Intuitionistic fuzzy set (IFS)

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A Comparative Analysis on Euclidean Measure In Intuitionistic Fuzzy Set And Interval-Valued Intuitionistic Fuzzy Set

A Comparative Analysis on Euclidean Measure In Intuitionistic Fuzzy Set And Interval-Valued Intuitionistic Fuzzy Set

Intuitionistic Fuzzy set (IFS) was proposed in early 80™s. It is a well known theory. As a developer in Fuzzy Mathematics, interval“ valued Intuitionistic Fuzzy sets (IVFS) were developed afterwards by Gargo and Atanssov. It has a wide range of applications in the field of Optimization and algebra. There are many distance measure in Fuzzy such as Hamming, Normalized Hamming, Euclidean, Normalized Euclidean, Geometric, Normalized Geometric etc¦ to calculate the distance between two fuzzy numbers. In this paper, the comparison between Euclidean distance measure in Intuitionistic Fuzzy set and interval “ valued Intuitionistic Fuzzy sets is explored. The step-wise conservation of Intuitionistic Fuzzy set and interval “ valued Intuitionistic Fuzzy sets is also proposed. A real life application for this comparison is explained briefly. This type of comparative analysis shows that the distance between Intuitionistic Fuzzy set and interval“ valued Intuitionistic Fuzzy sets varies slightly due to boundaries of interval “ valued Intuitionistic Fuzzy sets.

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Study on the Bid Decision System of Renewable Energy for Buildings Based on FAHP and Intuitionistic Fuzzy Set TOPSIS Method

Study on the Bid Decision System of Renewable Energy for Buildings Based on FAHP and Intuitionistic Fuzzy Set TOPSIS Method

To sum up, this study is organized to solve the problems that the front involves. Section II summarizes the previous studies about this topic; Section III analyzes the bid evaluation criteria of the renewable energy building; Section IV proposes the implementation bid decision framework of the renewable energy building. Herein, the FAHP is used to determine the relative weights of the evaluation criteria and the the intuitionistic fuzzy set technique for order preference by similarity to ideal solution (IFS-TOPSIS) is used to rank the alternatives. Based on the aforementioned contents, Section V gives the real case to prove aforementioned framework.

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Study on the Development of Decision Making Using Intuitionistic Fuzzy Set (IFS) and Interval Valued Intuitionistic Fuzzy Set (IVIFS)

Study on the Development of Decision Making Using Intuitionistic Fuzzy Set (IFS) and Interval Valued Intuitionistic Fuzzy Set (IVIFS)

Later on in year 1999 [18] Atanassov also discussed the possibility of using the interpretational triangle of intuitionistic fuzzy set in decision making. But the major contribution in this field comes from Szmidt and Kacprzyk [19-20] who intensively worked on the use of intuitionistic fuzzy sets for building soft decision- making models. They proposed two solution concepts about the intuitionistic fuzzy core and the consensus winner for group decision making. The concept of preference relation was considered by many authors, in the crisp case for example in [21] and in the fuzzy environment [22]. Szmidt and Kacprzyk [23] were also the first authors who generalized the concept of preference relation from the fuzzy case to the intuitionistic fuzzy one. They take into account intuitionistic fuzzy preference relations which are applied in group decision making problems where a solution from the individual preferences over some set of options should be derived. In year 2002 they used a new approach and calculate distance between intuitionistic fuzzy preferences to assess agreement of a group of experts [24]. In another article [25] they propose how to analyze the extent of agreement in a group of experts employing intuitionistic fuzzy sets. They used the concept of distances between intuitionistic fuzzy preferences as the main tool to evaluate how far the group is from full agreement (consensus in a traditional sense) and they also propose how to evaluate if it is possible for a considered group to come closer to the state of consensus. They used Entropy as the measure which makes it possible to say how strong the preferences of experts are.

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Intuitionistic Fuzzy Set with New Operators in Medical Diagnosis

Intuitionistic Fuzzy Set with New Operators in Medical Diagnosis

In real world, we frequently deal with vague or imprecise information. Information available is sometimes vague, sometimes inexact or sometimes insufficient. Out of several higher order fuzzy sets, intuitionistic fuzzy sets(IFS)[2,3] have been found to be highly useful to deal with vagueness. There are situations where due to insufficiency in the information available, the evaluation of membership values is not possible to our satisfaction. Due to some reason, evaluation of non-membership values is not also always possible and consequently there remains a part in deterministic on which hesitation survives. Certainly Fuzz y sets theory is not appropriate to deal with such problem, rather IFS theory is more suitable. Out of several generalizations of fuzzy set theory for various objectives, the notion introduced by Atanassov[2] in defining intuitionistic fuzzy sets is interesting and useful. Fuzzy sets are intuitionistic fuzzy sets but the converse is not necessarily true[2]. In fact there are situations where IFS theory is more appropriate to deal with[5]. Besides, it has been cultured in [6] that vague sets[10] are nothing but IFS.

