Showing papers on "Idempotence published in 2022"
TL;DR: Construction methods of overlap and grouping functions on complete lattices via complete homomorphisms and complete 0 L , 1 L -endomorphisms are investigated and the notion of O-generator triple of overlap functions is proposed.
18 citations
TL;DR: In this article , construction methods of overlap and grouping functions on complete lattices via complete homomorphisms and complete 0L, 1L-endomorphisms are investigated, and properties such as (α,B,C)-migrativity, (B, C)-homogeneity, idempotency and cancellation law for the overlap functions obtained by such generator triples are discussed.
15 citations
TL;DR: In this article , Paiva et al. give the concept of quasi-overlap functions on a finite chain L with n+2 elements and its arbitrary subchains together with three generalized forms of quasi overlap functions on any subchain of L. And then, they show some examples of quasi overlaps on L along with some of its specific subchains and study the idempotent property, Archimedean property and cancellation law.
11 citations
TL;DR: In this article, Paiva et al. give the concept of quasi-overlap functions on a finite chain L with n + 2 elements and its arbitrary subchains together with three generalized forms of quasi overlaps on any subchain of L. And then, they show some examples of quasi overlap functions on L along with some of its specific subchains and study the idempotent property, Archimedean property and cancellation law.
11 citations
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: This article introduces new q-rung Orthopair fuzzy (q-ROF) aggregation operators (AOs) as the consequence of Aczel–Alsina (AA) t-norm (TN) and t-conorm (TCN) and their specific advantages in handling real-world problems and develops new strategies based on these operators.
Abstract: A contribution of this article is to introduce new q-rung Orthopair fuzzy (q-ROF) aggregation operators (AOs) as the consequence of Aczel–Alsina (AA) t-norm (TN) (AATN) and t-conorm (TCN) (AATCN) and their specific advantages in handling real-world problems. In the beginning, we introduce a few new q-ROF numbers (q-ROFNs) operations, including sum, product, scalar product, and power operations based on AATN and AATCN. At that point, we construct a few q-ROF AOs such as q-ROF Aczel–Alsina weighted averaging (q-ROFAAWA) and q-ROF Aczel–Alsina weighted geometric (q-ROFAAWG) operators. It is illustrated that suggested AOs have the features of monotonicity, boundedness, idempotency, and commutativity. Then, to address multi-attribute decision-making (MADM) challenges, we develop new strategies based on these operators. To demonstrate the compatibility and performance of our suggested approach, we offer an example of construction material selection. The outcome demonstrates the new technique’s applicability and viability. Finally, we comprehensively compare current procedures with the proposed approach.
9 citations
TL;DR: It is shown that each idempotent 2-uninorm can be expressed as an ordinal sum of an idemPotent uninorm (possibly also of a countable number of idempotsent semigroups with operations min and max) and a 2- uninorm from Class 1 (possibly restricted to open or half-open unit square).
8 citations
TL;DR: In this paper , the dimension-free relations between basic communication and query complexity measures and various matrix norms are studied, where the goal is to obtain inequalities that bound a parameter solely as a function of another parameter, in contrast to perhaps the more common framework in communication complexity where poly-logarithmic dependencies on the number of input bits are tolerated.
Abstract: The purpose of this article is to initiate a systematic study of dimension-free relations between basic communication and query complexity measures and various matrix norms. In other words, our goal is to obtain inequalities that bound a parameter solely as a function of another parameter. This is in contrast to perhaps the more common framework in communication complexity where poly-logarithmic dependencies on the number of input bits are tolerated. Dimension-free bounds are also closely related to structural results, where one seeks to describe the structure of Boolean matrices and functions that have low complexity. We prove such theorems for several communication and query complexity measures as well as various matrix and operator norms. In several other cases we show that such bounds do not exist. We propose several conjectures, and establish that, in addition to applications in complexity theory, these problems are central to characterization of the idempotents of the algebra of Schur multipliers, and could lead to new extensions of Cohen’s celebrated idempotent theorem regarding the Fourier algebra.
7 citations
TL;DR: In this article , the notions of hybrid subsemimodule and hybrid right (resp., left) ideals are defined and discussed in semirings, and the characterization theorem is proved in terms of hybrid structures for fully idempotent semiirings.
