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Operations on Hesitant Linguistic terms sets Induced By Archimedean Triangular Norms And Conorms

Zhaoyan Li, Chenfang Zhao, Zheng Pei
2018 International Journal of Computational Intelligence Systems  
The aim of the paper is to discuss some new operations on hesitant fuzzy linguistic terms sets based on Archimedean t-norm and t-conorm.  ...  The advantage is that the operations on hesitant fuzzy linguistic terms sets are closed, by studying propositions of the operations on hesitant fuzzy linguistic terms sets, scalar-multiplication addition  ...  This work is partially supported by National Nature Science Foundation of China (Grant No. 61372187) and the fund of lab of Security Insurance of Cyberspace, Sichuan Province (SZJJ2016-038) and Sichuan  ... 
doi:10.2991/ijcis.11.1.38 fatcat:layw6l4fwrhmxixsnvjiwrd2y4

Prioritized Dual Hesitant Fuzzy Aggregation Operators Based on t-Norms and t-Conorms with Their Applications in Decision Making

Na ZHAO, Zeshui XU
2018 Informatica  
The main contributions of this paper are shown as: (1) we define dual hesitant fuzzy t-norms and t-conorms; (2) based on dual hesitant fuzzy t-norms and t-conorms, we introduce a family of prioritized  ...  dual hesitant fuzzy operators to aggregate dual hesitant fuzzy information of alternatives with regard to the prioritized attributes; (3) we propose a method to handle the dual hesitant fuzzy multi-attribute  ...  fuzzy power aggregation operators based on Archimedean t-conorm and t-norm; Zhang (2015) proposed the dual hesitant fuzzy Hamacher correlated geometric operator.  ... 
doi:10.15388/informatica.2018.183 fatcat:afzwlqusv5eg5hymiq5mpbbnyy

Hesitant Picture 2-Tuple Linguistic Aggregation Operators Based on Archimedean T-Norm and T-Conorm and Their Use in Decision-Making

Yanjun Wang, Lidong Wang, Huijuan Wang, Xinghua Feng
2018 Symmetry  
Some operational principles of hesitant picture 2-tuple linguistic variables on account of the Archimedean t-norm and t-conorm are initiated, on which two hesitant picture 2-tuple linguistic weighted operators  ...  This study focuses on the development of picture fuzzy sets and aims to design a managerial decision-making solving method.  ...  Some Aggregation Operators of HP2TLSs Based on Archimedean T-norm and T-conorm In this section, according to the Archimedean t-norm and the t-conorm [42, 43] , some pertinent aggregation operators are  ... 
doi:10.3390/sym10110629 fatcat:4ukqetuk4zhm7aeg3l36k2pmse

Symmetric Intuitionistic Fuzzy Weighted Mean Operators Based on Weighted Archimedean t-Norms and t-Conorms for Multi-Criteria Decision Making

Zhen Ming Ma, Wei Yang
2020 Informatica  
Using different operational laws on membership and non-membership information, various intuitionistic fuzzy aggregation operators based on Archimedean t-norm and t-conorm or their special cases have been  ...  In this paper, symmetric intuitionistic fuzzy weighted mean operators w.r.t. general weighted Archimedean t-norms and t-conorms are introduced to deal neutrally or fairly with membership and non-membership  ...  The authors would like to thank the editors and the anonymous reviewers for their insightful and constructive comments and suggestions that have led to this improved version of the paper.  ... 
doi:10.15388/20-infor390 fatcat:4ro3x7r6hfeq7l3u3e7rakqeia

Multi-Attribute Decision-Making Using Hesitant Fuzzy Dombi–Archimedean Weighted Aggregation Operators

