<abstract><p>Rough set theory is an advanced uncertainty tool that capable of processing sophisticated real-world data satisfactorily. Rough approximation operators are used to determine the confirmed and possible can be obtained by using subsets. Numerous rough models, inspired neighborhood systems, have been proposed in earlier studies for satisfying axioms Pawlak spaces (P-approximation spaces) improving accuracy measures. This work provides a formulation novel type...

Rough set theory was introduced by Pawlak, in 1982, as a methodology to discover structural relationships within imprecise and uncertain data. This has been generalized using the idea of neighborhood systems be more efficient get rid uncertainty deal with wide scope practical applications. Motivated this idea, work, we initiate novel rough models concepts "maximal left neighborhoods ideals". Their basic features are studied between them revealed. The main merits these models, prove, first...

The theory of rough set is a robust approach to face uncertainty by classifying the data under study into three main regions. principles this are approximation operators and accuracy measures, so improving them has been major goal for several works. intrinsic aim create new methods with high measures classify subsets data. These established combining an ideal structure four types maximal neighbourhoods. essential characterizations properties these amply studied. Thereafter, relationships...

Abstract A useful tool for expressing fuzziness and uncertainty is the recently developed n,m-rung orthopair fuzzy set (n,m-ROFS). Due to their superior ability manage uncertain situations compared theories of q-rung sets, sets have variety applications in decision-making daily life. To deal with ambiguity unreliability multi-attribute group decision-making, this study introduces a novel called $$k^{n}_{m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup>...

Abstract Fuzzy set (FS) theory and rough sets (RSs) are constructed to accommodate the data uncertainty. In contrast, bipolar FS (BFS) can tackle uncertainty bipolarity of in different circumstances. This article aims introduce idea fuzzy ideals semigroup (SG), which is a generalization concept BFSs (RBFSs) an SG. We also investigate roughness subsemigroup (BF-SSG) with help congruence relation (cng-R) defined on SG studied some relevant structural properties. Moreover, extended left ideal,...

Aczel-Alsina t-norm and t-conorm are intrinsically flexible endow aggregation operators with greater versatility robustness in the process than rooted other t-norms families. Moreover, linear Diophantine fuzzy set (LD-FS) is one of resilient extensions sets (FSs), intuitionistic (IFSs), Pythagorean (PyFSs), q-rung orthopair (q-ROFSs), which has acquired prominence decision analysis due to its exceptional efficacy resolving ambiguous data. Keeping view advantages both LD-FSs operators, this...

The current work concentrates on generating different topologies by using the concept of ideal. These are used to make more thorough studies generalized rough set theory. theory was first proposed Pawlak in 1982. Its core is upper and lower approximations. principal goal reducing vagueness a uncertainty areas at their borders increasing approximation decreasing approximation. For mentioned goal, methods based ideals achieve this aim. accurate than previous methods. Hence it very interesting...

The concept of continuity in topological spaces has a very important place. For this reason, great deal work been done on continuity, and many generalizations have obtained. In work, we seek to find new approach the study soft connection with an induced mapping based sets. By defining *-image set, define present its related properties. To elaborate obtained results relationships, furnish number illustrative examples.

&lt;abstract&gt;&lt;p&gt;Several tools have been put forth to handle the problem of uncertain knowledge. Pawlak (1982) initiated concept rough set theory, which is a completely new tool for solving imprecision and vagueness (uncertainty). The main notions in this theory are upper lower approximations. One most important aims reduce uncertainty areas at their borders by decreasing approximations increasing So, object study propose four types approximation spaces utilizing ideals type...

One of the most popular and important tools to deal with imperfect knowledge is rough set theory. It starts from dividing universe obtain blocks utilizing an equivalence relation. To make it more flexibility expand its scope applications, many generalized models have been proposed studied. contribute this area, we introduce new inspired by “maximal union neighborhoods ideals.” These are created aim help decision‐makers analysis evaluate given data accurately decreasing ambiguity regions. We...

The exponentiated exponential distribution has received great attention from many statisticians due to its popularity, applications, and the fact that it is an efficient alternative famous distributions such as Weibull gamma distributions. Many have studied mathematical properties of this estimated parameters under different censoring schemes. However, seems random sum, linear combination, value reliability index, R=P(X2&lt;X1), in case unequal scale parameters, were not known for...

Several different topologies utilizing ideals are created and compared with previous topologies. The results show that the ones weaker than current stronger. merits of these proposed, smallest largest among them identified; this merit distinguishes present study from ones. Afterwards, employed to conduct more in-depth investigations on broadened rough sets. proposed approximate models particularly significant as applied sets because they diminish vagueness uncertainty prior models. Moreover,...

The newly introduced n th power root fuzzy set is a useful tool for expressing ambiguity and vagueness. It has an improved ability to manage uncertain situations compared intuitionistic Pythagorean theories, making sets applicable in various everyday decision-making contexts. notions of complex are integrated this study offer (CnPR-FSs), explaining its fundamental ideas applications. proposed CnPR-FS integrates the advantages captures both quantitative qualitative analyses decision-makers....

Many statisticians resort to using the asymptotic normal approximation method carry out statistical inference for many tests, especially nonparametric ones. In this article, saddlepoint is proposed as an alternative a number of tests important type data that appears frequently in clinical studies such cancer and tumorigenicity studies. trials, there are strategies through which treatments assigned patients. Equal allocation both largely prevalent approach trials eliminate experimental bias...

&lt;abstract&gt;&lt;p&gt;Rough set theory is a mathematical technique to address the issues of uncertainty and vagueness in knowledge. An ideal considered be crucial extension this theory. It an efficacious tool dispose uncertainties by helping us approximate rough more general manner. Minimizing boundary region one pivotal substantial themes for studying sets which consequently aim maximize accuracy measure. effective successful followed methods achieve goal perfectly. So, objective work...

Rough set theory was introduced by Pawlak in 1982 to handle imprecision, vagueness, and uncertainty data analysis. It is dealing with vagueness (ambiguous) of the using concept lower upper approximations objects based on an equivalence relation. The main idea rough se ts corresponds study these approximations. So, this paper, we generalize frameworks topological spaces. Pawlak's model are replaced interior closure notions space. defined new δβj-open sets ⋀βj-sets. Such techniques open way...

&lt;p&gt;A multivariate data analysis (MVDA) is a powerful statistical approach to simultaneously analyze datasets with multiple variables. Unlike univariate or bivariate analyses, which focus on one two variables, respectively, MVDA considers the interactions and relationships among variables within dataset. Several nonparametric tests can be used in context of one-sample location problems. The exact distributions such cannot analytically computed are usually approximated using an...

&lt;p&gt;Rough set theory serves as an effective method for managing complicated real-world data. Through rough approximation operators, it discerns both confirmed and possible data attainable through subsets. Earlier studies have presented several models, drawing inspiration from neighborhood systems aimed at enhancing accuracy degree satisfying the axioms of traditional spaces (TAS) that were initiated by Pawlak. This article proposes easy to deal with information in most cases, wherein...

Abstract A large–scale mating disruption trial for the control of Pectinophora gossypiella (Saund.) was carried out in Fayoum Province Egypt during 1981 cotton season. Two areas, each 50 ha, were sprayed with a microencapsulated formulation sex pheromone (a 1:1 mixture (Z, Z)- and E)-1, 11-hexadecadienyl acetate) as sole means controlling this pest. Five applications 10 g a.i./ha made season using fixed-wing aircraft. The treatments compared conventional insecticide spray two other 50-ha...