Use of Grey Numbers for Evaluating a System's Performance Under Fuzzy Conditions

2021 ◽  
pp. 315-331
Author(s):  
Michael Voskoglou
Keyword(s):  
Fuzzy Numbers ◽  
Mean Value ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Quality Performance ◽  
Computational Burden ◽  
The Mean ◽  
Analogous Method

In the present research, a method using Grey Numbers as tools is developed for assessing a system's mean performance, which is useful when utilizing qualitative grades and not numerical scores for this purpose. Although this new method is proved to be equivalent with an analogous method using Triangular Fuzzy Numbers as tools developed in an earlier work, it reduces the required computational burden, since it requires the calculation of two components only (instead of three in the case of the Triangular Fuzzy Numbers) for obtaining the mean value of the Grey Numbers involved. Examples are also presented on student and athlete assessment illustrating the new method and showing that the system's quality performance, calculated by the traditional GPA index, may lead to different assessment conclusions.

scholarly journals Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
P. Phani Bushan Rao ◽  
N. Ravi Shankar
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Satisfactory Result ◽  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Distance Method ◽  
Fuzzy Environment ◽  
Index Of Optimism

Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking fuzzy numbers based on the Circumcenter of Centroids and uses an index of optimism to reflect the decision maker's optimistic attitude and also an index of modality that represents the neutrality of the decision maker. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of 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 A New Method for Fuzzy Ranking Based on Possibility and Necessity Measures

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Ranking

In this paper, a new method to rank fuzzy numbers is presented. The proposed method based on Possibility and Necessity Measures is called PNM. According to possibility and necessity measures, eight indexes are calculated to extract four rules to rank fuzzy numbers. Also a method to evaluate each rule validation especially when rules’ outcomes yield conflict conclusions is presented. To test PNM performance, some controversial triangular fuzzy numbers are considered. Additionally, four extracted rules are compared with each other and fully analyzed. Furthermore, PNM is compared with other recently proposed methods. Results confirm that PNM is capable to rank a variety of fuzzy numbers and their images with any selected bandwidths, interval and any degree of closeness

scholarly journals New Method to Calculate the Level of Consistency of the Pauli & Kraepelin Tests

2018 ◽  
Author(s):  
Sigit Haryadi ◽  
Salma Huda California
Keyword(s):  
Mean Value ◽  
The Other ◽  
New Method ◽  
Other Hand ◽  
The Mean ◽  
Different Levels ◽  
Made In

In this paper, we proposed a modification of the measurement of the personality consistency level of the Pauli & Kraepelin Test in the field of psychology, using the formula made in April 2016, by Sigit Haryadi, and named "the Harmony in Gradation" or “the Haryadi Index”. The purpose of this proposal is because the existing formula uses only the mean value of the deviation, which leads to the possibility that the result of consistency measurement on people whose facts are different levels of consistency will be considered to have the same consistency level, on the other hand, the proposed method will be more accurate and precise in terms of providing an assessment of the level of personality consistency of a person.

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.

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.

A NEW METHOD FOR RANKING TRIANGULAR FUZZY NUMBERS

2012 ◽  
Vol 20 (05) ◽  
pp. 729-740 ◽  
Author(s):  
EMRAH AKYAR ◽  
HANDAN AKYAR ◽  
SERKAN ALİ DÜZCE
Keyword(s):  
Decision Making ◽  
Risk Analysis ◽  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Application Systems ◽  
Systems Control

The ranking and comparing of fuzzy numbers have important practical uses, such as in risk analysis problems, decision-making, optimization, forecasting, socioeconomic systems, control and certain other fuzzy application systems. Several methods for ranking fuzzy numbers have been widely-discussed though most of them have shortcomings. In this paper, we present a new method for ranking triangular fuzzy numbers based on their incenter and inradius. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method.

scholarly journals A New Method for Defuzzification and Ranking of Fuzzy Numbers Based on the Statistical Beta Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
A. Rahmani ◽  
F. Hosseinzadeh Lotfi ◽  
M. Rostamy-Malkhalifeh ◽  
T. Allahviranloo
Keyword(s):  
Beta Distribution ◽  
Granular Computing ◽  
Fuzzy Numbers ◽  
Mean Value ◽  
Human Reasoning ◽  
Fuzzy Information ◽  
Numerical Examples ◽  
Novel Method ◽  
The Mean ◽  
Ranking Of Fuzzy Numbers

Granular computing is an emerging computing theory and paradigm that deals with the processing of information granules, which are defined as a number of information entities grouped together due to their similarity, physical adjacency, or indistinguishability. In most aspects of human reasoning, these granules have an uncertain formation, so the concept of granularity of fuzzy information could be of special interest for the applications where fuzzy sets must be converted to crisp sets to avoid uncertainty. This paper proposes a novel method of defuzzification based on the mean value of statistical Beta distribution and an algorithm for ranking fuzzy numbers based on the crisp number ranking system on R. The proposed method is quite easy to use, but the main reason for following this approach is the equality of left spread, right spread, and mode of Beta distribution with their corresponding values in fuzzy numbers within(0,1)interval, in addition to the fact that the resulting method can satisfy all reasonable properties of fuzzy quantity ordering defined by Wang et al. The algorithm is illustrated through several numerical examples and it is then compared with some of the other methods provided by literature.

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