scholarly journals Topological Structures via Interval-Valued Neutrosophic Crisp Sets

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2050
Author(s):  
Dongsik Jo ◽  
S. Saleh ◽  
Jeong-Gon Lee ◽  
Kul Hur ◽  
Chen Xueyou
Keyword(s):  
Real World ◽  
Vanishing Point ◽  
Algebraic Structures ◽  
Quotient Topology ◽  
Topological Structures ◽  
Interval Valued

In this paper, we introduce the new notion of interval-valued neutrosophic crisp sets providing a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. We also define an interval-valued neutrosophic crisp (vanishing) point and obtain some of its properties. Next, we define an interval-valued neutrosophic crisp topology, base (subbase), neighborhood, and interior (closure), respectively and investigate some of each property, and give some examples. Finally, we define an interval-valued neutrosophic crisp continuity and quotient topology and study some of each property.

Interval-Valued Fuzzy H-Ideals on ß-Algebra

2020 ◽  
pp. 244-274
Author(s):  
Prakasam Muralikrishna ◽  
Tapan Senapati ◽  
Perumal Hemavathi
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Algebraic Structures ◽  
Interval Valued

The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzzy sets. Using interval valued fuzzy set, various algebraic structures and related topics were discussed. This chapter extends fuzzy H-ideal into interval valued fuzzy H-ideals of β-algebra and deals some related results. It also provides the study on homomorphic images of an interval valued fuzzy H-ideals of β-algebra and the idea of Cartesian product of interval valued fuzzy H-ideals of β-algebra.

scholarly journals Matrix Games with Interval-Valued 2-Tuple Linguistic Information

Games ◽  
2018 ◽  
Vol 9 (3) ◽  
pp. 62 ◽  
Author(s):  
Anjali Singh ◽  
Anjana Gupta
Keyword(s):  
Linear Programming ◽  
Lower Bound ◽  
Real World ◽  
Upper Bound ◽  
Duality Theorem ◽  
Matrix Game ◽  
Matrix Games ◽  
Linguistic Information ◽  
The Real ◽  
Interval Valued

In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is formulated to obtain the linguistic lower bound and the linguistic upper bound of the interval-valued linguistic value of such class of games. The duality theorem of LLP is also adopted to establish the equality of values of the interval linguistic matrix game for players I and II. A flowchart to summarize the proposed algorithm is also given. The methodology is then illustrated via a hypothetical example to demonstrate the applicability of the proposed theory in the real world. The designed algorithm demonstrates acceptable results in the two-player constant-sum game problems with interval-valued 2-tuple linguistic payoffs.

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.

BI-IDEALS OF ORDERED SEMIGROUPS BASED ON THE INTERVAL-VALUED FUZZY POINT

2016 ◽  
Vol 78 (2) ◽  
Author(s):  
Hidayat Ullah Khan ◽  
Nor Haniza Sarmin ◽  
Asghar Khan ◽  
Faiz Muhammad Khan
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Fuzzy Set Theory ◽  
Fuzzy Subset ◽  
Ordered Semigroups ◽  
Fuzzy Point ◽  
Interval Valued ◽  
Real World Problems

Interval-valued fuzzy set theory (advanced generalization of Zadeh's fuzzy sets) is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. In this paper, we introduce the notion of generalized quasi-coincident with () relation of an interval-valued fuzzy point with an interval-valued fuzzy set. In fact, this new concept is a more generalized form of quasi-coincident with relation of an interval-valued fuzzy point with an interval-valued fuzzy set. Applying this newly defined idea, the notion of an interval-valued -fuzzy bi-ideal is introduced. Moreover, some characterizations of interval-valued -fuzzy bi-ideals are described. It is shown that an interval-valued -fuzzy bi-ideal is an interval-valued fuzzy bi-ideal by imposing a condition on interval-valued fuzzy subset. Finally, the concept of implication-based interval-valued fuzzy bi-ideals, characterizations of an interval-valued fuzzy bi-ideal and an interval-valued -fuzzy bi-ideal are considered. 

scholarly journals An Extension of Fuzzy Competition Graph and Its Uses in Manufacturing Industries