Peide Liu, Abhijit Saha, Debjit Dutta, Samarjit Kar
2020 International Journal of Computational Intelligence Systems  
Next, we bring up some HF weighted AOs based on Dombi and Archimedean operations. We discuss in detail some intriguing properties of the proposed AOs.  ...  For the first case it entails the hesitant fuzzy elements (HFEs) as a more flexible and general tool in comparison to fuzzy set theory and for the second one, we allow the aggregation operator (AO) as  ...  On the contrary, Archimedean t-norms and t-conorms [75] [76] [77] are the generalizations of many other t-norms and t-corms like algebraic t-norm and t-conorm, Einstein t-norm and t-conorm, Hamacher  ... 
doi:10.2991/ijcis.d.201215.003 fatcat:y2sphluz3jcvlbcvrfq6q7ttvi

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

Cengiz Kahraman, Başar Öztayşi, Sezi Çevik Onar
2016 International Journal of Computational Intelligence Systems  
In the recent years, ordinary fuzzy sets have been extended to new types and these extensions have been used in many areas such as energy, medicine, material, economics and pharmacology sciences.  ...  In this paper, a comprehensive literature review on the fuzzy set theory is realized.  ...  In addition, they proposed some hesitant interval-valued intuitionistic fuzzy number aggregation operators based on t-conorms and t-norms.  ... 
doi:10.1080/18756891.2016.1180817 fatcat:k5rtjlmy4ncivn2ejvxyitwd3y

Overview on the Developments and Applications of Hesitant Fuzzy Sets: An Uncertain Decision Making Tool

Bin Zhu, Zeshui Xu
2016 Journal of Risk Analysis and Crisis Response (JRACR)  
This paper reviews the main relevant papers, which are published in international academic journals from 2010 to 2016, relating to the interpretations, modellings, and applications of hesitant fuzzy sets  ...  Recently, hesitant fuzzy sets perform as an emerging tool in decision making under uncertainty.  ...  Recently, Chen and Xu (2014) derived the properties and relationships of basic operations on IVHFSs, Chen and Xu (2014) developed some new operations based on Archimedean t-norm and t-conorm.  ... 
doi:10.2991/jrarc.2016.6.2.2 fatcat:35ql55mkdffszoj3bk2aj7ghpe

Hesitant Fuzzy Linguistic Aggregation Operators Based on the Hamacher t-norm and t-conorm

Jianghong Zhu, Yanlai Li
2018 Symmetry  
hesitant fuzzy power aggregation operators [50], linguistic intuitionistic fuzzy power aggregation operators [51], dual hesitant fuzzy power aggregation operators based on Archimedean t-norm and t-conorm  ...  Furthermore, PA and PG operators have also been extended to other fuzzy environments to propose some new operators, such as intuitionistic fuzzy power aggregation operators based on entropy [49], linguistic  ...  Inspired by the idea of Hamacher t-norm and t-conorm, we defined some new basic operational laws on HFLEs based on the Hamacher t-norm and t-conorm.  ... 
doi:10.3390/sym10060189 fatcat:x36k7jqupvaobhthhla7eal62a

Aggregation Functions Considering Criteria Interrelationships in Fuzzy Multi-Criteria Decision Making: State-of-the-Art

LE SUN, HAI DONG, ALEX X. LIU
2019 Zenodo  
In this paper, we make a comprehensive survey on the aggregation operators (AOs) that consider the argument interrelationships in crisp and fuzzy settings.  ...  symmetric mean (MSM) operators, and introduce their extended (e.g., generalized or weighted) forms and their applications in different fuzzy sets.  ...  [215] proposed a variety of PA operators for the dual HFS (DHFS) based on the Archimedean t-norm and t-conorm. Keikha et al.  ... 
doi:10.5281/zenodo.3047021 fatcat:vy2mllhcazfpdnbpfrmy7yqw7i

Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms

Benjamin Bedregal, Renata Reiser, Humberto Bustince, Carlos Lopez-Molina, Vicenç Torra
2014 Information Sciences  
In [28] , the concept of hesitant fuzzy linguistic term set was introduced to manage hesitation in qualitative contexts and applied in group making decision in [29] .  ...  In [13] , some correlation coefficient formulas for HFSs are derived and applied to clustering analysis under hesitant fuzzy environments.  ...  PQ and universal, under the Process Numbers 307681/ 2012-2 and 480832/2011-0, respectively) and FAPERGS (Ed.  ... 
doi:10.1016/j.ins.2013.08.024 fatcat:lvjmklh4erfaxoi2xmqtxngisy

