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Fuzzy subalgebra

About: Fuzzy subalgebra is a research topic. Over the lifetime, 4231 publications have been published within this topic receiving 95282 citations.


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Book ChapterDOI
01 Jan 2002
TL;DR: This paper presents their overview encompassing scalar approaches as well as approaches in which cardinalities of fuzzy sets are themselves fuzzy sets of usual cardinals.
Abstract: Cardinality, one of the most basic characteristics of a fuzzy set, is a notion having many applications. One of them is elementary probability theory of imprecise events. Fuzzy and nonfuzzy approaches to probabilities of events like “a ball drawn at random from an urn containing balls of various sizes is large” do require an appropriate notion of the cardinality of a fuzzy set, e.g. of the fuzzy set of large balls in an urn. Contemporary fuzzy set cardinality theory offers a variety of options, including the use of triangular norms. This paper presents their overview encompassing scalar approaches as well as approaches in which cardinalities of fuzzy sets are themselves fuzzy sets of usual cardinals.
Posted Content
TL;DR: The major part of this thesis deals with fuzzy geometric Logic and fuzzy geometric logic with graded consequence and categorical relationship with fuzzy topology and frame is discussed in detail.
Abstract: The major part of this thesis deals with fuzzy geometric logic and fuzzy geometric logic with graded consequence. The first chapter mainly contains the concept of topological system introduced by S. Vickers in 1989. In Chapter 2 the notion of fuzzy topological system is introduced and categorical relationship with fuzzy topology and frame is discussed in detail. Also this chapter contains some methodology to make new fuzzy topological systems from the old one.Chapter 3 provides a generalization of fuzzy topological system which shall be called L topological system and categorical relationships with appropriate topological space and frame. Furthermore, two ways of constructing subspaces and subsystems of an L topological space and an L topological system are respectively provided.Chapter 4 deals with the concept of variable basis fuzzy topological space on fuzzy sets and contains a new notion of variable basis fuzzy topological systems whose underlying sets are fuzzy sets. In this chapter categorical relationship between space and system is established. Chapter 5 contains a different proof of one kind of generalized stone duality, which was done directly by Maruyama, introducing a notion of n fuzzy Boolean system. The last two chapters, Chapter 6 and Chapter 7 deal the ultimate objective. Chapter 6 deals with the question- From which logic fuzzy topology can be studied?. To answer this, the notion of fuzzy geometric logic is invented.
01 Jan 2003
TL;DR: It is proved that multi-variate fuzzy polynomials are universal approximators for multi-Variate fuzzy functions which are the extension principle of continuous real-valued function under fuzzy arithmetic operations for a distance measure that Buckley et al.(1999) used.
Abstract: In this paper, we prove that multi-variate fuzzy polynomials are universal approximators for multi-variate fuzzy functions which are the extension principle of continuous real-valued function under fuzzy arithmetic operations for a distance measure that Buckley et al.(1999) used. We also consider a class of fuzzy polynomial regression model. A mixed non-linear programming approach is used to derive the satisfying solution.
01 Jan 2013
TL;DR: The notion of fuzzy a-continuous mappings is studied, which is found to be very useful in solving many practical problems and to give several fundamental properties of fuzzyA-open sets.
Abstract: Different notions of Classical Topology which are defined through a-open sets resist a straightforward fuzzification due to the fact that unlike classical counterpart the collection of fuzzy a-open sets does not make a fuzzy topology in the sense of Chang. Expecting such interesting deviations, in this paper we study the notion of fuzzy a-continuous mappings. We first give several fundamental properties of fuzzy a-open sets. Using these results different characterizations of fuzzy a-continuous, fuzzy almost a-continuous and fuzzy semi-weakly continuous mappings have been obtained. Keywords: Fuzzy a-continuous mappings; Fuzzy a-open mappings; Fuzzy almost a-continuous mappings; Fuzzy semi-weakly continuous mappings; 1. Introduction The study of fuzzy sets was initiated by Zadeh [17] in 1965. Thereafter the paper of Chang [4] in 1968 paved way for the subsequent tremendous growth of the numerous fuzzy topological concepts. Recently Fuzzy Topology has been found to be very useful in solving many practical problems. Shihong Du
Proceedings ArticleDOI
07 Aug 2013
TL;DR: This paper proposes a justification of solvability of systems that are modified with “at least” (“at most”) quantifiers and shows that the respectively modified fuzzy sets are upper (lower) sets of a fuzzy preorder on the space of reals.
Abstract: In this paper, we utilize the theory of solvability of systems of fuzzy relation equations in a space with fuzzy preorder and propose a justification of solvability of systems that are modified with “at least” (“at most”) quantifiers. We show that the respectively modified fuzzy sets are upper (lower) sets of a fuzzy preorder on the space of reals. On the basis of this, we show that the systems with the sup ∗ composition and with the same type of modifications on both sides are solvable. Moreover, we explain why the solvability of the similarly modified systems with the inf →composition cannot be established. Last but not least we show that only opposite modifications on the left and right-hand sides of the modified system with the inf →composition guarantee its solvability.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202315
202243
20218
20205
201910
201823