<abstract><p>Many models of uncertain knowledge have been designed that combine expanded views fuzziness (expressions partial memberships) with parameterization (multiple subsethood indexed by a parameter set). The standard orthopair fuzzy soft set is very general example this successful blend initiated sets. It mapping from parameters to the family all sets (which allow for view acceptable membership and non-membership evaluations). To expand scope application theory,...

Orthopairs (pairs of disjoint sets) have points in common with many approaches to managing vaguness/uncertainty such as fuzzy sets, rough soft etc. Indeed, they are successfully employed address partial knowledge, consensus, and borderline cases. One the generalized versions orthopairs is intuitionistic sets which a well-known theory for researchers interested set theory. To extend area application more empirical situations, limitation that grades membership non-membership must be calibrated...

Soft topological spaces (STSs) have received a lot of attention recently, and numerous soft ideas been created from differing viewpoints. Herein, we put forth new class generalizations open sets called “weakly semi-open subsets” following an approach inspired by the components set. This opens door to reformulating existing concepts examining their behaviors. First, deliberate main structural properties this detect its relationships with previous assistance suitable counterexamples. In...

<abstract><p>In this work, we present some concepts that are considered unique ideas for topological structures generated by soft settings. We first define the concept of weakly $ \alpha $-open subsets and characterize it. It is demonstrated relationships between class generalizations open sets with help illustrative examples. Some interesting results obtained under stipulations like extended hyperconnected topologies. Then, introduce interior closure operators inspired classes...

Abstract In this manuscript, we first generate topological structures by subset neighborhoods and ideals apply to establish some generalized rough-set models. Then, present other types of models directly defined the concepts ideals. We explore main characterizations proposed approximation spaces compare them in terms operators accuracy measures. The obtained results given examples show that second type is better than one cases <m:math...

In a soft environment, we investigated several (classical) structures such as ideals, filters, grills, etc. It is well known that these are applied to expand abstract concepts; in addition, some of them offer vital tool address practical issues, especially those related improving rough approximation operators and accuracy measures. Herein, contribute this line research by presenting novel type structure, namely “soft primal”. We investigate its basic properties describe behaviors under...

&lt;abstract&gt;&lt;p&gt;This paper is devoted to study the concepts of compactness, Lindelöfness and connectedness via class soft somewhat open sets which represents one generalizations sets. Beside investigation main properties these concepts, it demonstrated, with help examples, that some their counterparts are invalid. Also, relationships between defined in classical topology (which studied herein under name parametric topology) discussed detail. Moreover, we provide sufficient...

This work makes a contribution to the theory of soft sets. It studies concepts semi-algebras and algebras, along with some operations. Then, it examines relations algebras set their ordinary (crisp) counterparts. Among other things, we show that every algebra sets induces collection By using formulas (in Theorem 7 Corollary 1), present novel construction, allowing us construct from system Two examples are presented how these can be used in practice. approach is general enough applied many...

&lt;abstract&gt;&lt;p&gt;Data uncertainty is a barrier in the decision-making (DM) process. The rough set (RS) theory an effective approach to study data, while bipolar soft sets (BSSs) can handle vagueness and as well bipolarity of data variety situations. In this article, we introduce idea (RBSSs) apply them find best decision two different DM problems medical science. first problem about deciding between risk factors disease. Our algorithm facilitates doctors investigate which factor...

It is well known that certain topological concepts such as the sum of topologies and product are defined by particular classes other topologies. In others, it crucial to look into connections between these topology generated them. One creates a family general soft topology, which over sets satisfying basic axioms topology. interesting investigate how notions behave when applied because enables us study qualities comparing them their counterparts in this paper, we benefit from fruitful...

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...

An nth power root fuzzy set is a useful extension of for expressing uncertain data. Because their wider range showing membership grades, sets can cover more ambiguous situations than intuitionistic sets. In this article, we present several novel operations on sets, as well various features. Besides, develop new weighted aggregated operator, namely, average (nPR-FWPA) over to deal with choice information and show some basic properties. addition, define scoring function ranking. Furthermore,...