A method to multi-attribute decision-making based on interval-valued q-rung dual hesitant linguistic Maclaurin symmetric mean operators

Xue Feng, Xiaopu Shang, Yuan Xu, Jun Wang
2020 Complex & Intelligent Systems  
linguistic MSM operator, the interval-valued q-rung dual hesitant linguistic dual MSM operator, as well as their weighted forms.  ...  To this end, we first propose the notion of interval-valued q-rung dual hesitant linguistic sets (IVq-RDHLSs) by combining interval-valued q-rung dual hesitant fuzzy (IVq-RDHF) sets with linguistic terms  ...  as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.  ... 
doi:10.1007/s40747-020-00141-8 fatcat:ujrhxu5mzfd7zmi2pgjoyga36q

A Novel MAGDM Method Based on Hesitant Picture Fuzzy Schweizer–Sklar Maclaurin Symmetric Mean Operators and Their Application

Tiedong Chen, Long Ye
2022 Entropy  
Subsequently, we introduced a novel Schweizer–Sklar t-norm and t-conorm operation rules of HPFSs and proposed a family of hesitant picture fuzzy Schweizer–Sklar Maclaurin symmetric mean operators.  ...  In this study, we first proposed hesitant picture fuzzy sets (HPFSs), which is a combination of the hesitant fuzzy set and picture fuzzy set.  ...  Based on the Schweizer-Sklar t-norm and t-conorm, we provide some Schweizer-Sklar operations for HPFEs. Definition 4.  ... 
doi:10.3390/e24020238 pmid:35205532 pmcid:PMC8870918 fatcat:lbckkmchjnebpibahs6ss2glii

Some Hesitant Fuzzy Hamacher Power-Aggregation Operators for Multiple-Attribute Decision-Making

Mi Jung Son, Jin Han Park, Ka Hyun Ko
2019 Mathematics  
In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm.  ...  Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems.  ...  To do so, this paper is organized as follows: In Section 2, some basic concepts and notions of HFSs and Hamacher operations of HFEs based on the Hamacher t-norm and t-conorm are reviewed.  ... 
doi:10.3390/math7070594 fatcat:fvhl2bahlrh7nibvjhe6hvsagu

A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management

Muhammad Riaz, Wojciech Sałabun, Hafiz Muhammad Athar Farid, Nawazish Ali, Jarosław Wątróbski
2020 Energies  
averaging (q-ROFEOWA) operator, q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator, and q-rung orthopair fuzzy Einstein ordered weighted geometric (q-ROFEOWG) operator.  ...  The key feature of q-ROFNs is to deal with the situation when the sum of the q th powers of membership and non-membership grades of each alternative in the universe is less than one.  ...  If is a t-norm, then S(ℵ, ∂) = 1 − (1 − ℵ, 1 − ∂) is a t-conorm, and vice versa. Thus, we obtain a dual pair of a t-norm and a t-conorm.  ... 
doi:10.3390/en13092155 fatcat:4v7zxzaao5anpc4y5jfip4sosm

Linguistic Interval-Valued Intuitionistic Fuzzy Copula Heronian Mean Operators for Multiattribute Group Decision-Making

Lei Xu, Yi Liu, Haobin Liu, Harish Garg
2020 Journal of Mathematics  
Extended copulas (ECs) and extended cocopulas (ECCs) are the promotion form of Archimedean t-norm and t-conorm (ATT).  ...  Moreover, we also propose a new MAGDM approach based on the proposed LIVIFWCHM operator.  ...  hesitant fuzzy set (LHFS) [6, 7] , linguistic neutrosophic set [8, 9] , linguistic intuitionistic fuzzy set (LIFS) [10] , and linguistic Pythagorean fuzzy set [11] .  ... 
doi:10.1155/2020/6179468 fatcat:m2slxkwvgzawxpgrlwfzpaaihi
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