Design of single and double acceptance sampling plans based on interval type-2 fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Gürkan Işık ◽  
İhsan Kaya
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Measurement Errors ◽  
Uncertainty Modeling ◽  
Characteristic Functions ◽  
Acceptance Sampling ◽  
Sampling Plans ◽  
Acceptance Sampling Plans ◽  
Interval Type

Defectiveness of items is generally considered as a certain value in acceptance sampling plans (ASPs). It is clear that, it may not be certainly known in some real-case problems. Uncertainties of the inspection process such as measurement errors, inspectors’ hesitancies or vagueness of the process etc. should be taken into account to obtain more reliable results. The fuzzy set theory (FST) is one of the best methods to overcome these problems. There are some studies in the literature formulating the ASPs with the help of FST. Deciding the right membership functions of the fuzzy sets (FSs) has a vital importance on the quality of the uncertainty modeling. Additionally, the fuzzy set extensions have been offered to model more complicated uncertainties to achieve better modeling. As one of these extensions, type-2 fuzzy sets (T2FSs) gives an ability to model uncertainty in situations where it is not possible to determine exact membership function parameters. In this study, single and double ASPs based on interval T2FSs (IT2FSs) have been designed for binomial and Poisson distributions. Thus, it becomes possible to make more flexible, sensitive and descriptive sensitivity analyzes. The main characteristic functions of ASPs have been derived and the suggested formulations have been illustrated on a comparative application from manufacturing process. Results allowing for more comprehensive analysis as against to the traditional and T1FSs based plans have been obtained.

Design of single and double acceptance sampling plans based on neutrosophic sets

2021 ◽  
pp. 1-18
Author(s):  
Gürkan Işik ◽  
İhsan Kaya
Keyword(s):  
Fuzzy Set ◽  
Acceptance Sampling ◽  
Good Representation ◽  
Neutrosophic Sets ◽  
Defective Items ◽  
Sample Number ◽  
Sampling Plans ◽  
Acceptance Sampling Plans ◽  
Different Sources ◽  
Average Sample

Although traditional acceptance sampling plans (ASPs) need certain mass quality characteristics, it is not easy to define them as crisp value in some real case problems. The fuzzy set theory (FST) is one of the popular techniques to model uncertainties of the process and therefore fuzzy ASPs have been offered in the literature. Fuzzy set extensions have been proposed recently for better modeling of the uncertainties having different sources and characteristics. One of these extensions named neutrosophic sets (NSs) can be used to increase the sensitiveness and flexibility of ASPs. The ASPs based on NSs can give ability to classify the items as defective, non-defective and indeterminate. Since the operator can become indecisive for slightly defective items, these plans can provide a good representation of human evaluations under uncertainty. In this study, single and double ASPs are designed based on NSs by using binomial and poisson distributions that are also re-analyzed based on NSs. For this aim, some characteristics functions of ASPs such as probability of accepting a lot (Pa), average outgoing quality (AOQ), average total inspection (ATI) and average sample number (ASN) have also been analyzed based on NSs. Numerical examples are presented to analyze the proposed plans.

A Comparative Investigation of Type-2 Fuzzy Sets, Nonstationary Fuzzy Sets and Cloud Models

2016 ◽  
Vol 24 (02) ◽  
pp. 213-227 ◽  
Author(s):  
Han-Chen Huang ◽  
Xiaojun Yang
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Cloud Model ◽  
Comparative Investigation ◽  
Mathematical Methods ◽  
Moderate Amount ◽  
Cloud Models ◽  
Interval Type

Since Zadeh introduced fuzzy sets, a lot of extensions of this concept have been proposed, such as type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models, to represent higher levels of uncertainty. This paper provides a comparative investigation of type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models. Type-2 fuzzy sets study the fuzziness of the membership function (MF) using primary MF and secondary MF based on analytic mathematical methods; nonstationary fuzzy sets study the randomness of the MF using primary MF and variation function based on type-1 fuzzy sets theory; cloud models study the randomness of the distribution of samples in the universe and generate random membership grades (MGs) using two random variables based on probability and statistic mathematical methods. They all concentrate on dealing with the uncertainty of the MF or the MG which type-1 fuzzy sets do not consider, and thus have many similarities. Moreover, we find out that, the same qualitative concept “moderate amount” can be represented by an interval type-2 fuzzy set, a nonstationary fuzzy set or a normal cloud model, respectively. Then, we propose a unified mathematical expression for the interval type-2 fuzzy set, nonstationary fuzzy set and normal cloud model. On the other hand, we also find out that, the theory fundament and underlying motivations of these models are quite different. Therefore, We summarize detailed comparisons of distinctive properties of type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models. Further, we study their diverse characteristics of distributions of MGs across vertical slices. The comparative investigation shows that these models are complementary to describe the uncertainty from different points of view. Thus, this paper provides a fundamental contribution and makes a basic reference for knowledge representation and other applications with uncertainty.

