scholarly journals Oriented Fuzzy Numbers vs. Fuzzy Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 523
Author(s):  
Krzysztof Piasecki ◽  
Anna Łyczkowska-Hanćkowiak
Keyword(s):  
Real World ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Formal Model ◽  
Original Study ◽  
Portfolio Analysis ◽  
Algebraic Structures ◽  
Equivalent Models ◽  
Real World Problems

A formal model of an imprecise number can be given as, inter alia, a fuzzy number or oriented fuzzy numbers. Are they formally equivalent models? Our main goal is to seek formal differences between fuzzy numbers and oriented fuzzy numbers. For this purpose, we examine algebraic structures composed of numerical spaces equipped with addition, dot multiplication, and subtraction determined in a usual way. We show that these structures are not isomorphic. It proves that oriented fuzzy numbers and fuzzy numbers are not equivalent models of an imprecise number. This is the first original study of a problem of a dissimilarity between oriented fuzzy numbers and fuzzy numbers. Therefore, any theorems on fuzzy numbers cannot automatically be extended to the case of oriented fuzzy numbers. In the second part of the article, we study the purposefulness of a replacement of fuzzy numbers by oriented fuzzy numbers. We show that for a portfolio analysis, oriented fuzzy numbers are more useful than fuzzy numbers. Therefore, we conclude that oriented fuzzy numbers are an original and useful tool for modelling a real-world problems.

scholarly journals The Use of Trapezoidal Oriented Fuzzy Numbers in Portfolio Analysis

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1722
Author(s):  
Anna Łyczkowska-Hanćkowiak
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Portfolio Analysis ◽  
Discount Factor ◽  
Weighted Sum ◽  
Investment Portfolio ◽  
Present Value ◽  
Discount Factors ◽  
Theoretical Considerations

Oriented fuzzy numbers are a convenient tool to manage an investment portfolio as they enable the inclusion of uncertain and imprecise information about the financial market in a portfolio analysis. This kind of portfolio analysis is based on the discount factor. Thanks to this fact, this analysis is simpler than a portfolio analysis based on the return rate. The present value is imprecise due to the fact that it is modelled with the use of oriented fuzzy numbers. In such a case, the expected discount factor is also an oriented fuzzy number. The main objective of this paper is to conduct a portfolio analysis consisting of the instruments with the present value estimated as a trapezoidal oriented fuzzy number. We consider the portfolio elements as being positively and negatively oriented. We test their discount factor. Due to the fact that adding oriented fuzzy numbers is not associative, a weighted sum of positively oriented discount factors and a weighted sum of negatively oriented factors is calculated and consequently a portfolio discount factor is obtained as a weighted addition of both sums. Also, the imprecision risk of the obtained investment portfolio is estimated using measures of energy and entropy. All theoretical considerations are illustrated by an empirical case study.

scholarly journals Calculating the Fuzzy Project Network Critical Path

2012 ◽  
Vol 1 (2) ◽  
pp. 58 ◽  
Author(s):  
Nasser Shahsavari Pour ◽  
Samira Zeynali ◽  
Mansoor Kheradmand
Keyword(s):  
Real World ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Special Importance ◽  
Activity Time ◽  
Simple Method ◽  
Project Completion ◽  
Project Network ◽  
Ranking Of Fuzzy Numbers

A project network consists of various activities. To determine the length of project time and the amount of the needed sources, the time of project completion must correctly and exactly be calculated, so the critical path is calculated. The activities on this path have no floating. It means that there is no delay on these activities. As a result the calculation of the critical path in a project network has a special importance. In this paper a simple method for calculation the critical path is proposed. Assignment an exact time on any activity in real world is not correct; So the fuzzy and uncertainty theories are used to assigned a length of time on any activities. In the present study the trapezoidal fuzzy numbers are assigned to the length of activity time, and the total time of the project is also a fuzzy number. In addition, to compare the fuzzy numbers, ranking of fuzzy numbers are used. Finally a practical example will show the efficiency of the method.

NEAREST SYMMETRIC TRAPEZOIDAL FUZZY NUMBER APPROXIMATION PRESERVING EXPECTED INTERVAL

2013 ◽  
Vol 21 (05) ◽  
pp. 777-794 ◽  
Author(s):  
C. VEERAMANI ◽  
C. DURAISAMY ◽  
M. SUMATHI
Keyword(s):  
Real World ◽  
Fuzzy Number ◽  
Trapezoidal Fuzzy Number ◽  
Fuzzy Partition ◽  
Real World Problems

Fuzzy number approximation has been investigated by many researchers. It is still useful to develop new approximations in order to better fit real world problems. This paper proposes a method for symmetric trapezoidal fuzzy number approximation which preserves the expected interval. Some properties of approximation are proved and a fuzzy partition is generated by using the proposed method.

scholarly journals The Pentagonal Fuzzy Number:Its Different Representations, Properties, Ranking, Defuzzification and Application in Game Problems

