Top

Granular Computing

Published in:

25-04-2018 | Original Paper

Quasiconvex possibility distribution with application in decision-making

Authors: Lesheng Jin, Jian Wang, Gang Qian

Published in: Granular Computing | Issue 2/2019

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Possibility distribution was originally introduced by Negoita et al. (Fuzzy Sets Syst 1:61–72, 1978), which has some relation to fuzzy sets while has its own practical meaning. During more than three decades, it has some developments especially in theoretical studies. As an alternative way to model uncertainty, possibility theory has its own advantages just as fuzzy sets did. In this study, we review the concepts of possibility distribution and propose quasiconvex possibility distribution with their mathematical properties and applications. Together with some properties of them, we also put emphasis on their special application cases in decision-making practices. Throughout this study, we propose several new concepts and definitions with reasonable illustrative examples, from which it can be seen that quasiconvex possibility distributions are powerful tools and can be widely used in other applications.

previous article Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making

next article Granular computing-based approach of rule learning for binary classification

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Ammar E, Metz J (1992) On fuzzy convexity and parametric fuzzy optimization. Fuzzy Sets Syst 49:135–141. https://doi.org/10.1016/0165-0114(92)90319-Y MathSciNetCrossRefMATH

Chatterjee K, Kar S (2017) Unified granular-number-based AHP-VIKOR multi-criteria decision framework. Granul Comput 2:199–221. https://doi.org/10.1007/s41066-017-0039-4 CrossRef

Chen SM, Chang TH (2001) Finding multiple possible critical paths using fuzzy PERT. IEEE Trans Syst Man Cybern Part B Cybern 31:930–937CrossRef

Chen SM, Hong JA (2014a) Fuzzy multiple attributes group decision making based on ranking interval type-2 fuzzy sets and the TOPSIS method. IEEE Trans Syst Man Cybern Syst 44:1665–1673CrossRef

Chen SM, Hong JA (2014b) Multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets. Inf Sci 286:63–74CrossRef

Chen SM, Lin TE, Lee LW (2014) Group decision making using incomplete fuzzy preference relations based on the additive consistency and the order consistency. Inf Sci 259:1–15MathSciNetCrossRefMATH

Das S, Kar S, Pal T (2017) Robust decision making using intuitionistic fuzzy numbers. Granul Comput 2:41–54CrossRef

Dubois D, Foulloy L, Mauris G, Prade H (2004) Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Reliab Comput 10:273–297. https://doi.org/10.1023/B:REOM.0000032115.22510.b5 MathSciNetCrossRefMATH

Geer JF, Klir GJ (1992) A mathematical analysis of information-preserving transformations between probabilistic and possibilistic formulations of uncertainty. Int J Gen Syst 20:143–176. https://doi.org/10.1080/03081079208945024 CrossRefMATH

Grabisch M, Marichal JL, Mesiar R, Pap E (2009) Aggregation functions. Cambridge University Press, CambridgeCrossRefMATH

Janiš V, Renčová M (2013) Aggregation operators preserving quasiconvexity. Inf Sci 228:37–44. https://doi.org/10.1016/j.ins.2012.12.003 MathSciNetCrossRefMATH

Jin L (2015) Some properties and representation methods for ordered weighted averaging operators. Fuzzy Sets Syst 261:60–86. https://doi.org/10.1016/j.fss.2014.04.019 MathSciNetCrossRefMATH

Jin L (2016) Vector t-norms with applications. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2016.2617371

Jin L, Mesiar R (2017) The metric space of ordered weighted average operators with distance based on accumulated entries. Int J Intell Syst 32:665–675. https://doi.org/10.1002/int.21869 CrossRef

Jin L, Qian G (2016) OWA generation function and some adjustment methods for OWA operators with application. IEEE Trans Fuzzy Syst 24:68–178. https://doi.org/10.1109/TFUZZ.2015.2450772 CrossRef

Jin L, Kalina M, Qian G (2017) Discrete and continuous recursive forms of OWA operators. Fuzzy Sets Syst 308:106–122. https://doi.org/10.1016/j.fss.2016.04.017 MathSciNetCrossRefMATH

Klement EP, Mesiar R, Pap E (2000) Triangular norms. Springer, BerlinCrossRefMATH

Klir GJ (1990) A principle of uncertainty and information invariance. Int J Gen Syst 17:249–275. https://doi.org/10.1080/03081079008935110 CrossRefMATH

Lee LW, Chen SM (2008) Fuzzy multiple attributes group decision-making based on the extension of TOPSIS method and interval type-2 fuzzy sets. In: Proceedings of the 2008 international conference on machine learning and cybernetics, Kunming, China, vol 6, pp 3260–3265

Liu X (2005) On the properties of equidifferent RIM quantifier with generating function. Int J Gen Syst 34:579–594. https://doi.org/10.1080/00268970500067880 MathSciNetCrossRefMATH

Liu H, Gegov A, Cocea M (2016) Rule-based systems: a granular computing perspective. Granul Comput 1:259–274. https://doi.org/10.1007/s41066-016-0021-6 CrossRef

