WebAn Introduction to Fuzzy Sets - Witold Pedrycz 1998 The concept of fuzzy sets is one of the most fundamental and influential tools in computational intelligence. Fuzzy sets can provide solutions to a broad range of problems of control, pattern classification, reasoning, planning, and computer vision. This book bridges the gap that has developed
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WebBipolar theorem. In mathematics, the bipolar theorem is a theorem in functional analysis that characterizes the bipolar (that is, the polar of the polar) of a set. In convex analysis, … 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
WebWe interact the theory of possibility Pythagorean bipolar fuzzy soft sets, possibility bipolar fuzzy soft sets and define complementation, union, intersection, AND and OR. The possibility Pythagorean bipolar fuzzy soft sets are presented as … Webideal, bipolar Pythagorean fuzzy subalgebra, bipolar Pythagorean fuzzy A-ideal, bipolar Pythagorean fuzzy level-cut. 1 Introduction Fuzzy sets were introduced by Zadeh [14] …
WebBipolar fuzzy relations was given by Bosc and Pivert [3] where a pair of satisfaction degrees is made with each tuple. In 1994, an development of fuzzy set termed bipolar fuzzy was given by Zhang [40].By the notion of fuzzy sets, Lee [16] illustrate bipolar fuzzy sets. Manemaran and Chellappa [20] provide some WebFeb 16, 2024 · The risk is associated with the loss function of DTRSs, which is evaluated by the decision makers. As a new extension of fuzzy sets, Pythagorean fuzzy sets can handle uncertain information more flexibly than intuitionistic fuzzy sets in the process of decision making and it gives a new measure for the determination of loss functions of …
http://fs.unm.edu/neut/BipolarNeutrosophicSetsAndTheirApplication.pdf
WebFor many multi-attribute decision-making (MADM) problems, linguistic variables are more convenient for people to express the attribute values. In this paper, a novel shadowed set-based method is proposed to deal with linguistic terms, where the linguistic term sets are symmetrical both in meaning and form. Firstly, to effectively express the linguistic … seur san roqueWebFeb 1, 2002 · A crisp bipolar combinational logic BCLI and its fuzzy counterpart BCLF are proposed for bipolar modeling based on the ancient … seur santsWeb1 Affiliation : Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia panini tout faitWebThe proposed set is the generalization of the sets of fuzzy, intuitionistic fuzzy, hesitant fuzzy, and Pythagorean fuzzy. Additionally, a multiple-attribute decision-making approach is established based on these operators under hesitant Pythagorean fuzzy environment and an example is given to illustrate the application of it. seur santiagoWebJul 5, 2024 · In this research article, we present a new framework for handling imprecisely acquired bipolar information along with parameterized graded descriptions. The formal model that implements all these desirable features is called bipolar fuzzy N-soft set (also BFNS $$_\\text {f}$$ f S for brevity). We discuss basic operations of our proposed hybrid … panini\u0027s locationsWebApr 10, 2024 · A q-rung orthopair fuzzy set (q-ROFS), an extension of the Pythagorean fuzzy set (PFS) and intuitionistic fuzzy set (IFS), is very helpful in representing vague information that occurs in real ... panini tour romaWebideal, bipolar Pythagorean fuzzy subalgebra, bipolar Pythagorean fuzzy A-ideal, bipolar Pythagorean fuzzy level-cut. 1 Introduction Fuzzy sets were introduced by Zadeh [14] and he discussed only membership function. After the extensions of fuzzy set theory, Atanassov [1] generalized this concept and introduced a new concept called ... seur sestao