, the drawbacks of the existing computational models of generalized fuzzy numbers are analyzed, and a new computational model of fuzzy numbers is proposed, which is further extended to TT2FNs. Besides, a MCDM method is proposed to deal with the evaluation information given in the form of TT2FNs. Finally, an illustrative example and comparison analysis are provided to demonstrate the feasibility and validity of the proposed method.

Multi-objective vendor managed inventory system with interval type-2 fuzzy demand and order quantities

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zubair Ashraf ◽  
Mohammad Shahid
Keyword(s):  
Fuzzy Numbers ◽  
Vendor Managed Inventory ◽  
Content Type ◽  
Multi Objective ◽  
Demand Rate ◽  
Order Quantities ◽  
Interval Type ◽  
Pareto Fronts

PurposeThe proposed IT2FMOVMI model intends to concurrently minimize total cost and warehouse space for the single vendor-retailer, multi-item and a consolidated vendor store. Regarding demand and order quantities with the deterministic and type-1 fuzzy numbers, we have also formulated the classic/crisp MOVMI model and type-1 fuzzy MOVMI (T1FMOVMI) model. The suggested solution technique can solve both crisp MOVMI and T1FMOVMI problems. By finding the optimal ordered quantities and backorder levels, the Pareto-fronts are constructed to form the solution sets for the three models.Design/methodology/approachA multi-objective vendor managed inventory (MOVMI) is the most recognized marketing and delivery technique for the service provider and the retail in the supply chain in Industry 4.0. Due to the evolving market conditions, the characteristics of the individual product, the delivery period and the manufacturing costs, the demand rate and order quantity of the MOVMI device are highly unpredictable. In such a scenario, a MOVMI system with a deterministic demand rate and order quantity cannot be designed to estimate the highly unforeseen cost of the problem. This paper introduces a novel interval type-2 fuzzy multi-objective vendor managed inventory (IT2FMOVMI) system, which uses interval type-2 fuzzy numbers (IT2FNs) to represent demand rate and order quantities. As the model is an NP-hard, the well-known meta-heuristic algorithm named NSGA-II (Non-dominated sorted genetic algorithm-II) with EKM (Enhanced Karnink-Mendel) algorithm based solution method has been established.FindingsThe experimental simulations for the five test problems that demonstrated distinct conditions are considered from the real-datasets of SAPCO company. Experimental study concludes that T1FMOVMI and crisp MOVMI schemes are outclassed by IT2FMOVMI model, offering more accurate Pareto-Fronts and efficiency measurement values.Originality/valueUsing fuzzy sets theory, a significant amount of work has been already done in past decades from various points of views to model the MOVMI. However, this is the very first attempt to introduce type-2 fuzzy modelling for the problem to address the realistic implementation of the imprecise parameters.

scholarly journals Interval Type-2 Fuzzy Standardized Cumulative Sum Control Charts in Production of Fertilizers

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Nur Hidayah Mohd Razali ◽  
Lazim Abdullah ◽  
Zabidin Salleh ◽  
Ahmad Termimi Ab Ghani ◽  
Bee Wah Yap
Keyword(s):  
Process Control ◽  
Statistical Process Control ◽  
Control Chart ◽  
Control Charts ◽  
Fuzzy Numbers ◽  
Cusum Chart ◽  
Statistical Process ◽  
Interval Type

Statistical process control is a method used for controlling processes in which causes of variations and correction actions can be observed. Control chart is one of the powerful tools of statistical process control that are used to control nonconforming products. Previous literature suggests that fuzzy charts are more sensitive than conventional control charts, and hence, they provide better quality and conformance of products. Nevertheless, some of the data used are more suitable to be presented in interval type-2 fuzzy numbers compared to type-1 fuzzy numbers as interval type-2 fuzzy numbers have more ability to capture uncertain and vague information. In this paper, we develop an interval type-2 fuzzy standardized cumulative sum (IT2F-SCUSUM) control chart and apply it to data of fertilizer production. This new approach combines the advantages of interval type-2 fuzzy numbers and standardized sample means which can control the variability. Twenty samples with a sample size of six were examined for testing the conformance. The proposed IT2F-SCUSUM control chart unveils that 15 samples are “out of control.” The results are also compared to the conventional CUSUM chart and type-1 fuzzy CUSUM chart. The conventional chart shows that 13 samples are “out of control.” In contrast, the type-1 fuzzy CUSUM chart shows that the process is “out of control” for 14 samples. In the analysis of average run length, the proposed IT2F-SCUSUM chart outperforms the other two CUSUM charts. Thus, we can conclude that the IT2F-SCUSUM chart is more sensitive and takes lesser number of observations to identify the shift in the process. The analyses suggest that the IT2F-SCUSUM chart is a promising tool in examining conformance of the quality of the fertilizer production.