Abstract: The concept of a hybrid structure in X -semimodules, where X is a semiring, is introduced in this paper. The notions of hybrid subsemimodule and hybrid right (resp., left) ideals are defined and discussed in semirings. We investigate the representations of hybrid subsemimodules and hybrid ideals using hybrid products. We also get some interesting results on t-pure hybrid ideals in X . Furthermore, we show how hybrid products and hybrid intersections are linked. Finally, the characterization theorem is proved in terms of hybrid structures for fully idempotent semirings.
6 citations
14 Apr 2022
TL;DR: In this article , the sober objects for a probability monad are identified and defined, and an idempotent sobrification functor is defined for the Giry monad on measurable spaces, which allows us to sharpen de Finetti's theorem for Markov categories.
Abstract: Probability theory can be studied synthetically as the computational effect embodied by a commutative monad. In the recently proposed Markov categories, one works with an abstraction of the Kleisli category and then defines deterministic morphisms equationally in terms of copying and discarding. The resulting difference between ‘pure’ and ‘deterministic’ leads us to investigate the ‘sober’ objects for a probability monad, for which the two concepts coincide. We propose natural conditions on a probability monad which allow us to identify the sober objects and define an idempotent sobrification functor. Our framework applies to many examples of interest, including the Giry monad on measurable spaces, and allows us to sharpen a previously given version of de Finetti’s theorem for Markov categories.
5 citations
TL;DR: In this article , a multi-attribute group decision-making (MAGDM) strategy based on power Maclaurin symmetric mean (PMSM) operators is proposed to assess the performance of the smart grids in Pakistan.
Abstract: Traditional electricity networks are replaced by smart grids to increase efficiency at a low cost. Several energy projects in Pakistan have been developed, while others are currently in the planning stages. To assess the performance of the smart grids in Pakistan, this article employs a multi-attribute group decision-making (MAGDM) strategy based on power Maclaurin symmetric mean (PMSM) operators. We proposed a T-spherical fuzzy (TSF) power MSM (TSFPMSM), and a weighted TSFPMSM (WTSFPMSM) operator. The proposed work aims to analyze the problem involving smart grids in an uncertain environment by covering four aspects of uncertain information. The idempotency, boundedness, and monotonicity features of the proposed TSFPMSM are investigated. In order to assess Pakistan’s smart grid networks based on the suggested TSFPMSM operators, a MAGDM algorithm has been developed. The sensitivity analysis of the proposed numerical example is analyzed based on observing the reaction of the variation of the sensitive parameters, followed by a comprehensive comparative study. The comparison results show the superiority of the proposed approach.
TL;DR: In this article , the authors studied the Finite Basis Problem for additively idempotent semirings whose multiplicative reducts are inverse semigroups, and they showed that for any such semiring, there is no finite identity basis.
Abstract: We study the Finite Basis Problem for finite additively idempotent semirings whose multiplicative reducts are inverse semigroups. In particular, we show that each additively idempotent semiring whose multiplicative reduct is a nontrivial rook monoid admits no finite identity basis, and so do almost all additively idempotent semirings whose multiplicative reducts are combinatorial inverse semigroups.
TL;DR: The necessary and sufficient conditions for the solutions of the α-migrativity equation when the uninorm U becomes a t-norm or a conjunctive uninorm locally internal on the boundary are given.
TL;DR: In 2018, Qiao and Hu as discussed by the authors studied the α -migrativity of uninorms over overlap and grouping functions when the uninorm U belongs to one certain class (e.g., U min , U max , the family of idempotent inorms).
TL;DR: In this article , the authors derived two different types of aggregation operators under the consideration of algebraic t-norm and t-conorm for CIF set theory and compared them with various existing aggregation operators with the help of various suitable examples for showing the reliability and stability of the derived approaches.
Abstract: The main influence of this analysis is to derive two different types of aggregation operators under the consideration of algebraic t-norm and t-conorm and Einstein t-norm and t-conorm for CIF set theory. Because these operators are very effective for evaluating the collection of information into a singleton preference. For this, first, we discover the Algebraic and Einstein operational laws for CIF sets. Then, we aim to discover the theory of CCIFWA, CCIFOWA, CCIFWG, CCIFOWG operators and their valuable properties "idempotency, monotonicity and boundedness" and results. Furthermore, we also derive the theory of CCIFEWA, CCIFEOWA, CCIFEWG, CCIFEOWG operators and their valuable properties "idempotency, monotonicity, and boundedness" and results. Some special cases of the derived work are also described in detail. Finally, we illustrate a MADM procedure under the consideration of derived operators to enhance the worth of the presented information. Finally, we compare the presented operators with various existing operators with the help of various suitable examples for showing the reliability and stability of the derived approaches.