Meng S, Liu N, He Y (2017) GIFIHIA operator and its application to the selection of cold chain logistics enterprises. Granul Comput 2:187–197CrossRef

Merigó JM, Gil-Lafuente AM (2009) The induced generalized OWA operator. Inf Sci 179:729–741. https://doi.org/10.1016/j.ins.2008.11.013 MathSciNetCrossRefMATH

Mesiar R, Stupňanová A, Yager RR (2015) Generalizations of OWA operators. IEEE Trans Fuzzy Syst 23:2154–2162. https://doi.org/10.1109/TFUZZ.2015.2406888 CrossRef

Mesiar R, Borkotokey S, Jin L, Kalina M (2017a) Aggregation functions and capacities. Fuzzy Sets Syst. https://doi.org/10.1016/j.fss.2017.08.007 MATH

Mesiar R, Sipeky L, Gupta P, Jin L (2017b) Aggregation of OWA operators. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2017.2654482

Negoita C, Zadeh L, Zimmermann H (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:61–72MathSciNetCrossRef

Ouyang Y (2013) Generalizing the migrativity of continuous t-norms. Fuzzy Sets Syst 211:73–83. https://doi.org/10.1016/j.fss.2012.03.008 MathSciNetCrossRefMATH

Ouyang Y (2015) Improved minimax disparity model for obtaining OWA operator weights: issue of multiple solutions. Inf Sci 320:101–106. https://doi.org/10.1016/j.ins.2015.05.021 MathSciNetCrossRefMATH

Pedrycz W, Chen SM (2015) Granular computing and decision-making: interactive and iterative approaches. Springer, HeidelbergCrossRef

Prade DDH, Dubois D (1988) Possibility theory: an approach to computerized processing of uncertainty. Plenum, New YorkMATH

Sanchez MA, Castro JR, Castillo O, Mendoza O, Rodriguez-Diaz A, Melin P (2017) Fuzzy higher type information granules from an uncertainty measurement. Granul Comput 2:95–103. https://doi.org/10.1007/s41066-016-0030-5 CrossRef

Syau YR, Skowron A, Lin EB (2017) Inclusion degree with variable-precision model in analyzing inconsistent decision tables. Granul Comput 2:65–72. https://doi.org/10.1007/s41066-016-0027-0 CrossRef

Wang J, Merigó JM, Jin L (2017) S-H OWA operators with moment measure. Int J Intell Syst 32:51–66. https://doi.org/10.1002/int.21829 CrossRef

Xu Z, Gou X (2017) An overview of interval-valued intuitionistic fuzzy information aggregations and applications. Granul Comput 2:13–39CrossRef

Xu Z, Wang H (2016) Managing multi-granularity linguistic information in qualitative group decision making: an overview. Granul Comput 1:21–35CrossRef

Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern 18:183–190. https://doi.org/10.1109/21.87068 CrossRefMATH

Yager RR (1993) Families of OWA operators. Fuzzy Sets Syst 59:125–148. https://doi.org/10.1016/0165-0114(93)90194-M MathSciNetCrossRefMATH

Yager RR (2001) Determining equivalent values for possibilistic variables. IEEE Trans Syst Man Cybern Part B (Cybern) 31:19–31. https://doi.org/10.1109/3477.907562 CrossRef

Yager RR (2003) Induced aggregation operators. Fuzzy Sets Syst 137:59–69. https://doi.org/10.1016/S0165-0114(02)00432-3 MathSciNetCrossRefMATH

Yager RR (2008) Time series smoothing and OWA aggregation. IEEE Trans Fuzzy Syst 16:994–1007. https://doi.org/10.1109/TFUZZ.2008.917299 CrossRef

Yager RR (2010) Norms induced from OWA operators. IEEE Trans Fuzzy Syst 18:57–66. https://doi.org/10.1109/TFUZZ.2009.2035812 CrossRef

Yager RR (2012) Conditional approach to possibility-probability fusion. IEEE Trans Fuzzy Syst 20:46–56. https://doi.org/10.1109/TFUZZ.2011.2165847 CrossRef

Yager RR, Filev DP (1999) Induced ordered weighted averaging operators. IEEE Trans Syst Man Cybern Part B (Cybern) 29:141–150. https://doi.org/10.1109/3477.752789 CrossRef

Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353. https://doi.org/10.1016/S0019-9958(65)90241-X CrossRefMATH

Title: Quasiconvex possibility distribution with application in decision-making
Authors: Lesheng Jin
Jian Wang
Gang Qian
Publication date: 25-04-2018
Publisher: Springer International Publishing
Published in: Granular Computing / Issue 2/2019
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI: https://doi.org/10.1007/s41066-018-0096-3

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 2/2019

The determination of three-way decisions with decision-theoretic rough sets considering the loss function evaluated by multiple experts

Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision-making

Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making

Type-2 fuzzy reliability–redundancy allocation problem and its solution using particle-swarm optimization algorithm

Computing with words for student strategy evaluation in an examination

Optimization of granulation for fuzzy controllers of autonomous mobile robots using the Firefly Algorithm

Premium Partner