Multiple Criteria Decision Making Based on Probabilistic Interval-Valued Hesitant Fuzzy Sets by Using LP Methodology

M Sarwar Sindhu,Agha Kashif,Tabasam Rashid,Juan Luis García Guirao

doi:10.1155/2019/1527612

Abstract

Probabilistic interval-valued hesitant fuzzy sets (PIVHFSs) are an extension of interval-valued hesitant fuzzy sets (IVHFSs) in which each hesitant interval value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. PIVHFSs describe the belonging degrees in the form of interval along with probabilities and thereby provide more information and can help the decision makers (DMs) to obtain precise, rational, and consistent decision consequences than IVHFSs, as the correspondence of unpredictability and inaccuracy broadly presents in real life problems due to which experts are confused to assign the weights to the criteria. In order to cope with this problem, we construct the linear programming (LP) methodology to find the exact values of the weights for the criteria. Furthermore these weights are employed in the aggregation operators of PIVHFSs recently developed. Finally, the LP methodology and the actions are then applied on a certain multiple criteria decision making (MCDM) problem and a comparative analysis is given at the end.

Highlights

Vagueness usually appears in real life issues, like risk management, intelligent computations, or applications in the field of engineering, etc
The rest of the paper is managed in the following way: In Section 2, we briefly describe the core ideas of hesitant fuzzy sets, probabilistic hesitant fuzzy set, interval-valued hesitant fuzzy sets (IVHFSs), Probabilistic interval-valued hesitant fuzzy sets (PIVHFSs), and an linear programming (LP) model which is constructed to evaluate the weights of criteria and used in the aggregation operators of PIVHFSs for multiple criteria decision making (MCDM)
We have proposed PIVHFSs and PIVHFEs

Summary

Introduction

Vagueness usually appears in real life issues, like risk management, intelligent computations, or applications in the field of engineering, etc. In order to overcome such problems, Chen et al [15, 16] presented the idea of interval-valued hesitant fuzzy sets (IVHFSs), which is the extended form of HFSs. IVHFSs permit the belonging level of a component to have various possible interval values in [0, 1] rather than real numbers and can deal better with intrinsic hesitancy and instability in the human decision making process. The rest of the paper is managed in the following way: In Section 2, we briefly describe the core ideas of hesitant fuzzy sets, probabilistic hesitant fuzzy set, IVHFSs, PIVHFSs, and an LP model which is constructed to evaluate the weights of criteria and used in the aggregation operators of PIVHFSs for MCDM.

Some Fundamental Concepts

Illustrative Example

Comparative Analysis

E2 E3 E4

Conclusions