<abstract> Herein, we applied soft somewhere dense sets to initiate six sorts of spaces called almost (nearly, mildly) $ SD $-compact and $-Lindelöf spaces. We study the master properties these illustrate relations between them with help examples. In addition, clarify that are equivalent under a $-partition. Moreover, relationships initiated enriched topological other well-known such as S $-connected indicated. </abstract>

In this investigation, the coupled between electrons and holes is studied during a theoretical mathematical-physical model of semiconductor medium. The elasto-thermodiffusion (ETD) theory photothermal transport processes taken into consideration. governing equations are examined under effect external magnetic field. This used to improve outside weak electric one-dimensional (1D) deformation constructed when thermoelastic (TD) electronic (ED) with occurred. dimensionalized field quantities...

Many generalizations of soft topology were studied in the literature, an infra is recent one these generalizations. In this paper, we put on view two classes separation axioms frame topologies, namely pp-soft Tj and pt-soft Tj-spaces (j = 0, 1, 2, 3, 4). Both them are formulated with respect to distinct ordinary points such that first class defined using partial belong non-belong relations, second total relations. Following systematic lines type study, show relationships between aid...

Obtaining a weaker condition that preserves some inspired topological properties is always desirable. As result, we introduce the concept of infra-fuzzy topology, which subset family degrades fuzzy topology by omitting closedness under arbitrary unions. Fundamental spaces are investigated, including open and closed sets, interior closure operators, boundary set. It not possible to expect latter concepts have identical those in ordinary spaces. More precisely, set need be open, may closed....

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...

&lt;abstract&gt;&lt;p&gt;The paper presents a novel analysis of interrelations between ordinary (crisp) $ \sigma $-algebras and soft $-algebras. It is known that each $-algebra produces system crisp (parameterized) The other way round also possible. That to say, one can generate from Different methods producing are discussed by implementing two formulas. demonstrated how these formulas be used in practice with the aid some examples. Furthermore, we study fundamental properties Lastly, show...

In this work, we adopt a new approach to study class of soft sets depending on the generalizations open subsets in parametric topological spaces. We first define somewhat-open and explore its basic features. illustrate represents proper extension under full topology. derive next formula1+∏η∈H(|Θη|-1)≤|Ϝ|≤1+(2|U|-1)|H|, which determines lower upper bounds cardinality number Ϝ family space (U,Θ,H), where Θη is topology inspired by Θ. Then, introduce two novel kinds compact Lindelöf spaces...

In this paper, we purposed further study on rough functions and introduced some concepts based it. We investigated the of topological lower upper approximations near‐open sets studied their basic properties. defined new neighborhood approach functions. generalized to continuous by different structures. addition, a function as relation were studied. Finally, applied our in finding images patient classification data using

Tareq M. Al-shami, Hariwan Z. Ibrahim, Abdelwaheb Mhemdi, and Radwan Abu-Gdairi. International Journal of Fuzzy Logic Intelligent Systems 2022;22:350-65. https://doi.org/10.5391/IJFIS.2022.22.4.350

&lt;abstract&gt;&lt;p&gt;To contribute to soft topology, we originate the notion of bioperators $ \tilde{\gamma} and {\tilde{\gamma}}^{'} $. Then, apply them analyze (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-open sets study main properties. We also prove that every set is open; however, converse true only when topological space $-regular. After that, define two classes closures namely Cl_{(\tilde{\gamma}, {\tilde{\gamma}}^{'})} \tilde{\tau}_{(\tilde{\gamma}, $-$ Cl operators, interior...

In this article, we apply the concept of fuzzy soft <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>δ</a:mi> </a:math> -open sets to define new types compactness in topological spaces, namely, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>δ</c:mi> </c:math> -compactness and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:msup> <e:mrow> <e:mi>δ</e:mi> </e:mrow> <e:mi>∗</e:mi> </e:msup> </e:math> -compactness. We explore some their...