Bipolar pythagorean fuzzy sets examples
WebJan 4, 2024 · Mandal [40] has developed bipolar pythagorean fuzzy sets and their application in multi-attribute decision making problems. Das [41] has developed multi … Let p_{j} = \left( {\mu_{j}^{ + } ,v_{j}^{ + } ,\mu_{j}^{ - } ,v_{j}^{ - } } \right) \;\left( {j = 1,2, \ldots ,n} \right)be a collection of BPFNs, then we define the bipolar Pythagorean fuzzy weighted average (BPFWA) operator as below: where w = \left( {w_{1} ,w_{2} , \ldots ,w_{n} } \right)^{T} be the weight vector of … See more Let p_{j} = \left( {\mu_{j}^{ + } ,v_{j}^{ + } ,\mu_{j}^{ - } ,v_{j}^{ - } } \right) \;\left( {j = 1,2, \ldots ,n} \right) be a collection of BPFNs, then their aggregated value by using the BPFWA operator is also a BPFNs, and where w … See more We can prove the theorem by utilizing the technique of mathematical induction. Therefore, we follow as. (a) For j= 2, since and Then, (b) Suppose that outcome is true for j = mthat is, (c) Now we have to prove that outcome … See more (Idempotency) Let p_{j} = \left( {\mu_{j}^{ + } ,v_{j}^{ + } ,\mu_{j}^{ - } ,v_{j}^{ - } } \right) \;\left( {j = 1,2, \ldots ,n} \right) be any collection of BPFNs. … See more Let is the four bipolar Pythagorean fuzzy numbers with weight vector w = \left( {0.1,0.2,0.3,0.4} \right)^{T}respectively, then we have There are some properties which are fulfilled by the BPFWA operator obviously. See more
Bipolar pythagorean fuzzy sets examples
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WebNov 1, 2024 · The concept of Pythagorean fuzzy sets (PFSs) was initially developed by Yager in 2013, which provides a novel way to model uncertainty and vagueness with high precision and accuracy compared to intuitionistic fuzzy sets (IFSs). The concept was concretely designed to represent uncertainty and vagueness in mathematical way and to … Webcalled fuzzy open sets. A fuzzy set Kis called fuzzy closed if Kc 2˝. We denote by ˝c the collection of all fuzzy closed sets in this fuzzy topological space. Obviously, we have: (a) c2˝, (b) if K;M2˝ c, then K_M2˝ and (c) if fK j: j2Jg2˝c, then ^fK j: j2Jg2˝c. Example 2.1.2 [6]. Let X = fa;bg. Let Abe a fuzzy set on X de ned as A(a) = 1 ...
WebApr 7, 2024 · The innovative approach of this article is to devise the key notion on bipolar complex Pythagorean fuzzy set (\({\mathcal{B}\mathcal{C}\mathcal{P}\mathcal{F}}s\)), … WebPythagorean fuzzy sets were a react... Abstract Many scholars have been challenged by multi-attribute group decision-making problems that have stimulated the appearance of increasingly general models.
WebJun 25, 2024 · 1. Introduction . Many uncertain theories are put forward as fuzzy set [], intuitionistic fuzzy set [], bipolar fuzzy sets [] and Pythagorean fuzzy set [].Zadeh [] …
WebJul 17, 2024 · The linear Diophantine fuzzy set (LDFS) has been proved to be an efficient tool in expressing decision maker (DM) evaluation values in multicriteria decision-making (MCDM) procedure. To more effectively represent DMs’ evaluation information in complicated MCDM process, this paper proposes a MCDM method based on proposed … grassley alexander pension planWebJan 19, 2024 · Thereom 3. Let be a saturated fuzzy cycle with n vertices. For , set ,,, and as the positive membership value of -strong edge, positive membership value of -strong edge, negative membership value of -strong edge, and negative membership value of -strong edge incident to , respectively. Let be the edge of all -strong edges in C.Set ,,, and (allow … grassless yard ideasWebYager[32] proposed the Pythagorean fuzzy set(PFS) as a result of this. It is the latest tool developed to deal with imprecision with a wider scope of applications. It is a generalization of the fuzzy set and intuitionistic fuzzy set. The Pythagorean fuzzy set has a close connection with the intuitionistic fuzzy set. chj industryWebwww.ijaema.com grassless landscape ideasWebJan 1, 2024 · Three minimal decomposition theorems for picture fuzzy sets are introduced by lower (, ,)-cut, strong lower (, ,)-cut and level set of picture fuzzy sets with illustrations by a numerical example. ch jones ltd companies houseWebHindawi grassless yards imagesWebideal, bipolar Pythagorean fuzzy subalgebra, bipolar Pythagorean fuzzy A-ideal, bipolar Pythagorean fuzzy level-cut. 1 Introduction Fuzzy sets were introduced by Zadeh [14] … chjild missing week of school to vacation