<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...

Abstract Orthopair fuzzy sets are in which every element is represented by a pair of values the unit interval, one refers to membership and other non-membership. The different types orthopair given literature distinguished according proposed constrain for non-membership grades. aim writing this manuscript familiarize new class called “(2,1)-Fuzzy sets” good enough control some real-life situations. We compare (2,1)-Fuzzy with IFSs their celebrated extensions. Then, we put forward fundamental...

The main aim of the present paper is to define new soft separation axioms which lead us, first, generalize existing comparable properties via general topology, second, eliminate restrictions on shape open sets regular spaces given in [22], and third, obtain a relationship between Hausdorff similar those exists topology. To this end, we partial belong total non relations, investigate many related these two relations. We then introduce axioms, namely p-soft Ti-spaces (i = 0,1,2,3,4), depending...

Abstract In this paper, we introduce a topological method to produce new rough set models. This is based on the idea of “somewhat open sets” which one celebrated generalizations sets. We first generate some topologies from different types $$N_\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>N</mml:mi><mml:mi>ρ</mml:mi></mml:msub></mml:math> -neighborhoods. Then, define approximations and accuracy measures with respect somewhat closed study their main...

In this work, we introduce new types of soft separation axioms called <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><mi>p</mi><mi>t</mi></math> -soft id="M2"><mi>α</mi></math> regular and id="M3"><mi>p</mi><mi>t</mi></math> id="M4"><mi>α</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></math> -spaces id="M5"><mfenced open="(" close=")" separators="|"><mrow><mi>i</mi><mo>=</mo><mn>0,1,2,3,4</mn></mrow></mfenced></math> using partial belong total nonbelong relations...

An intuitionistic fuzzy set is one of the efficient generalizations a for dealing with vagueness/uncertainties in information. Under this environment, manuscript, we familiarize new type extensions sets called square-root (briefly, SR-Fuzzy sets) and contrast Pythagorean sets. We discover essential operations along their several properties. In addition, define score function ranking To study multiattribute decision-making problems, introduce four weighted aggregated operators, namely,...

As daily problems involve a great deal of data and ambiguity, it has become vital to build new mathematical ways cope with them, soft set theory is the greatest tool for doing so. result, we study methods generating topologies through several operators. A topology known be determined by system special sets, which are called open (dually closed) sets. The relationship between specific types their classical (known as parametric topologies) linked idea symmetry. Under this symmetry, can...

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...

The desire of generalizing some set-theoretic properties to the soft set theory motivated many researchers define various types operators. For example, they redefined complement a set, and union intersection between two sets in way that satisfies De Morgan's laws. In this paper, we introduce study concepts $T$-soft subset equality relations. Then, utilize them for arbitrary family sets. By union, successfully keep classical via theory. We conclude work by giving investigating new linear...

In this paper, we introduce the concept of sum soft topological spaces using pairwise disjoint and study its basic properties. Then, define additive finitely properties which are considered a link between their sum. regard, show that being p-soft T i , paracompactness, extremally disconnectedness, continuity additive. We provide some examples to elucidate compactness separability additive; however, hyperconnected, indiscrete, door not addition, prove interior, closure, limit, boundary points...

It is well known every soft topological space induced from information system compact. In this study, we integrate between compactness and partially ordered set to introduce new types of on the finite spaces investigate their application system. First, initiate a notion monotonic sets establish its main properties. Second, concepts compact show relationships them with help examples. We give complete description for each one by making use intersection property. Also, study some properties...

The purpose of this paper is to define the concept (3, 2)-fuzzy sets and discuss their relationship with other kinds fuzzy sets. We describe some basic set operations on 2)-Fuzzy can deal more uncertain situations than Pythagorean intuitionistic because larger range describing membership grades. Furthermore, we familiarize notion topological space master properties continuous maps. Then, introduce points study types separation axioms in space. Moreover, establish idea relation present...

Bipolar soft set is formulated by two sets; one of them provides us the positive information and other negative information. The philosophy bipolarity that human judgment based on sides, negative, we choose which stronger. In this paper, introduce novel belong nonbelong relations between a bipolar an ordinary point. These are considered as unique characteristics sets somewhat expression degrees membership nonmembership element. We discuss essential properties derive sufficient conditions...

This paper puts forward some rough approximations which are motivated from topology. Given a subset R ⊆ U × , we can use 8 types of E ‐neighborhoods to construct an arbitrary X on the one hand. On other hand, also relying topology is induced by ‐neighborhood. Properties these and relationships between them studied. For convenience use, give useful easy‐to‐understand examples make comparison our those in published literature.