Attribute Implications in a Fuzzy Setting

2006 ◽  
pp. 45-60 ◽  
Author(s):  
Radim Bělohlávek ◽  
Vilém Vychodil
Keyword(s):  
Fuzzy Setting

Induced L-bornological vector spaces and L-Mackey convergence1

2021 ◽  
Vol 40 (1) ◽  
pp. 1277-1285
Author(s):  
Zhen-yu Jin ◽  
Cong-hua Yan
Keyword(s):  
Complete Lattice ◽  
Vector Spaces ◽  
Specific Description ◽  
Equivalent Characterization ◽  
Fuzzy Setting

Motivated by the concept of lattice-bornological vector spaces of J. Paseka, S. Solovyov and M. Stehlík, which extends bornological vector spaces to the fuzzy setting over a complete lattice, this paper continues to study the theory of L-bornological vector spaces. The specific description of L-bornological vector spaces is presented, some properties of Lowen functors between the category of bornological vector spaces and the category of L-bornological vector spaces are discussed. In addition, the notions and some properties of L-Mackey convergence and separation in L-bornological vector spaces are showed. The equivalent characterization of separation in L-bornological vector spaces in terms of L-Mackey convergence is obtained in particular.

scholarly journals Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management

2021 ◽  
Vol 2 (1) ◽  
pp. 105-134
Author(s):  
Zeeshan Ali ◽  
◽  
Tahir Mahmood ◽  
Kifayat Ullah ◽  
Qaisar Khan ◽  
...  
Keyword(s):  
Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Unit Interval ◽  
Pythagorean Fuzzy Set ◽  
Operational Laws ◽  
Special Cases ◽  
Supplier Chain ◽  
Valuable Procedure ◽  
Interval Valued ◽  
Fuzzy Setting

The principle of a complex interval-valued Pythagorean fuzzy set (CIVPFS) is a valuable procedure to manage inconsistent and awkward information genuine life troubles. The principle of CIVPFS is a mixture of the two separated theories such as complex fuzzy set and interval-valued Pythagorean fuzzy set which covers the truth grade (TG) and falsity grade (FG) in the form of the complex number whose real and unreal parts are the sub-interval of the unit interval. The superiority of the CIVPFS is that the sum of the square of the upper grade of the real part (also for an unreal part) of the duplet is restricted to the unit interval. The goal of this article is to explore the new principle of CIVPFS and its algebraic operational laws. By using the CIVPFSs, certain Einstein operational laws by using the t-norm and t-conorm are also developed. Additionally, we explore the complex interval-valued Pythagorean fuzzy Einstein weighted geometric (CIVPFEWG), complex interval-valued Pythagorean fuzzy Einstein ordered weighted geometric (CIVPFEOWG) operators and utilized their special cases. Moreover, a multicriteria decision-making (MCDM) technique is explored based on the elaborated operators by using the complex interval-valued Pythagorean fuzzy (CIVPF) information. To determine the consistency and reliability of the elaborated operators, we illustrated certain examples by using the explored principles. Finally, to determine the supremacy and dominance of the explored theories, the comparative analysis and graphical expressions of the developed principles are also discussed.

scholarly journals On fuzzy regular volterra spaces

10.26524/cm63 ◽  
2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Thangaraj G ◽  
Soundara Rajan S
Keyword(s):  
First Category ◽  
Dense Sets ◽  
Residual Sets ◽  
Fuzzy Setting

The aim of this paper is to introduce the concepts of regular Gδ-sets, regular Fσ-sets and regular Volterra spaces in fuzzy setting are introduced and studied. Several characterizations offuzzy regular Volterra spaces in terms of fuzzy regular Fσ-sets, fuzzy first category sets, fuzzy residual sets and fuzzy σ-nowhere dense sets are also established in this paper.

scholarly journals A comprehensive survey on formal concept analysis, its research trends and applications

2016 ◽  
Vol 26 (2) ◽  
pp. 495-516 ◽  
Author(s):  
Prem Kumar Singh ◽  
Cherukuri Aswani Kumar ◽  
Abdullah Gani
Keyword(s):  
Incomplete Data ◽  
Granular Computing ◽  
Possibility Theory ◽  
Formal Concept ◽  
Research Papers ◽  
Emerging Trends ◽  
Comprehensive Survey ◽  
Interval Valued ◽  
Fuzzy Setting ◽  
Significant Attention

AbstractIn recent years, FCA has received significant attention from research communities of various fields. Further, the theory of FCA is being extended into different frontiers and augmented with other knowledge representation frameworks. In this backdrop, this paper aims to provide an understanding of the necessary mathematical background for each extension of FCA like FCA with granular computing, a fuzzy setting, interval-valued, possibility theory, triadic, factor concepts and handling incomplete data. Subsequently, the paper illustrates emerging trends for each extension with applications. To this end, we summarize more than 350 recent (published after 2011) research papers indexed in Google Scholar, IEEE Xplore, ScienceDirect, Scopus, SpringerLink, and a few authoritative fundamental papers.

Donsker’s fuzzy invariance principle under the Lindeberg condition

2021 ◽  
Vol 71 (2) ◽  
pp. 439-454
Author(s):  
Roman Urban
Keyword(s):  
Continuous Process ◽  
Unit Interval ◽  
Partial Sums ◽  
Standard Brownian Motion ◽  
Triangular System ◽  
Fuzzy Random Variables ◽  
Support Functions ◽  
Lindeberg Condition ◽  
Fuzzy Setting ◽  
Fuzzy Random

Abstract We prove an analogue of the Donsker theorem under the Lindeberg condition in a fuzzy setting. Specifically, we consider a certain triangular system of d-dimensional fuzzy random variables { X n , i ∗ } , $\begin{array}{} \{X_{n,i}^*\}, \end{array}$ n ∈ ℕ and i = 1, 2, …, kn , which take as their values fuzzy vectors of compact and convex α-cuts. We show that an appropriately normalized and interpolated sequence of partial sums of the system may be associated with a time-continuous process defined on the unit interval t ∈ [0, 1] which, under the assumption of the Lindeberg condition, tends in distribution to a standard Brownian motion in the space of support functions.

Evidence-Based Uncertainty Modeling

2014 ◽  
pp. 54-74
Author(s):  
Tazid Ali
Keyword(s):  
Evidence Theory ◽  
Uncertainty Modeling ◽  
Possibility Theory ◽  
Dempster Shafer Theory ◽  
Uncertainty Measurement ◽  
Frame Work ◽  
Shafer Theory ◽  
Relationship Of ◽  
Different Sources ◽  
Fuzzy Setting

Evidence is the essence of any decision making process. However in any situation the evidences that we come across are usually not complete. Absence of complete evidence results in uncertainty, and uncertainty leads to belief. The framework of Dempster-Shafer theory which is based on the notion of belief is overviewed in this chapter. Methods of combining different sources of evidences are surveyed. Relationship of probability theory and possibility theory to evidence theory is exhibited. Extension of the classical Dempster-Shafer Structure to fuzzy setting is discussed. Finally uncertainty measurement in the frame work of Dempster-Shafer structure is dealt with.

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