A New Method for Ranking Interval Type-2 Fuzzy Numbers Based on Mellin Transform

2020 ◽  
Vol 28 (04) ◽  
pp. 591-611
Author(s):  
Yanbing Gong ◽  
Lin Xiang ◽  
Shuxin Yang ◽  
Hailiang Ma
Keyword(s):  
Fuzzy Sets ◽  
Degrees Of Freedom ◽  
Mellin Transform ◽  
Fuzzy Numbers ◽  
Mean Value ◽  
Distance Measures ◽  
Mean Values ◽  
Interval Type

Interval type-2 fuzzy sets provide us with additional degrees of freedom to represent the uncertainty and the fuzziness of the real word than traditional type-1 fuzzy sets. Interval type-2 fuzzy numbers ranking has an important role in the decision making analysis. In this paper, the probatilistic mean value and variance of interval type-2 fuzzy numbers are proposed based on the Mellin transform for type-1 fuzzy numbers. The interval type-2 fuzzy number with the higher mean is ranked higher. If the mean values are equal the one with the smaller variance is judged higher rank. On this basis, some new distance measures and possibility degree formula are proposed to comparing interval type-2 fuzzy numbers based on their Mellin mean value and variance. Some benchmarking numerical examples are given, and some interpretation issues are explained.

An interval type-2 hesitant fuzzy best-worst method

2021 ◽  
pp. 1-28
Author(s):  
Ashraf Norouzi ◽  
Hossein Razavi hajiagha
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Fuzzy Ahp ◽  
Uncertain Data ◽  
Interval Type ◽  
Best Worst Method

Multi criteria decision-making problems are usually encounter implicit, vague and uncertain data. Interval type-2 fuzzy sets (IT2FS) are widely used to develop various MCDM techniques especially for cases with uncertain linguistic approximation. However, there are few researches that extend IT2FS-based MCDM techniques into qualitative and group decision-making environment. The present study aims to adopt a combination of hesitant and interval type-2 fuzzy sets to develop an extension of Best-Worst method (BWM). The proposed approach provides a flexible and convenient way to depict the experts’ hesitant opinions especially in group decision-making context through a straightforward procedure. The proposed approach is called IT2HF-BWM. Some numerical case studies from literature have been used to provide illustrations about the feasibility and effectiveness of our proposed approach. Besides, a comparative analysis with an interval type-2 fuzzy AHP is carried out to evaluate the results of our proposed approach. In each case, the consistency ratio was calculated to determine the reliability of results. The findings imply that the proposed approach not only provides acceptable results but also outperforms the traditional BWM and its type-1 fuzzy extension.

Type–reduction of Interval Type–2 fuzzy numbers via the Chebyshev inequality

2021 ◽  
Author(s):  
Juan Carlos Figueroa-García ◽  
Heriberto Román-Flores ◽  
Yurilev Chalco-Cano
Keyword(s):  
Fuzzy Numbers ◽  
Chebyshev Inequality ◽  
Type Reduction ◽  
Interval Type

scholarly journals Selection of solar tracking system using extended TOPSIS technique with interval type-2 pythagorean fuzzy numbers

2021 ◽  
Author(s):  
Rimsha Umer ◽  
Muhammad Touqeer ◽  
Abdullah Hisam Omar ◽  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
...  
Keyword(s):  
Fuzzy Numbers ◽  
Tracking System ◽  
Weighted Averaging ◽  
Distance Method ◽  
Novel Approach ◽  
Solar Tracking ◽  
Interval Type ◽  
Topsis Technique ◽  
Pythagorean Fuzzy Numbers

AbstractThe Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is considered among the most frequently used techniques to deal with multi-criteria group decision-making (MCGDM) conflicts. In this article, we have presented an extended TOPSIS technique in the framework of interval type-2 trapezoidal Pythagorean fuzzy numbers (IT2TrPFN). We first projected a novel approach to evaluate the distance between them using ordered weighted averaging operator and $$(\alpha ,\beta )$$ ( α , β ) -cut. Subsequently, we widen the concept of TOPSIS method formed on the distance method with IT2TrPFNs and applied it on MCGDM dilemma by considering the attitudes and perspectives of the decision-makers. Lastly, an application of solar tracking system and numerous contrasts with the other existing techniques are presented to express the practicality and feasibility of our projected approach.

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