PMID- 37362734
OWN - NLM
STAT- Publisher
LR  - 20230928
IS  - 1380-7501 (Print)
IS  - 1573-7721 (Electronic)
IS  - 1380-7501 (Linking)
DP  - 2023 Apr 12
TI  - Einstein exponential operation laws of spherical fuzzy sets and aggregation 
      operators in decision making.
PG  - 1-24
LID - 10.1007/s11042-023-14532-9 [doi]
AB  - The spherical fuzzy set (SFS) model is one of the newly developed extensions of 
      fuzzy sets (FS) for the purpose of dealing with uncertainty or vagueness in 
      decision making. The aim of this paper is to define new exponential and Einstein 
      exponential operational laws for spherical fuzzy sets and their corresponding 
      aggregation operators. We introduce the operational laws for exponential and 
      Einstein exponential SFSs in which the base values are crisp numbers and the 
      exponents (weights) are spherical fuzzy numbers. Some of the properties and 
      characteristics of the proposed operations are then discussed. Based on these 
      operational laws, some new aggregation operators for the SFS model, namely 
      Spherical Fuzzy Weighted Exponential Averaging (SFWEA) and Spherical Fuzzy 
      Einstein Weighted Exponential Averaging (SFEWEA) operators are introduced. 
      Finally, a decision-making algorithm based on these newly introduced aggregation 
      operators is proposed and applied to a multi-criteria decision making (MCDM) 
      problem related to ranking different types of psychotherapy.
CI  - (c) The Author(s), under exclusive licence to Springer Science+Business Media, LLC, 
      part of Springer Nature 2023, Springer Nature or its licensor (e.g. a society or 
      other partner) holds exclusive rights to this article under a publishing 
      agreement with the author(s) or other rightsholder(s); author self-archiving of 
      the accepted manuscript version of this article is solely governed by the terms 
      of such publishing agreement and applicable law.
FAU - Ajay, D
AU  - Ajay D
AD  - Department of Mathematics, Sacred Heart College, Tamilnadu, India. GRID: 
      grid.473479.a. ISNI: 0000 0004 1769 0984
FAU - Selvachandran, Ganeshsree
AU  - Selvachandran G
AD  - Institute of Actuarial Science and Data Analytics, UCSI University, Jalan Menara 
      Gading, 56000 Cheras, Kuala Lumpur Malaysia. GRID: grid.444472.5. ISNI: 0000 0004 
      1756 3061
AD  - Symbiosis Institute of Technology Symbiosis International University, Pune, 
      412115 India. GRID: grid.444681.b. ISNI: 0000 0004 0503 4808
FAU - Aldring, J
AU  - Aldring J
AD  - Department of Mathematics, Sacred Heart College, Tamilnadu, India. GRID: 
      grid.473479.a. ISNI: 0000 0004 1769 0984
AD  - Panimalar Engineering College, Department of Mathematics, Chennai, 600 123 Tamil 
      Nadu India. GRID: grid.252262.3. ISNI: 0000 0001 0613 6919
FAU - Thong, Pham Huy
AU  - Thong PH
AD  - VNU Information Technology Institute, Vietnam National University, Hanoi, 
      Vietnam. GRID: grid.267852.c. ISNI: 0000 0004 0637 2083
FAU - Son, Le Hoang
AU  - Son LH
AD  - VNU Information Technology Institute, Vietnam National University, Hanoi, 
      Vietnam. GRID: grid.267852.c. ISNI: 0000 0004 0637 2083
FAU - Cuong, Bui Cong
AU  - Cuong BC
AD  - Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, 
      Vietnam. GRID: grid.472707.1. ISNI: 0000 0001 2203 4787
LA  - eng
PT  - Journal Article
DEP - 20230412
PL  - United States
TA  - Multimed Tools Appl
JT  - Multimedia tools and applications
JID - 101555932
PMC - PMC10090759
OTO - NOTNLM
OT  - Aggregate operator
OT  - Decision making
OT  - Einstein exponential operational laws
OT  - Exponential operational laws
OT  - Spherical fuzzy set
EDAT- 2023/06/26 19:07
MHDA- 2023/06/26 19:07
PMCR- 2023/04/12
CRDT- 2023/06/26 13:08
PHST- 2021/03/24 00:00 [received]
PHST- 2021/05/21 00:00 [revised]
PHST- 2023/01/31 00:00 [accepted]
PHST- 2023/06/26 19:07 [pubmed]
PHST- 2023/06/26 19:07 [medline]
PHST- 2023/06/26 13:08 [entrez]
PHST- 2023/04/12 00:00 [pmc-release]
AID - 14532 [pii]
AID - 10.1007/s11042-023-14532-9 [doi]
PST - aheadofprint
SO  - Multimed Tools Appl. 2023 Apr 12:1-24. doi: 10.1007/s11042-023-14532-9.