A generalized belief interval-valued soft set with applications in decision making

Possibility Fermatean fuzzy soft set and its application in decision-making

This paper aims to introduce a new multiple attribute decision-making model named possibility Fermatean fuzzy soft set (PFFSS), which is a combination of the generalized fuzzy soft sets and Fermatean fuzzy sets. Some operations and properties of the new model, including complement, restricted union, and extended intersection are discussed. Further, an application of PFFSSs is modeled for multiple attribute decision-making and solved with the help of our newly launched algorithm, that is, the selection of the best eco-system model based on a computer simulation report. Finally, a comparative analysis between the initiated PFFSS model and some existing approaches is provided to show its reliability over them.

Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems

In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.

Possibility belief interval-valued soft set and its application in decision making

The aim of this article is to present the concept of restricted union and extended intersection of belief interval-valued soft sets, along with its properties. In addition, we propose the concept of possibility belief interval-valued soft set theory and investigate their properties. For suitability of possible applications, there are seven kinds of operations (e.g., union, intersection, restricted union, extended intersection, complement, soft max-AND, and soft min-OR) on the possibility belief interval-valued soft sets are defined and their basic theoretical are given. Then, we construct two algorithms by using soft max-AND and soft min-OR operations of possibility interval-valued soft sets for fuzzy decision-making problem. Lastly, we introduce an algorithm using a possibility interval-valued soft set to solve the decision-making problems and clarify its applicability by a numerical example.

A new type of generalized picture fuzzy soft set and its application in decision making

 In this article, we propose a novel concept of the generalized picture fuzzy soft set by combining the picture fuzzy soft set and the fuzzy parameter set. For possible applications, we explain five kinds of operations (e.g., subset, equal, union, intersection, and complement) based on generalized picture fuzzy soft sets. Then, we establish several theoretical operations of generalized picture fuzzy soft sets. In addition, we present the new type by using the AND operation of the generalized picture fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example. Finally, we give a comparison between the picture fuzzy soft set theory and the generalized picture fuzzy soft set theory. It is shown that our proposed (i.e., generalized picture fuzzy soft set theory) is viable and provide decision makers a more mathematical insight before making decisions on their options.