An approach to MCGDM based on multi-granulation Pythagorean fuzzy rough set over two universes and its application to medical decision problem

Sun, Baiqing; Tong, Sirong; Ma, Weimin; Wang, Ting; Jiang, Chao

doi:10.1007/s10462-021-10048-6

Cited by 30 publications

(7 citation statements)

References 43 publications

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“…The first aspect is the background researches on three-way decisions. These researches mainly focus on the generalization of Pawlak's rough sets, such as decision-theoretic rough sets (Yao 2003(Yao , 2007(Yao , 2008, game-theoretic rough sets (Azam and Yao 2014), fuzzy rough sets/rough fuzzy sets (Dubois et al 1990), variable precision rough sets (Ziarko 1993), fuzzy covering-based rough sets (Yang and Hu 2016;Yang and Hu 2017), multi-granulation rough sets (Lin et al 2013;Sun et al 2021), and so on.…”

Section: A Short Review Of Three-way Decisionsmentioning

confidence: 99%

New constructions of decision evaluation functions in three-way decision spaces based on uninorms

Jia

Qiao

2022

Artif Intell Rev

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In 2014, Hu introduced the concept of three-way decision spaces and axiomatic definition of decision evaluation functions. In three-way decision spaces, decision evaluation function satisfies minimum element axiom, monotonicity axiom and complement axiom. Since then, the research on construction method of decision evaluation functions from commonly used binary aggregation functions becomes a research hotspot. Meanwhile, uninorms, as one class of binary aggregation functions, have been successfully applied in various application problems, such as in decision making, image processing, data mining, etc. This paper continues to consider this research topic and mainly explores the new construction methods of decision evaluation functions based on uninorms. Firstly, we show two novel transformation methods from semi-decision evaluation functions to decision evaluation functions based on uninorms. Secondly, using known semi-decision evaluation functions, we give some new construction methods of semi-decision evaluation functions. Thirdly, we give some novel construction methods of decision evaluation functions and semi-decision evaluation functions related to fuzzy sets, interval-valued fuzzy sets, fuzzy relations and hesitant fuzzy sets. Based on them, decision maker can obtain more useful decision evaluation functions, thereby more choices can be used for realistic decision-making problems. Finally, we consider two real evaluation problems to illustrate the results obtained in this paper. The three-way decisions results of evaluation problem show that the construction method proposed in this paper is superior to some existing construction methods under some conditions. Keywords (Semi-)three-way decision spaces • Three-way decisions • Uninorms • Decision evaluation functions & Junsheng Qiao

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Section: A Short Review Of Three-way Decisionsmentioning

confidence: 99%

New constructions of decision evaluation functions in three-way decision spaces based on uninorms

Jia

Qiao

2022

Artif Intell Rev

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“…Further studies on MCDM with FSs and aggregation operators can be found in. 1,9,17,27,29,[39][40][41] As a generalization of IFS, the concept of Pythagorean fuzzy set (PFS) was developed by Yager, 33,34 which is defined by a membership function µ A : X → [0, 1] and a non-membership function ν A : X → [0, 1] under the condition µ 2 A (x) + ν 2 A (x) ≤ 1 for x ∈ X. A PFS is more capable than an IFS to express uncertainty.…”

Section: Introductionmentioning

confidence: 99%

A new type of neutrosophic set in Pythagorean Fuzzy environment and Applications to multi-criteria decision making

Boziygit¹,

Olgun²,

Smarandache³

2023

IJNS

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In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. First of all, we propose the concepts of Pythagorean fuzzy t-norm and t-conorm and show that some Pythagorean fuzzy t-norms and t-conorms are expressed via ordinary continuous Archimedean tnorms and t-conorms. Then we define the concepts of PFVNS and PFVNV and provide a tool to construct a PFVNV from an ordinary neutrosophic fuzzy value. We also define some set theoretic operations between PFVNSs and some algebraic operations between PFVNVs via t-norms and t-conorms. With the help of these algebraic operations we propose some weighted aggregation operators. To measure discrimination information of PFVNVs, we define a simplified neutrosophic valued modified fuzzy cross-entropy measure. Moreover, we introduce a multi-criteria decision making method in Pythagorean fuzzy valued neutrosophic environment and practice the proposed theory to a real life multi-criteria decision making problem. Finally, we study the comparison analysis and the time complexity of the proposed method.

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“…The aforementioned theories are imperfectly designed to tackle MAGDM situations involving multiple decision‐makers simultaneously, see also Chen (2022); Naz et al (2022); Peng et al (2020); and Sun et al (2022). To account for simultaneous evaluations, Alkhazaleh and Salleh (2011) proposed the notion of soft expert (SE) sets.…”

Section: Introductionmentioning

confidence: 99%

A new method of multi‐attribute group decision making based on hesitant fuzzy soft expert information

2023

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Interesting insights into uncertain multi‐attribute decision‐making systems have come from the theory of hesitant fuzzy sets. Outputs become more reliable when a decision‐maker is not forced to produce one single assessment in the presence of hesitation. Hesitancy in fuzzy environments grants more flexibility to the decision‐maker, therefore enhancing the validity of all subsequent results. Due to these facts, hesitation has become a landmark in the enhancement of fuzzy‐soft‐inspired theories, and techniques using models such as hesitant fuzzy soft sets or hesitant (fuzzy) ‐soft sets have thrived. However, the literature lacks a comparable improvement for fuzzy soft expert information. The main goal of this paper is the integration of both hesitation and fuzziness with the characteristics of soft expert sets. The resulting hybrid model is therefore called hesitant fuzzy soft expert set, and its utilization for multiple attribute group decision‐making (MAGDM) will be investigated too. To that purpose, we first study the required algebraic operations and properties (subsethood and equality, complement, union, intersection, plus AND and OR operation). Respective numerical examples illustrate their utilization. We also establish some important laws for hesitant fuzzy soft expert sets, including commutativity, associativity, distributivity, and De Morgan's laws. Moreover, we define four novel types of level soft expert sets for fuzzy soft expert sets, and three types of fuzzy soft expert sets for hesitant fuzzy soft expert sets, which are: ‐level soft expert sets, level soft expert sets regarding fuzzy threshold, mid‐level soft expert sets and top‐level soft expert sets. Armed with these tools, we present a natural algorithm for MAGDM under hesitant fuzzy soft expert information that is accompanied by an illustrative application that concerns a selection problem for the samples of electric vehicles manufactured by different companies. This is followed by a comparison with existing mathematical tools such as hesitant fuzzy soft sets and fuzzy soft expert sets, in order to show the advantages of our work over them. In the end, we provide some future research directions.

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An approach to MCGDM based on multi-granulation Pythagorean fuzzy rough set over two universes and its application to medical decision problem

Cited by 30 publications

References 43 publications

New constructions of decision evaluation functions in three-way decision spaces based on uninorms

New constructions of decision evaluation functions in three-way decision spaces based on uninorms

A new type of neutrosophic set in Pythagorean Fuzzy environment and Applications to multi-criteria decision making

A new method of multi‐attribute group decision making based on hesitant fuzzy soft expert information

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