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We talk about possibility spherical fuzzy soft set (shortly PSFS set) has much stronger ability than possibility Pythagorean fuzzy soft set (shortly PPFS set) and intuitionistic fuzzy soft set. The PSFS soft set is a generalization of PPFS set and soft set. Here we talk through some operations consisting of complement, union, intersection, AND and OR. We verify that the De Morgan’s laws, associate laws and distributive laws are satisfied in the case of PSFS sets. Also we discuss comparative analysis for the soft set model under the scheme of PSFS sets. Finally, an illustrative example is mentioned for the soft set model using PSFS set. [ABSTRACT FROM AUTHOR]

We discuss the theory of possibility Pythagorean interval valued fuzzy soft set, possibility interval valued fuzzy soft set and define some related the operations namely complement, union, intersection, AND and OR. The possibility Pythagorean interval valued fuzzy soft sets are a generalization of soft sets. Notably, we showed De-Morgan's laws that are valid in possibility Pythagorean interval valued fuzzy soft set theory. Also, we propose an algorithm to solve the decision making problem based on soft set method. To compare two possibilities Pythagorean interval valued fuzzy soft sets for dealing with decision making problems and find a similarity measure is obtained. Finally, an illustrative example is discussed to prove that they can be effectively used to solve problems with uncertainties. [ABSTRACT FROM AUTHOR]

In the present communication, we introduce the concept of Type-I generalized spherical interval valued fuzzy soft set and define some operations. It is a generalization of the interval valued fuzzy soft set and the spherical fuzzy soft set. The spherical interval valued fuzzy soft set theory satisfies the condition that the sum of its degrees of positive, neutral, and negative membership does not exceed unity and that these parameters are assigned independently. We also propose an algorithm to solve the decision making problem based on a Type-I generalized soft set model. We introduce a similarity measure based on the Type-I generalized soft set model for two Type-I generalized spherical interval valued fuzzy soft sets and discuss its application in a medical diagnosis problem. Illustrative examples are mentioned to show that they can be successfully used to solve problems with uncertainties. [ABSTRACT FROM AUTHOR]

Pythagorean neutrosophic soft set (PNSS set) is a new approach towards decision making under uncertainty. The PNSS set has much stronger abilities than the neutrosophic soft set and the Pythagorean fuzzy soft set. In this paper, we discuss aggregated operations for aggregating the PNSS decision matrix. The TOPSIS and VIKOR methods are strong approaches for multi criteria group decision making (MCGDM), which is various extensions of neutrosophic soft sets. In this approach, we propose a score function based on aggregating TOPSIS and VIKOR methods to the PNSS-positive ideal solution and the PNSS-negative ideal solution. Also, the TOPSIS and VIKOR methods provide the weights of decision-making. Afterward, a revised closeness is introduced to identify the optimal alternative. [ABSTRACT FROM AUTHOR]

In the present communication, we discuss the theory of possibility Pythagorean neutrosophic soft set(shortly PPNSSS), possibility neutrosophic soft set(shortly PNSSS), and define some related operations such as complement, union, intersection, AND, and OR. Also, we study interact commutative law's, De Morgan's laws, associative laws, and distributive laws of holds for PPNSSSs. The possibility Pythagorean neutrosophic soft set is a new generalization of Pythagorean soft set and neutrosophic soft set. To compare PPNSSSs and PNSSSs for dealing with decision making problems and find a similarity measure is obtained. Practical examples are provided to strengthen our results. [ABSTRACT FROM AUTHOR]