To handle complex, risk-illustrating, and asymmetric information, the theory discussed in this analysis is much more suitable for evaluating above dilemmas. manage ambiguity inconsistency real-life problems, principle of Aczel–Alsina (AA) t-norm t-conorm was initiated 1980. These norms are massively modified different from prevailing due to parameter p, where 0<p<+∞. The major contribution analyze AA operational laws (addition, multiplication, score value, accuracy value) under complex...

The collection of Hamacher t-norms was created by in 1970, which played a critical and significant role computing aggregation operators. All operators that are derived based on norms very powerful beneficial because the parameter 0≤ζ≤+∞. Choquet first posited theory integral (CI) 1953, is used for evaluating awkward unreliable information to address real-life problems. In this manuscript, we analyze several CI, operators, t-norm t-conorm, Atanassov intuitionistic fuzzy (A-IF) information....

In this paper, we define essential ideals and 0-essential of semigroups investigate some properties them. Moreover, fuzzy semigroups. We give relationships between ideals.

Let [Formula: see text] be a semigroup of all transformations on set fixed nonempty subset and Then is subsemigroup which leaves invariant. If then In this paper, we give necessary sufficient conditions for elements in to left or right magnifying.

The problem of energy crisis and environmental pollution has been mitigated by the generation use solar power; however, choice locations for power plants is a difficult task because decision-making process includes political, socio-economic, aspects. Thus, several adverse consequences have created suboptimal locations. objective this paper to address integrated qualitative quantitative multicriteria framework selection plant Neutrosophic sets (NSs) are latest extension ordinary fuzzy sets....

An element a of semigroup S is called left [right] magnifying if there exists proper subset M such that = aM [S Ma]. Let X be nonempty set and T(X) the all transformation from into itself under composition functions. For partition P {X_α | α ∈ I} X, let T(X,P) {f (X_α)f ⊆ X_α for I}. Then subsemigroup {X}, T(X). Our aim in this paper to give necessary sufficient conditions elements or right magnifying. Moreover, we apply those some generalized linear semigroups.

This article manages vagueness, asymmetric data, and risk demonstrated in awkward information. The ambiguity is handled with the help of possibility strategic decision-making theory. A MADM (multi-attribute decision-making) tool, sub-part decision theory, plays an important role circumstances fuzzy data. major influence this analysis to initiate mathematical ideology cubic intuitionistic complex (CICF) information its well-known properties such as algebraic laws, score values, accuracy...

Let L(V) be the linear transformation semigroup on a vector space V. It is well-known that contains left [right] magnifying elements if and only dimension of V infinite. In case its infinite, α ϵ it surjective not injective right surjective. To generalize this result, let W subspace S(V, W) = {f ∈ | (W) f ⊆ W}. Then subsemigroup V, then V) L(V). Our purpose in paper to give necessary sufficient conditions for magnifying.

Let $Y$ be a nonempty subset of set $X$ and let $T(X,Y)$ the semigroup (under composition) all functions $X\rightarrow X$ whose range is $Y$. We give necessary sufficient conditions for elements in to left right magnifying.

In this paper, we introduce the notion of $S$-$M$-cyclic submodules, which is a generalization $M$-cyclic submodules. Let $M, N$ be right $R$-modules and $S$ multiplicatively closed subset ring $R$. A submodule $A$ $N$ said to an submodule, if there exist $s\in S$ $f \in Hom_R(M,N)$ such that $As \subseteq f(M) A$. Besides giving many properties generalize some results on submodules Furthermore, principally injective modules pseudo-principally $S$-principally $S$-pseudo-principally modules,...

The aim of this work was to generalizegenerator, $M$-generated modules in order apply them a widerclass rings and modules. We started by establishing new conceptwhich is called fully-$M$-cyclic module. defined notationby using $Hom_R(M,*)$ operators which are helpful contract thenew construction describe their properties. Finally, we couldsee the structure module quasi-fully-cyclicmodule $M$.

An element a of semigroup S is called left [right] magnifying if there exists proper subset M such that = aM [S Ma]. Let P(X) be all partial transformations on set X under the composition maps. A number results concerning necessary and sufficient conditions for elements in some interesting generalized semigroups to or right magnifiers are presented.

The aim of this paper is to introduce the notion nearly prime submodules as a generalization submodules. We investigate some their basic properties and point out similarities between these also indicate applications These show how control structure modules they recover earlier relative theorems.

In this paper, cyclic $c-$injective modules are introduced and investigated. It is shown that a commutative Noetherian domain Dedekind if only every simple module $c-$injective. Finally, it injectivity, principal mininjectivity, injectivity all equal to characterize right V-rings, GV-rings, pV-rings, WV-rings.

In this paper, we introduce the concept of slightly compressible-injective modules, following this, a right R-module N is called an M-slightly module, if every R-homomorphism from non-zero compressible submodule M to can be extended M. We give some characterizations and properties modules.

In this paper, we give a generalization of slightly compressible modules. We introduce the notion M-slightly modules, i.e. right R module N is called if for every nonzero submodule A there exists R-homomorphism s from M to such that . Many examples modules are provided. Some results on obtained, which interesting and important.

In this paper, we introduce and investigate essentially M-slightly compressible modules injective modules. It has been shown that over hereditary ring R M is an right R-module. If N module then every essential submodule A of containing a direct summand N. For any uniform R-module M, can show if only module.

An element x in a semigroup S is called BQ-element of if the bi-ideal and quasi-ideal generated by coincide. It known that every regular BQ-element. In 2010, Danpattanamongkon Kemprasit characterized elements BQ-elements ℤn. this paper, we characterize generalized semigroups

In this research paper, the concepts of uniform fuzzy modules and semiuniform were studied. We discussed necessary sufficient conditions between (and modules) in set theory module theory.