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 248 ◽  
Author(s):  
Avishek Chakraborty ◽  
Sankar Prasad Mondal ◽  
Shariful Alam ◽  
Ali Ahmadian ◽  
Norazak Senu ◽  
...  
Keyword(s):  
Real World ◽  
Level Sets ◽  
Fuzzy Numbers ◽  
Evaluation Process ◽  
Game Problem ◽  
Ranking Method ◽  
Membership Functions ◽  
Linear And Nonlinear ◽  
Interval Valued ◽  
Real World Problems

In this paper, different measures of interval-valued pentagonal fuzzy numbers (IVPFN) associated with assorted membership functions (MF) were explored, considering significant exposure of multifarious interval-valued fuzzy numbers in neoteric studies.Also, the idea of MF is generalized somewhat to nonlinear membership functions for viewing the symmetries and asymmetries of the pentagonal fuzzy structures. Accordingly,the construction of level sets, for each case of linear and nonlinear MF was also carried out. Besides, defuzzification was undertaken using three methods and a ranking method, which were also the main features of this framework.The developed intellects were implemented in a game problem by taking the parameters as PFNs, ultimately resulting in a new direction for modeling real world problems and to comprehend the uncertainty of the parameters more precisely in the evaluation process.

scholarly journals Z-Distance Based IF-THEN Rules

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
R. A. Aliev ◽  
O. H. Huseynov ◽  
R. X. Zulfugarova
Keyword(s):  
Decision Making ◽  
Real World ◽  
Imperfect Information ◽  
Fuzzy Numbers ◽  
Approximate Reasoning ◽  
Suggested Approach ◽  
Psychological Issues ◽  
First Time ◽  
Real World Problems

Decision making, reasoning, and analysis in real-world problems are complicated by imperfect information. Real-world imperfect information is mainly characterized by two features. In view of this, Professor Zadeh suggested the concept of aZ-number as an ordered pairZ=(A,B)of fuzzy numbersAandB, the first of which is a linguistic value of a variable of interest, and the second one is a linguistic value of probability measure of the first one, playing a role of its reliability. The concept of distance is one of the important concepts for handling imperfect information in decision making and reasoning. In this paper, we, for the first time, apply the concept of distance ofZ-numbers to the approximate reasoning withZ-number based IF-THEN rules. We provide an example on solving problem related to psychological issues naturally characterized by imperfect information, which shows applicability and validity of the suggested approach.

scholarly journals Handrails through the Swamp? A Pilot to Test the Integration and Implementation Science Framework in Complex Real-World Research

2021 ◽  
Vol 13 (10) ◽  
pp. 5491
Author(s):  
Melissa Robson-Williams ◽  
Bruce Small ◽  
Roger Robson-Williams ◽  
Nick Kirk
Keyword(s):  
Pilot Study ◽  
Case Studies ◽  
Implementation Science ◽  
Real World ◽  
Environmental Problems ◽  
Environmental Research ◽  
Integrative Framework ◽  
The World ◽  
Science Framework ◽  
Real World Problems

The socio-environmental challenges the world faces are ‘swamps’: situations that are messy, complex, and uncertain. The aim of this paper is to help disciplinary scientists navigate these swamps. To achieve this, the paper evaluates an integrative framework designed for researching complex real-world problems, the Integration and Implementation Science (i2S) framework. As a pilot study, we examine seven inter and transdisciplinary agri-environmental case studies against the concepts presented in the i2S framework, and we hypothesise that considering concepts in the i2S framework during the planning and delivery of agri-environmental research will increase the usefulness of the research for next users. We found that for the types of complex, real-world research done in the case studies, increasing attention to the i2S dimensions correlated with increased usefulness for the end users. We conclude that using the i2S framework could provide handrails for researchers, to help them navigate the swamps when engaging with the complexity of socio-environmental problems.

scholarly journals Combined Games with Randomly Delayed Beginnings

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 534
Author(s):  
F. Thomas Bruss
Keyword(s):  
Discrete Time ◽  
Real World ◽  
Optimal Stopping ◽  
Random Variables ◽  
Approximate Solutions ◽  
Real World Problems

This paper presents two-person games involving optimal stopping. As far as we are aware, the type of problems we study are new. We confine our interest to such games in discrete time. Two players are to chose, with randomised choice-priority, between two games G1 and G2. Each game consists of two parts with well-defined targets. Each part consists of a sequence of random variables which determines when the decisive part of the game will begin. In each game, the horizon is bounded, and if the two parts are not finished within the horizon, the game is lost by definition. Otherwise the decisive part begins, on which each player is entitled to apply their or her strategy to reach the second target. If only one player achieves the two targets, this player is the winner. If both win or both lose, the outcome is seen as “deuce”. We motivate the interest of such problems in the context of real-world problems. A few representative problems are solved in detail. The main objective of this article is to serve as a preliminary manual to guide through possible approaches and to discuss under which circumstances we can obtain solutions, or approximate solutions.

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