Related papers: Fuzzy $\alpha$-cut and related structures
In this book super interval matrices using the special type of intervals of the form [0, a] are introduced. Several algebraic structures like semigroups, groups, semirings, rings, semivector spaces and vector spaces are introduced. Special…
The definition of the complement of a fuzzy subset is algebraic in nature and when it is used in the context of fuzzy topological spaces it does not share any similarity with the usual property of topological spaces that the complement of…
In this paper, we introduce a new type fuzzy boundary and study some related set theoretic identities. Further, this new type of fuzzy boundary is compared with different existing fuzzy boundaries.
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
In fuzzy theory of sets and groups, the use of $\alpha$--levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong $\alpha$--levels, it is possible to establish a one to one correspondence which makes…
The relationship between fuzzy algebras and semirings is explored with fuzzy algebra operators replacing the arithmetic operators of semirings. A new class of fuzzy structures which are similar to semirings is defined. Results of partial…
Intuitionistic fuzzy Banach algebra is introduced and a few properties of it is studied. The properties of invertible elements and relation among invertible elements, open set, closed set are emphasized. Topological divisors of zero is…
The paper aims to develop a framework for coalgebraic fuzzy geometric logic by adding modalities to the language of fuzzy geometric logic. Using the methods of coalgebra, the modal operators are introduced in the language of fuzzy geometric…
Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi\'{c}'s and Winkler's relations play an important role in the theory of partial cubes. These structures are employed in the…
We introduce shift algebras as certain crossed product algebras based on general function spaces and study properties, as well as the classification, of a particular class of modules depending on a set of matrix parameters. It turns out…
We give some inclusion relations for arbitrary fuzzy sets with reference to famous inequalities. In particular, we can know that the bounded sum and the algebraic product go well together. We would like to propose the concept of `Fuzzy Set…
This paper aims to present objective methods for constructing new fuzzy sets from known fuzzy or classical sets, defined over the elements of a finite universe's superstructure. The paper proposes rules for assigning membership functions to…
We provide a rigorous framework for handling uncertainty in quantitative fault tree analysis based on fuzzy theory. We show that any algorithm for fault tree unreliability analysis can be adapted to this framework in a fully general and…
Fuzzy anti-norm and corresponding $\alpha$-norms are defined. A few properties of finite dimensional fuzzy anti-normed linear space are studied. Fuzzy $\alpha$-anti-convergence and fuzzy $\alpha$-anti-complete linear space are defined and a…
In this contribution, I discuss an algebraic treatment of alpha-cluster nuclei based on the introduction of a spectrum generating algebra for the relative motion of the alpha-clusters. Particular attention is paid to the discrete symmetry…
A detailed study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion is already done in our earlier paper. The notions of graded fuzzy topological system and fuzzy topological space with graded…
Atomic system in fuzzy Hilbert space is introduced and the existence of the fuzzy atomic systems for a strongly fuzzy bounded linear operator is studied. The notion of a K-frame in fuzzy Hilbert space is presented and some of their…
The most general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy subset is considered, and generalization of fuzzy fated of $R_0$-algebras is discussed. The notion of an $(\epsilon , \epsilon \vee q_k)$-fuzzy fated…
By exploiting the description of topological spaces by either neighborhood systems or filter convergence, we obtain a neighborhood-like presentation of categories of lax algebras. A notable advantage of this approach is that it does not…
Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…