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1008 ◽  
Author(s):  
Tarasankar Pramanik ◽  
G. Muhiuddin ◽  
Abdulaziz M. Alanazi ◽  
Madhumangal Pal
Keyword(s):  
Real World ◽  
Ecological Status ◽  
Manufacturing Industries ◽  
Network System ◽  
World Systems ◽  
Food Crisis ◽  
Competitive Network ◽  
Competition Graph ◽  
Interval Valued ◽  
Strength Of Competition

Competition graph is a graph which constitutes from a directed graph (digraph) with an edge between two vertices if they have some common preys in the digraph. Moreover, Fuzzy competition graph (briefly, FCG) is the higher extension of the crisp competition graph by assigning fuzzy value to each vertex and edge. Also, Interval-valued FCG (briefly, IVFCG) is another higher extension of fuzzy competition graph by taking each fuzzy value as a sub-interval of the interval [ 0 , 1 ] . This graph arises in many real world systems; one of them is discussed as follows: Each and every species in nature basically needs ecological balance to survive. The existing species depends on one another for food. If there happens any extinction of any species, there must be a crisis of food among those species which depend on that extinct species. The height of food crisis among those species varies according to their ecological status, environment and encompassing atmosphere. So, the prey to prey relationship among the species cannot be assessed exactly. Therefore, the assessment of competition of species is vague or shadowy. Motivated from this idea, in this paper IVFCG is introduced and several properties of IVFCG and its two variants interval-valued fuzzy k-competition graphs (briefly, IVFKCG) and interval-valued fuzzy m-step competition graphs (briefly, IVFMCG) are presented. The work is helpful to assess the strength of competition among competitors in the field of competitive network system. Furthermore, homomorphic and isomorphic properties of IVFCG are also discussed. Finally, an appropriate application of IVFCG in the competition among the production companies in market is presented to highlight the relevance of IVFCG.

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 An Extended TOPSIS Method with Unknown Weight Information in Dynamic Neutrosophic Environment

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 401 ◽  
Author(s):  
Nguyen Tho Thong ◽  
Luong Thi Hong Lan ◽  
Shuo-Yan Chou ◽  
Le Hoang Son ◽  
Do Duc Dong ◽  
...  
Keyword(s):  
Real World ◽  
Human Life ◽  
Decision Makers ◽  
Decision Problems ◽  
Distance Measures ◽  
Neutrosophic Set ◽  
Topsis Method ◽  
Correlation Measure ◽  
The Times ◽  
Interval Valued

Decision-making activities are prevalent in human life. Many methods have been developed to address real-world decision problems. In some practical situations, decision-makers prefer to provide their evaluations over a set of criteria and weights. However, in many real-world situations, problems include a lack of weight information for the times, criteria, and decision-makers (DMs). To remedy such discrepancies, an optimization model has been proposed to determine the weights of attributes, times, and DMs. A new concept related to the correlation measure and some distance measures for the dynamic interval-valued neutrosophic set (DIVNS) are defined in this paper. An extend Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method in the interval-valued neutrosophic set with unknown weight information in dynamic neutrosophic environments is developed. Finally, a practical example is discussed to illustrate the feasibility and effectiveness of the proposed method.

scholarly journals Method of Camera Calibration Using Concentric Circles and Lines through Their Centres

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Yue Zhao ◽  
Xuechun Wang ◽  
Fengli Yang
Keyword(s):  
Camera Calibration ◽  
Real World ◽  
Cross Ratio ◽  
Lens Distortion ◽  
Vanishing Point ◽  
Vanishing Points ◽  
Novel Method ◽  
Ideal Points ◽  
Concentric Circles ◽  
The Ideal

A novel method for camera calibration is proposed based on an analysis of lens distortion in camera imaging. In the method, a line through the centre of concentric circles is used as a template in which orthogonal directions can be determined from an angle of circumference that corresponds to a diameter. By using three lines through the centre of concentric circles, based on the invariance of the cross-ratio, an image at the centre of the concentric circles can be used to obtain the vanishing point. The intrinsic parameters of the camera can be computed based on the constraints of the orthogonal vanishing points and the imaged absolute conic. The lens distortion causes points in the template to have a position offset. In the proposed method, we optimize the positions of the distortion points such that they gradually approach those of the ideal points. The simulated and real-world experiments demonstrate that the proposed method is efficient and feasible.

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