PMID- 31408506
OWN - NLM
STAT- MEDLINE
DCOM- 20200302
LR  - 20200302
IS  - 1932-6203 (Electronic)
IS  - 1932-6203 (Linking)
VI  - 14
IP  - 8
DP  - 2019
TI  - Modeling of linear programming and extended TOPSIS in decision making problem 
      under the framework of picture fuzzy sets.
PG  - e0220957
LID - 10.1371/journal.pone.0220957 [doi]
LID - e0220957
AB  - Picture fuzzy sets (PFSs) are comparatively a new extension of fuzzy sets which 
      describe the human opinions that has more answers like acceptance, rejection, 
      neutral and desist, which cannot be correctly presented in fuzzy sets (FSs) and 
      intuitionistic fuzzy sets (IFSs). The PFSs are categorized by three objects, the 
      degree of belonging, the degree of neutral belonging and the degree of non- 
      belonging such that the total of these three degrees must not be more than one. 
      So far, there is no such work presented in the literature which deals with 
      unknown weights of criteria based on PFSs. In the present work, we have developed 
      a linear programming (LP) model to find the exact weights from the given 
      constraints of weights for the criteria and construct a modified distance based 
      on similarity measure between picture fuzzy sets. Then we have utilized this 
      similarity measure to achieve the best option in the multiple criteria decision 
      making (MCDM) problem. Lastly, two practical examples for the selection of 
      alternatives are presented to compare the obtained results with the existing 
      similarity measures.
FAU - Sindhu, M Sarwar
AU  - Sindhu MS
AUID- ORCID: 0000-0003-1223-2629
AD  - Department of Mathematics University of Management and Technology, Lahore - 
      54770, Pakistan.
FAU - Rashid, Tabasam
AU  - Rashid T
AD  - Department of Mathematics University of Management and Technology, Lahore - 
      54770, Pakistan.
FAU - Kashif, Agha
AU  - Kashif A
AD  - Department of Mathematics University of Management and Technology, Lahore - 
      54770, Pakistan.
LA  - eng
PT  - Journal Article
DEP - 20190813
PL  - United States
TA  - PLoS One
JT  - PloS one
JID - 101285081
SB  - IM
MH  - *Algorithms
MH  - *Decision Making
MH  - *Fuzzy Logic
MH  - *Programming, Linear
PMC - PMC6692018
COIS- The authors have declared that no competing interests exist.
EDAT- 2019/08/14 06:00
MHDA- 2020/03/03 06:00
PMCR- 2019/08/13
CRDT- 2019/08/14 06:00
PHST- 2019/05/24 00:00 [received]
PHST- 2019/07/26 00:00 [accepted]
PHST- 2019/08/14 06:00 [entrez]
PHST- 2019/08/14 06:00 [pubmed]
PHST- 2020/03/03 06:00 [medline]
PHST- 2019/08/13 00:00 [pmc-release]
AID - PONE-D-19-14309 [pii]
AID - 10.1371/journal.pone.0220957 [doi]
PST - epublish
SO  - PLoS One. 2019 Aug 13;14(8):e0220957. doi: 10.1371/journal.pone.0220957. 
      eCollection 2019.