TL;DR: In this article , the authors studied nullnorms which arise from well-known classes of t-norms and t-conorms, such as idempotent, Archimedean, cancellative, positive and nilpotent tnorms, and presented the concept of h-pseudo-homogeneous nullnorm.
TL;DR: In this paper , the R-linear category FFppkΔ of diagonal p-permutation functors over R was studied, and the notion of functorial equivalence was introduced.
TL;DR: In this article , the authors define a higher unitary idempotent completion for C⁎ 2-categories called Q-system completion and study its properties, and show that the right correspondences of unital C ⁎-algebras is q-system complete by constructing an inverse realization †-2-functor.
TL;DR: In this article , the authors introduce the category modadm(E) of admissibly finitely presented functors and use it to give a version of Auslander correspondence for any exact category E.
TL;DR: The concept of h-pseudo-homogeneous nullnorm is presented and when these classes of nullnorms fullfill it is studied, such as idempotent, Archimedean, cancellative, positive and nilpotent t-norms and t-conorms.
TL;DR: In this paper , the distributivity equations between overlap (grouping) functions and null-uninorms, which are the generalization of uninorms and nullnorms, are studied.
TL;DR: The authors partially supported by grant PID2019-110525GB-I00 from Agencia Estatal de Investigacion (AEI) and from Fondo Europeo de Desarrollo Regional (FEDER).
TL;DR: This work proposes unex-plored, complementary proof principles that establish hyper-triples (i.e. hypersafety judgments) as a unifying compositional building block for proofs, and uses them to develop a Logic for Hyper-triple Composition (LHC), which supports forms of proof compositionality that were not achievable in previous relational logics.
Abstract: Hypersafety properties of arity n are program properties that relate n traces of a program (or, more generally, traces of n programs). Classic examples include determinism, idempotence, and associativity. A number of relational program logics have been introduced to target this class of properties. Their aim is to construct simpler proofs by capitalizing on structural similarities between the n related programs. We propose an unexplored, complementary proof principle that establishes hyper-triples (i.e. hypersafety judgments) as a unifying compositional building block for proofs, and we use it to develop a Logic for Hyper-triple Composition (LHC), which supports forms of proof compositionality that were not achievable in previous logics. We prove LHC sound and apply it to a number of challenging examples.
TL;DR: In this article , the automorphism group of an idempotent evolution algebra is studied, and it is shown that any finite group can be a group of automorphisms in an evolution algebra.
TL;DR: A linear relation E acting on a Hilbert space is idempotent if E2=E as mentioned in this paper , and a triplet of subspaces is needed to characterize a given linear relation.
TL;DR: In this article , a characterization theorem for idempotent uninorms on a complete chain in terms of decreasing unary functions with a symmetry-related property is presented, and the notion of left-continuity is introduced.
TL;DR: The structure of idempotent n-uninorms is studied in this article , where it is shown that each 2-inorm can be expressed as an ordinal sum of a 2-minimizer and a 1-inforcer.
TL;DR: In this article , the Peirce decomposition of a Jordan algebra with respect to an idempotent is taken one step further and generalized recently by Hall, Rehren and Shpectorov, with their introduction of axial algebras.
Abstract: The Peirce decomposition of a Jordan algebra with respect to an idempotent is well known. This decomposition was taken one step further and generalized recently by Hall, Rehren and Shpectorov, with their introduction of axial algebras, and in particular primitive axial algebras of Jordan type (PAJs for short). It turns out that these notions are closely related to three-transposition groups and vertex operator algebras. De Medts, Peacock, Shpectorov and M. Van Couwenberghe generalized axial algebras to decomposition algebras which, in particular, are not necessarily commutative. This paper deals with decomposition algebras which are non-commutative versions of PAJs.
TL;DR: In this paper , it was shown that any multiplicative centrally-extended derivation of a ring is a centrallyextended derived derivation, i.e., any derivation that satisfies some conditions is a centralised derivation.
Abstract: Abstract The purpose of this paper is to prove the following assertion. Let S be a ring having a nontrivial idempotent element e which satisfies some conditions. We prove that any multiplicative centrally-extended derivation of S is a centrally-extended derivation.