Assessment of national innovation capabilities of OECD countries using trapezoidal interval type-2 fuzzy ELECTRE III method

2020 ◽  
Author(s):  
Geetha Selvaraj ◽  
Jeonghwan Jeon
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Research Work ◽  
Oecd Countries ◽  
Content Type ◽  
Electre Iii ◽  
Standard Values ◽  
Interval Type ◽  
Credibility Degree

PurposeFor a nation to become a superpower, it's scientific and technological advancement is essential. Each country is exploring how to improve themselves in terms of science and technology. The authors analyzed the innovation capabilities of 35 OECD countries that have not recently joined Lithuania.Design/methodology/approachIn recent years, a lot of research work has been done on trapezoidal interval type-2 fuzzy sets (TIT-2 FS), and many research works have been published. The trapezoidal interval type-2 fuzzy set helps effectively to represent the uncertainty comparatively than the type-1 fuzzy set. Taking advantage of this effectiveness, the authors extend the best multi-criteria decision making method (MCDM) for trapezoidal interval type-2 fuzzy sets. Here, ELimination and Choice Expressing REality III (ELECTRE III) method in the trapezoidal interval type-2 fuzzy set environment is proposed.FindingsThis analysis helps to the OECD countries to develop their level of innovation in the criteria. The authors are making this evaluation for the year 2018 based on the 31 criteria. Application of the proposed method expressed by evaluation of the national innovation capability problem. Based on the obtained results, the top five countries are United States, Switzerland, Canada, Germany and Japan.Originality/valueThe authors collected required data from different available data sources like OECD, IMD, USPTO, ITU and surveyed data reported by KISTEP. After collecting all the data from different sources, the authors calculated the standard values as KISTEP. After converting the standard values into trapezoidal interval type-2 fuzzy values, the authors construct a decision matrix based on these values. Then, the authors determined the possibility mean values and preference. Then, they calculated the concordance and discordance credibility degree values. Finally, they ranked OECD countries by the net credibility degree. The results are computed by using the MATLAB software.

An Entropy of Interval Type-2 Fuzzy Sets

2013 ◽  
Vol 321-324 ◽  
pp. 1999-2003 ◽  
Author(s):  
Gao Zheng ◽  
Shi Wei Yin
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Entropy ◽  
Calculation Formula ◽  
Membership Functions ◽  
Axiomatic Definition ◽  
Fuzzy Degree ◽  
Interval Type

The entropy shows the fuzzy degree of a fuzzy set (FS) and can be used in various areas. Aiming at the characteristics of the fuzzy entropy and type-2 fuzzy sets (IT2 FSs), we introduce a new entropy of IT2 FSs in this paper. At first, we select an axiomatic definition for it. Then, considering a fact that the operations of IT2 FSs depend on the upper membership functions (UMFs) and lower membership functions (LMFs), we propose a calculation formula and verify it accords with the four axioms of the selected definition. Finally, we use an example to illuminate its reasonable performance.

scholarly journals Reliability Test Plan for an Extended Birnbaum-Saunders Distribution

2021 ◽  
Author(s):  
Jiju Gillariose ◽  
Lishamol Tomy
Keyword(s):  
Operating Characteristic ◽  
Optimal Number ◽  
Characteristic Functions ◽  
Acceptance Sampling ◽  
Sampling Plans ◽  
Lifetime Test ◽  
Acceptance Sampling Plans ◽  
Mean Lifetime ◽  
The Mean ◽  
Termination Time

Birnbaum-Saunders distribution has been widely studied in statistical literature because this distribution accommodates several interesting properties. The purpose of this paper is to introduce a new parametric distribution based on the Birnbaum-Saunders model and develop a new acceptance sampling plans for derived extended Birnbaum-Saunders distribution when the mean lifetime test is truncated at a predetermined time. For various acceptance numbers, confidence levels and values of the ratio of the fixed experimental time to the specified mean life, the minimum sample size necessary to assure a specified mean lifetime worked out. The results are illustrated by a numerical example. The operating characteristic functions of the sampling plans and producer’s risk and the ratio of true mean life to a specified mean life that ensures acceptance with a pre-assigned probability are tabulated. This paper presents relevant characteristics of the new distribution and a new acceptance sampling plans when the lifetime of a product adopts an extended Birnbaum-Saunders distribution. Based on this study, the optimal number of testers demanded is decreases as test termination time increases. Moreover, the operating characteristic values increases as the mean life ratio increases, which indicate that items with increased mean life will be accepted with higher probability compared with items with lower mean life ratio.

Representing a probabilistic linguistic term set with an interval type-2 fuzzy set and the application in green supplier selection

2021 ◽  
pp. 1-18
Author(s):  
Le Jiang ◽  
Hongbin Liu
Keyword(s):  
Decision Making ◽  
Membership Function ◽  
Fuzzy Set ◽  
Supplier Selection ◽  
Symbolic Model ◽  
Green Supplier Selection ◽  
Linguistic Term ◽  
Interval Type ◽  
Decision Making Model

The use of probabilistic linguistic term sets (PLTSs) means the process of computing with words. The existing methods computing with PLTSs mainly use symbolic model. To provide a semantic model for computing with PLTSs, we propose to represent a PLTS by using an interval type-2 fuzzy set (IT2FS). The key step is to compute the footprint of uncertainty of the IT2FS. To this aim, the upper membership function is computed by aggregating the membership functions of the linguistic terms contained in the PLTS, and the lower membership function is obtained by moving the upper membership function downward with the step being total entropy of the PLTS. The comparison rules, some operations, and an aggregation operator for PLTSs are introduced. Based on the proposed method of computing with PLTSs, a multi-criteria group decision making model is introduced. The proposed decision making model is then applied in green supplier selection problem to show its feasibility.

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