Einstein-operations on fuzzy soft multi sets and decision making

Anjan Mukherjee,Ajoy Kant Das

doi:10.5269/bspm.32546

Abstract

In this paper, we define Einstein product and Einstein sum of fuzzy soft multi sets (FSM-sets) and using these products, we introduce an adjustable approach to FSM-set based decision-making, for solving decision-making in an uncertain situation. The feasibility of our proposed FSM-set based decision-making procedure in practical application is shown by some numerical examples.

Highlights

[3] introduced the idea of FSM-set as a speculation of soft multiset and concentrated on the utilization of FSM-set based decision-making issues using Roy-Maji Algorithm [37]
It is seen that every one of these theories has their own troubles, that is the reason in this paper, we define Einstein product and Einstein sum of FSM-sets and using these products, we introduce an adjustable approach to FSM-set based decision-making, for solving decisionmaking in an uncertain situation
We define Einstein product and Einstein sum of FSM-sets. Using these products, we introduce an adjustable approach to FSM-set based decision-making and the feasibility of our proposed FSM-set based decision-making procedure in practical application is shown by some numerical models (Section 4)

Summary

Preliminary Notes

Let U be a starting universe, E be an arrangement of parameters and P (U ) mean the power set of U with A ⊆ E. A pair (F, A) is called a fuzzy soft multi set over U , where F is a mapping given by F : A → U. We denote the sets of all F SM -sets over U by F SM S(U, A), where the parameter set A is fixed To illustrate this let us consider the following example: Example 1 Let us consider three universes U1 = {h1, h2, h3, h4}, U2 = {c1, c2, c3} and U3 = {v1, v2, v3} which are the collections of houses, autos and inns respectively. [3] For any F SM -set (F, A), a pair (eUi,j , FeUi,j ) is called a Ui-fuzzy soft multi set part (Ui-FSMS-part) for all eUi,j ∈ a and FeUi,j , ⊆F(A) is a fuzzy approximate value set, where a∈A, i, j ∈ I. The t-conorm product of (F, A) and (G, A), denoted by (F, A)

F SM -set μH

Application of FSM-sets in decision-making

Advantages

Conclusion and future work