Multi-fuzzy set theory is an extension of L-fuzzy set theory. In this paper we introduce the conc... more Multi-fuzzy set theory is an extension of L-fuzzy set theory. In this paper we introduce the concepts of multi-fuzzy topology, multi-fuzzy extension of functions, multi-fuzzy continuity and compactness. These concepts are extensions of the respective concepts in L-fuzzy set theory.
This paper introduces the concept of Atanassov intuitionistic fuzzy sets generating map AIFSGM on... more This paper introduces the concept of Atanassov intuitionistic fuzzy sets generating map AIFSGM on L-fuzzy spaces. AIFSGMs produce intuitionistic fuzzy sets from lattice valued fuzzy sets.
Multi-fuzzy set theory is an extension of fuzzy set theory and intuitionistic fuzzy set theory. I... more Multi-fuzzy set theory is an extension of fuzzy set theory and intuitionistic fuzzy set theory. In this paper we present the notion of p-complement operations of multi-fuzzy sets and their compositions with the family of multi-fuzzy operations T, S. We study the relation between various intuitionistic fuzzy operations and multi-fuzzy operations. We present some relations and operations on intuitionistic fuzzy sets in terms of multi-fuzzy operations. We discuss some multi-fuzzy operations which produce ordinary fuzzy sets or intuitionistic fuzzy sets from multi-fuzzy sets.
In this paper, we study various properties of multi-fuzzy extensions of crisp functions using ord... more In this paper, we study various properties of multi-fuzzy extensions of crisp functions using order homomorphisms, complete lattice homomorphisms, L-fuzzy lattices, and strong L-fuzzy lattices as bridge functions.
Multi-fuzzy set theory is an extension of fuzzy set theory, L-fuzzy set theory and Atanassov intu... more Multi-fuzzy set theory is an extension of fuzzy set theory, L-fuzzy set theory and Atanassov intuitionistic fuzzy set theory. In this paper we study the relation between Atanassov intuitionistic fuzzy and the proposed extension called Multi-fuzzy. Also we present the notion of Multi-fuzzy mappings and Atanassov Intuitionistic Fuzzy Sets Generating Maps. Mathematics Subject Classification: MSC: 03E72; 47S40; 08A72
In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets ... more In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T , S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multifuzzy sets, a method for obtaining Atanassov's intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov's intuitionistic fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh's fuzzy set theory, Atanassov's intuitionsitic fuzzy set theory and L-fuzzy set theory.
Multi-fuzzy set theory is an extension of fuzzy set theory, which deals with the multi dimensiona... more Multi-fuzzy set theory is an extension of fuzzy set theory, which deals with the multi dimensional fuzziness. In this paper we introduce the concepts of multi-fuzzy subgroups and normal multi-fuzzy subgroups. Mathematics Subject Classification: MSC: 20N25; 03E72; 08A72
Multi-fuzzy extension of crisp functions using bridge functions
In this paper we investigate various bridge functions like lattice homomorphisms, order homomorph... more In this paper we investigate various bridge functions like lattice homomorphisms, order homomorphisms, L-fuzzy lattices and strong L-fuzzy lattices for multi-fuzzy extensions of crisp functions and discuss properties of such multi-fuzzy extensions.
International Journal of Applied and Computational Mathematics, 2015
This paper introduces $$(I-A)^{\alpha }$$(I-A)α for every real number $$\alpha ,$$α, when A is a ... more This paper introduces $$(I-A)^{\alpha }$$(I-A)α for every real number $$\alpha ,$$α, when A is a bounded linear operator on a Banach space $${\mathbb {X}}$$X with norm of A less than 1. The principal value of $$(I-A)^{\alpha }$$(I-A)α is defined as the limit of a series in the operator norm topology. Convergence of the series is proved using the Newton’s binomial theorem and this can be regarded as a noncommutative analogue of binomial theorem. Use this to introduce the generalized notion of spectrum of a bounded operator and finally, propose a method for finding some square roots of matrices in $$M_{n}({\mathbb {C}}),$$Mn(C), the set of all $$n\times n$$n×n matrices with complex entries.
In this paper, we generalize the definition of Neutrosophic sets and present a method for extendi... more In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.
This paper discusses the properties of multi-fuzzy sets with product order and dictionary order o... more This paper discusses the properties of multi-fuzzy sets with product order and dictionary order on their membership functions. In particular the relationship between multi-fuzzy sets and other sets such as intuitionistic fuzzy sets, type-2 fuzzy sets, multisets and fuzzy multisets are studied.
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Papers by Sabu Sebastian