An Extended Relational Model & SQL for Fuzzy Multidatabases

2011 ◽  
pp. 185-219
Author(s):  
Awadhesh Kumar Sharma ◽  
A. Goswami ◽  
D.K. Gupta
Keyword(s):  
Query Processing ◽  
Fuzzy Sets ◽  
Real World ◽  
Relational Model ◽  
Ambiguous Information ◽  
Fuzzy Query ◽  
Algebraic Properties ◽  
Recent Trends ◽  
Real World Problems

Many real world problems involve imprecise and ambiguous information rather than crisp information. Recent trends in the database paradigm are to incorporate fuzzy sets to tackle imprecise and ambiguous information of real world problems. Fuzzy query processing in multidatabases have been extensively studied, however, the same has rarely been addressed for fuzzy multidatabases. This chapter attempts to extend the SQL to formulate a global fuzzy query on a fuzzy multidatabase under FTS relational model discussed earlier. The chapter provides architecture for distributed fuzzy query processing with a strategy for fuzzy query decomposition and optimization. Proofs of consistent global fuzzy operations and some of algebraic properties of FTS Relational Model are also supplemented.

scholarly journals An Approach to Increase the Sustainability of Projects and their Outcomes in Public Sector through Improving Project Definition

2020 ◽  
Vol 12 (12) ◽  
pp. 4804 ◽  
Author(s):  
Dorota Kuchta ◽  
Jagoda Mrzygłocka-Chojnacka
Keyword(s):  
Public Sector ◽  
Fuzzy Sets ◽  
Real World ◽  
Project Success ◽  
Bottom Line ◽  
Systematic Analysis ◽  
Ambiguous Information ◽  
Sufficient Degree ◽  
Project Sustainability ◽  
Sustainability Principles

The pressure to incorporate sustainability principles and objectives into policies and activities is growing, particularly in project management. A successful project cannot disregard any of the three triple bottom line (TBL) sustainability pillars (economic, social and environmental). Stakeholders representing each of those pillars have to be satisfied to a certain degree in each successful project, even if the way of balancing the three pillars varies depending on project type. Project definition is of primary importance for the proper addressing of stakeholder expectations during the project, and thus for project success. The problem is that project definitions in practice are not written in a way which would guarantee a sufficient degree of project sustainability. However, the hypothesis can be formulated that a systematic analysis and modification of project definition can increase the degree of project sustainability, and thus the degree of project success. That is why we propose here a method of checking and improving existing project definitions in order to improve the chances of project success through increasing the satisfaction of the stakeholders representing the three TBL pillars. The method is based on a careful identification of missing and ambiguous information in a project definition and on correcting it on the basis of TBL stakeholders’ opinions and preferences. These preferences are modelled, wherever possible, by means of fuzzy sets, in order to provide a systematic, formal measurement of sustainability degree in TBL sustainability pillars, represented by project stakeholders. The method’s use and potential advantages are illustrated by means of two real world projects. The initial verification of the method allows us to formulate the hypothesis that analysing and improving project definition may considerably contribute to increasing the sustainability degree of projects, and thus to their success.

A Semantic-Ambiguity-Free Relational Model for Handling Imperfect Information1

1999 ◽  
Vol 3 (1) ◽  
pp. 3-12 ◽  
Author(s):  
Michinori Nakata ◽  
Keyword(s):  
Query Processing ◽  
Fuzzy Sets ◽  
Imperfect Information ◽  
Cartesian Product ◽  
Relational Algebra ◽  
Integrity Constraints ◽  
Relational Model ◽  
Semantic Ambiguity ◽  
Model Features ◽  
Attribute Value

An extended relational model without semantic ambiguity, called a semantic-ambiguity-free relational model, is proposed using fuzzy sets and the theory of possibility. The model features every attribute having a membership attribute whose value consists of a pair of values based on necessity and possibility measures. The membership attribute value of an attribute in a base relation is the degree to which the attribute value is compatible with integrity constraints imposed on the base relation. This clarifies the source of the membership attribute value. The model has no semantic ambiguity for interpreting membership attribute values, unlike models consisting of relations with membership attribute values attached to tuple values. We show the formulation of 8 operations - union, intersection, difference, Cartesian product, projection, join, selection, and quotient - consisting of relational algebra proposed by Codd for query processing. This approach shows how to prevent users from misinterpreting tuples in databases allowing imperfect information.

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 m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Juanjuan Chen ◽  
Shenggang Li ◽  
Shengquan Ma ◽  
Xueping Wang
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Real World ◽  
Ordinal Number ◽  
Information Uncertainty ◽  
Multi Index ◽  
Limit Process ◽  
Multi Agent ◽  
Bipolar Fuzzy Sets ◽  
Real World Problems

Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and0,12-sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion ofm-polar fuzzy set (actually,0,1m-set which can be seen as a generalization of bipolar fuzzy set, wheremis an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case ofm-polar fuzzy sets. We also give examples to show how to applym-polar fuzzy sets in real world problems.

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 L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1538-1546
Author(s):  
Xin Zhou ◽  
Liangyun Chen ◽  
Yuan Chang
Keyword(s):  
Fuzzy Sets ◽  
Homomorphic Image ◽  
Quotient Algebra ◽  
Algebraic Properties ◽  
Novikov Algebras ◽  
Fuzzy Ideal

Abstract In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal.

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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