scholarly journals Power Muirhead Mean Operators for Interval-Valued Linear Diophantine Fuzzy Sets and Their Application in Decision-Making Strategies

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 70
Author(s):  
Tahir Mahmood ◽  
Izatmand Haleemzai ◽  
Zeeshan Ali ◽  
Dragan Pamucar ◽  
Dragan Marinkovic
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Fuzzy Sets ◽  
Objective Data ◽  
Algebraic Laws ◽  
Multi Attribute Decision Making ◽  
Interval Valued

It is quite beneficial for every company to have a strong decision-making technique at their disposal. Experts and managers involved in decision-making strategies would particularly benefit from such a technique in order to have a crucial impact on the strategy of their company. This paper considers the interval-valued linear Diophantine fuzzy (IV-LDF) sets and uses their algebraic laws. Furthermore, by using the Muirhead mean (MM) operator and IV-LDF data, the IV-LDF power MM (IV-LDFPMM) and the IV-LDF weighted power MM (IV-LDFWPMM) operators are developed, and some special properties and results demonstrated. The decision-making technique relies on objective data that can be observed. Based on the multi-attribute decision-making (MADM) technique, which is the beneficial part of the decision-making strategy, examples are given to illustrate the development. To demonstrate the advantages of the developed tools, a comparative analysis and geometrical interpretations are also provided.

Hesitant fuzzy β covering rough sets and applications in multi-attribute decision making

2021 ◽  
pp. 1-16
Author(s):  
Jia-Jia Zhou ◽  
Xiang-Yang Li
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Fuzzy Information ◽  
Hesitant Fuzzy Sets ◽  
Application Model ◽  
Rough Approximation ◽  
Multi Attribute Decision Making ◽  
The Universe

 In present paper, we put forward four types of hesitant fuzzy β covering rough sets (HFβCRSs) by uniting covering based rough sets (CBRSs) and hesitant fuzzy sets (HFSs). We firstly originate hesitant fuzzy β covering of the universe, which can induce two types of neighborhood to produce four types of HFβCRSs. We then make further efforts to probe into the properties of each type of HFβCRSs. Particularly, the relationships of each type of rough approximation operators w.r.t. two different hesitant fuzzy β coverings are groped. Moreover, the relationships between our proposed models and some other existing related models are established. Finally, we give an application model, an algorithm, and an illustrative example to elaborate the applications of HFβCRSs in multi-attribute decision making (MADM) problems. By making comparative analysis, the HFβCRSs models proposed by us are more general than the existing models of Ma and Yang and are more applicable than the existing models of Ma and Yang when handling hesitant fuzzy information.

scholarly journals Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 145
Author(s):  
Yun Jin ◽  
Zareena Kousar ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Nimet Yapici Pehlivan ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Evaluation Process ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

Image development in the framework of ξ –complex fuzzy morphisms

2021 ◽  
pp. 1-13
Author(s):  
Aneeza Imtiaz ◽  
Umer Shuaib ◽  
Abdul Razaq ◽  
Muhammad Gulistan
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Fuzzy Sets ◽  
Unit Disk ◽  
Homomorphic Image ◽  
Significant Role ◽  
Original Form ◽  
Mathematical Tool ◽  
Fuzzy Subgroups ◽  
Fundamental Theorems

The study of complex fuzzy sets defined over the meet operator (ξ –CFS) is a useful mathematical tool in which range of degrees is extended from [0, 1] to complex plane with unit disk. These particular complex fuzzy sets plays a significant role in solving various decision making problems as these particular sets are powerful extensions of classical fuzzy sets. In this paper, we define ξ –CFS and propose the notion of complex fuzzy subgroups defined over ξ –CFS (ξ –CFSG) along with their various fundamental algebraic characteristics. We extend the study of this idea by defining the concepts of ξ –complex fuzzy homomorphism and ξ –complex fuzzy isomorphism between any two ξ –complex fuzzy subgroups and establish fundamental theorems of ξ –complex fuzzy morphisms. In addition, we effectively apply the idea of ξ –complex fuzzy homomorphism to refine the corrupted homomorphic image by eliminating its distortions in order to obtain its original form. Moreover, to view the true advantage of ξ –complex fuzzy homomorphism, we present a comparative analysis with the existing knowledge of complex fuzzy homomorphism which enables us to choose this particular approach to solve many decision-making problems.

Sign in / Sign up

Export Citation Format

Share Document