Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
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TL;DR: In this paper , a decision-making method utilizing the 2-tuple linguistic $T $-spherical fuzzy numbers (2TL$ T $-SFNs) was introduced to select the best alternative to manufacturing a linear delta robot.
Abstract: In the literature, extensions of common fuzzy sets have been proposed one after another. The recent addition is spherical fuzzy sets theory, which is based on three independent membership parameters established on a unit sphere with a restriction linked to their squared summation. This article uses the new extension that presents bigger domains for each parameter for production design. A systematic approach for determining customer demands or requirements, Quality Function Deployment (QFD) converts them into the final production to fulfill these demands in a decision-making environment. In order to prevent information loss during the decision-making process, it offers a useful technique to describe the linguistic analysis in terms of 2-tuples. This research introduces a novel decision-making method utilizing the 2-tuple linguistic $ T $-spherical fuzzy numbers (2TL$ T $-SFNs) in order to select the best alternative to manufacturing a linear delta robot. Taking into account the interaction between the attributes, we develop the 2TL$ T $-SF Hamacher (2TL$ T $-SFH) operators by using innovative operational rules. These operators include the 2TL$ T $-SFH weighted average (2TL$ T $-SFHWA) operator, 2TL$ T $-SFH ordered weighted average (2TL$ T $-SFHOWA) operator, 2TL$ T $-SFH hybrid average (2TL$ T $-SFHHA) operator, 2TL$ T $-SFH weighted geometric (2TL$ T $-SFHWG) operator, 2TL$ T $-SFH ordered weighted geometric (2TL$ T $-SFHOWG) operator, and 2TL$ T $-SFH hybrid geometric (2TL$ T $-SFHHG) operator. In addition, we discuss the properties of 2TL$ T $-SFH operators such as idempotency, boundedness, and monotonicity. We develop a novel approach according to the CODAS (Combinative Distance-based Assessment) model in order to deal with the problems of the 2TL$ T $-SF multi-attribute group decision-making (MAGDM) environment. Finally, to validate the feasibility of the given strategy, we employ a quantitative example to select the best alternative to manufacture a linear delta robot. The suggested information-based decision-making methodology which is more extensively adaptable than existing techniques prevents the risk of data loss and makes rational decisions.
9 citations
TL;DR: In this paper, an alternative derivation of the exponential generating function of the number of idempotent elements in symmetric semigroups is given, where the generator is defined in terms of a number of elements.
Abstract: : An alternative derivation of the exponential generating function of the number of idempotent elements in symmetric semigroups is given. (Author)
9 citations
TL;DR: The trace of the lifting of an idempotent is independent of lifting and is a function only of the equivalence class of a nonzero idemomorphism as discussed by the authors, and it is always a p-adic integer.
9 citations
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TL;DR: In this article, the authors describe an alternative structure, more compatible with valuation theory, that permits fuller use of algebraic theory especially in understanding the underlying tropical geometry, and provide a robust algebraic foundation for tropical linear algebra, in which many classical tools are available.
Abstract: Tropical mathematics often is defined over an ordered cancellative monoid $\tM$, usually taken to be $(\RR, +)$ or $(\QQ, +)$ Although a rich theory has arisen from this viewpoint, cf [L1], idempotent semirings possess a restricted algebraic structure theory, and also do not reflect certain valuation-theoretic properties, thereby forcing researchers to rely often on combinatoric techniques
In this paper we describe an alternative structure, more compatible with valuation theory, studied by the authors over the past few years, that permits fuller use of algebraic theory especially in understanding the underlying tropical geometry The idempotent max-plus algebra $A$ of an ordered monoid $\tM$ is replaced by $R: = L\times \tM$, where $L$ is a given indexing semiring (not necessarily with 0) In this case we say $R$ layered by $L$ When $L$ is trivial, ie, $L=\{1\}$, $R$ is the usual bipotent max-plus algebra When $L=\{1,\infty\}$ we recover the "standard" supertropical structure with its "ghost" layer When $L = \NN $ we can describe multiple roots of polynomials via a "layering function" $s: R \to L$ Likewise, one can define the layering $s: R^{(n)} \to L^{(n)}$ componentwise; vectors $v_1, \dots, v_m$ are called tropically dependent if each component of some nontrivial linear combination $\sum \a_i v_i$ is a ghost, for "tangible" $\a_i \in R$ Then an $n\times n$ matrix has tropically dependent rows iff its permanent is a ghost
We explain how supertropical algebras, and more generally layered algebras, provide a robust algebraic foundation for tropical linear algebra, in which many classical tools are available In the process, we provide some new results concerning the rank of d-independent sets (such as the fact that they are semi-additive),put them in the context of supertropical bilinear forms, and lay the matrix theory in the framework of identities of semirings
9 citations
TL;DR: In this article, the authors provide a complete characterization of the equivariant commutative ring structures of all the factors in the idempotent splitting of the G-equivariant sphere spectrum, including their Hill-Hopkins-Ravenel norms, where G is any finite group.
9 citations