Abstract In this paper, a comprehensive review and critical analyses of methods based on the ordinary fuzzy set, Atanassov’s intuitionistic its extensions have been conducted to show their limitations defects. Then, novel similarity measure generalized score function has introduced that incorporates significance (importance) information, making it more intuitive compare them. The proposed metho...

Interval-valued Pythagorean fuzzy so set (IVPFSS) is a generalization of the interval-valued intuitionistic (IVIFSS) and (IVPFS). The IVPFSS handled more uncertainty comparative to IVIFSS; it most signicant technique for explaining information in decision-making process. In this work, some novel operational laws have been proposed. Based on presented laws, two innovative aggregation operators (...

A p-rung orthopair fuzzy set (p-ROFS) describes a generalization of intuitionistic and Pythagorean in the case where we face larger representation space acceptable membership grades, moreover, it gives decision maker more flexibility expressing his/her real preferences. Under environment, are going to propose novel parametrized score function p-ROFSs by incorporating idea weighted average degre...

A polynomial Pythagorean–hodograph (PH) curve r(t) = (x1(t), . . . , xn(t)) in R n is characterized by the property that its derivative components satisfy the Pythagorean condition x′2 1 (t)+ · · ·+x ′2 n (t) = σ 2(t) for some polynomial σ(t), ensuring that the arc length s(t) = ∫ σ(t) dt is simply a polynomial in the curve parameter t. PH curves have thus far been extensively studied in R2 and...

In many decision-making situations, we are not restricted to two kinds of aspects, such as membership degree or nonmembership degree, and sometimes need include the abstinence (AD). However, fuzzy set theories fail cover issues, an intuitionistic soft set, Pythagorean q-rung orthopair set. All above notions can only consider a in their structures. The spherical compensates for these drawbacks i...

Rail transit systems, one of the important public transportation (PT) are widespread in large cities to satisfy passengers or commuters for their daily trips. However, rail (RT) investments costly, and budgets minimal. Thus assessing RT systems big play a crucial role deciding on best investment. In this study, first time, two-stage fuzzy set is used among multi-criteria decision-making (MCDM) ...

Cosine and cotangent similarity measurements are critical in applications for determining degrees of difference between objects. In the literature, numerous measures various extensions fuzzy set, soft Intuitionistic Fuzzy Sets (IFSs), Pythagorean (PFSs) HyperSoft (HSSs) have been explored. Neutrosophic (NHSSs), on other hand, has fewer cosine measures. this paper, we propose trigonometric NHSSs...