Classification of Ordered Semigroups in Terms of Generalized Interval-Valued Fuzzy Interior Ideals

2016 ◽  
Vol 25 (2) ◽  
pp. 297-318
Author(s):  
Hidayat Ullah Khan ◽  
Nor Haniza Sarmin ◽  
Asghar Khan ◽  
Faiz Muhammad Khan
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Decision Making Process ◽  
Ordered Semigroup ◽  
New Approach ◽  
Ordered Semigroups ◽  
Applied Fields ◽  
Interval Valued

AbstractSeveral applied fields dealing with decision-making process may not be successfully modeled by ordinary fuzzy sets. In such a situation, the interval-valued fuzzy set theory is more applicable than the fuzzy set theory. Using a new approach of “quasi-coincident with relation”, which is a central focused idea for several researchers, we introduced the more general form of the notion of (α,β)-fuzzy interior ideal. This new concept is called interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal of ordered semigroup. As an attempt to investigate the relationships between ordered semigroups and fuzzy ordered semigroups, it is proved that in regular ordered semigroups, the interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy ideals and interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals coincide. It is also shown that the intersection of non-empty class of interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals of an ordered semigroup is also an interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal.

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 A method for classification of red, blue, and green galaxies using fuzzy set theory

2020 ◽  
Vol 499 (1) ◽  
pp. L31-L35
Author(s):  
Biswajit Pandey
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Sloan Digital Sky Survey ◽  
Sky Survey ◽  
Blue Galaxies ◽  
Boundary Sets ◽  
Red Galaxies

ABSTRACT Red and blue galaxies are traditionally classified using some specific cuts in colour or other galaxy properties, which are supported by empirical arguments. The vagueness associated with such cuts are likely to introduce a significant contamination in these samples. Fuzzy sets are vague boundary sets that can efficiently capture the classification uncertainty in the absence of any precise boundary. We propose a method for classification of galaxies according to their colours using fuzzy set theory. We use data from the Sloan Digital Sky Survey (SDSS) to construct a fuzzy set for red galaxies with its members having different degrees of ‘redness’. We show that the fuzzy sets for the blue and green galaxies can be obtained from it using different fuzzy operations. We also explore the possibility of using fuzzy relation to study the relationship between different galaxy properties and discuss its strengths and limitations.

Negations With Respect to Admissible Orders in the Interval-Valued Fuzzy Set Theory

2018 ◽  
Vol 26 (2) ◽  
pp. 556-568 ◽  
Author(s):  
Maria J. Asiain ◽  
Humberto Bustince ◽  
Radko Mesiar ◽  
Anna Kolesarova ◽  
Zdenko Takac
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Admissible Orders ◽  
Interval Valued

Estimating facilities maintenance cost using post-occupancy evaluation and fuzzy set theory

2018 ◽  
Vol 24 (4) ◽  
pp. 449-467 ◽  
Author(s):  
Adel Alshibani ◽  
Mohammad A. Hassanain
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Maintenance Cost ◽  
New Approach ◽  
Content Type ◽  
Post Occupancy Evaluation ◽  
Complex Simulation ◽  
Alternative Approach ◽  
Facility Maintenance

Purpose The purpose of this paper is to introduce a new general approach for estimating the maintenance cost of constructed facilities. The proposed approach consists of four components, including: facility work breakdown structure; historical maintenance cost and cost contingency data of actual completed projects; feedback obtained from the post-occupancy evaluation (POE); and fuzzy set theory (FST) to define the uncertainty associated with the maintenance cost and cost contingency as an alternative approach to simulation. Design/methodology/approach Literature review of the existing methods used for estimating maintenance cost of constructed facilities was conducted to highlight the limitations of the existing methods and models. The paper then introduced a new approach in which the results obtained from POE are integrated with the estimator’s judgment in estimating maintenance cost of constructed facility. As a proof of concept, the developed approach is tested on a private school facility in the city of Khobar, Saudi Arabia. The application of the proposed approach in this case project demonstrates its applicability and features in comparison with the existing practice. Findings The application of the developed approach on a school case project demonstrated that the developed approach can provide a reliable facility maintenance cost estimate, narrow the uncertainties and vagueness associated with the estimated cost, and provide the estimator with the necessary information to conduct risk analysis with less effort, less computations and less complexity comparing with that provided by complex simulation. The results also showed that integrating POE in the estimating process can provide more accurate cost estimate with high level of confidence. Originality/value The paper presents a new approach for estimating facility maintenance cost. The developed approach introduced a new concept that assists maintenance contractors in preparing facility maintenance estimate with improved accuracy while satisfying the facility user’s needs. The proposed approach integrates the estimator’s judgment with POE to model the uncertainties associated with cost using FST as an alternative approach for complex simulation.

Decision Making in Medical Diagnosis via Distance Measures on Interval Valued Fuzzy Sets

2017 ◽  
Vol 6 (4) ◽  
pp. 63-83 ◽  
Author(s):  
Palash Dutta
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Distance Measures ◽  
Medical Documentation ◽  
Interesting Area ◽  
Interval Valued

The uncertain and sometimes vague, imprecise nature of medical documentation and information make the field of medical diagnosis is the most important and interesting area for applications of fuzzy set theory (FST), intuitionistic fuzzy set (IFS) and interval valued fuzzy set (IVFS). In this present study, first resemblance between IFS and IVFS has been established along with reviewed some existing distance measures for IFSs. Later, an attempt has been made to derive distance measures for IVFSs from IFSs and establish some properties on distance measures of IVFSs. Finally, medical diagnosis has been carried out and exhibits the techniques with a case study under this setting.

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