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Intuitionistic Fuzzy Set (IFS), Multi-agent system (MAS), Quality criteria, Quality factor

Intuitionistic Fuzzy Set (IFS), Multi-agent system (MAS), Quality criteria, Quality factor

Abstract — Agents are being recommended as a next generation model for revising and restructuring the complex distributed applications. So the task of engineering quality for agent systems has also become significant. As different stakeholders such as project managers, users, and practitioners have different interpretations of quality; an integrated specification of MAS quality that could satisfy all the stakeholders in the project is required. The quality specifications of stakeholders are subjective and, there is a fair chance of non-zero hesitation part in recommending quality specifications; Intuitionistic Fuzzy Sets (IFS) have been used to capture the uncertainties associated with stakeholders’ recommendations. IFS are generalization of fuzzy sets having membership, non-membership and hesitation, and this paper proposes a methodology to obtain prioritization of quality specifications that assists quality engineer in achieving the desired level of quality for Multi-agent systems.

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Intuitionistic Fuzzy WI-Ideals of Lattice Wajsberg Algebras

Intuitionistic Fuzzy WI-Ideals of Lattice Wajsberg Algebras

In this paper, the concept of intuitionistic fuzzy set is applied to WI-ideal, that is we introduce the notions of intuitionistic fuzzy WI-ideal and intuitionistic fuzzy lattice ideal of lattice Wajsberg algebras. We show that every intuitionistic fuzzy WI-ideal of lattice Wajsberg algebra is an intuitionistic fuzzy lattice ideal of lattice Wajsberg algebra. Also, we verify its converse part. Further, we discuss the relationship between intuitionistic fuzzy WI-ideal and intuitionistic fuzzy lattice ideal in lattice H-Wajsberg algebra. Also, we investigate some properties of intuitionistic fuzzy WI-ideal of lattice Wajsberg algebras. Finally, we show that collection of WI-ideals of lattice Wajsberg algebra is an intuitionistic fuzzy WI-ideal of lattice Wajsberg algebra.

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A note on connectedness in intuitionistic fuzzy special topological spaces

A note on connectedness in intuitionistic fuzzy special topological spaces

1. Introduction. After the introduction of the concept of fuzzy sets by Zadeh [12], several researches were conducted on the generalizations of the notion of fuzzy set. The idea of “intuitionistic fuzzy set” was first given by Atanassov [2, 3]. Later this concept is generalized to intuitionistic sets in Çoker [6] and intuitionistic topological spaces in [5, 9, 10]. An introduction to connectedness in these spaces is given in [10].

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Cut of N-Generated Intuitionistic Fuzzy Groups

Cut of N-Generated Intuitionistic Fuzzy Groups

After the introduction of the concept of fuzzy sets b L.A.Zadeh [1], researchers were conducted the generalizations of the notion of fuzzy sets, A. Rosenfeld [2] introduced the concept of fuzzy group and the idea of “intuitionistic fuzzy set” was first published by K.T. Atanassov *3+.Multi set theory was introduced by W.D.Blizard[4]. As a generalization of Multisets Yager [5] introduced the concept of Fuzzy Multi set (FMS). Shinoj. T.K and Sunil Jacob John [6] introduced the concept of Intuitionistic Fuzzy Multi sets and proved some basic operations such as union, intersection, addition, multiplication, etc. Cartesian product and  -cut of Intuitionistic Fuzzy Multi sets are defined and their various properties are discussed. A.solairaju, S.rethinakumar,M Maria Arockia Raj[7] introduce the concept of . n  Generated fuzzy sets and its subgroups. P.K.Sharma develop the idea of ( , ) -   cut of intuitionistic fuzzy subgroup. In this chapter we introduce some basic properties of ( , ) -   cut of n  generated fuzzy subgroups of a group

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I- sets and C- sets

I- sets and C- sets

We have that an intuitionistic fuzzy topological space can be associated with two fuzzy topological spaces and vice versa [1]. . If (X, 𝜏) is an IFTS and 𝜏₁= { μₐ / ∃ γₐ ∊ Iˣ such that (μₐ , γₐ) ∊ 𝜏 }, 𝜏₂ = { 1- γₐ / ∃ μₐ ∊ Iˣ such that (μₐ, γₐ) ∊ 𝜏},then (X, 𝜏₁) and (X, 𝜏₂) are fuzzy topological spaces. Similarly if (X, 𝜏₁) and (X, 𝜏₂) are two fuzzy topological space, 𝜏 = {(u,1- v)/ u∊ 𝜏₁, v∊ 𝜏₂ and u ⊆ v} is an intuitionistic fuzzy topology and (X, 𝜏) is an intuitionistic fuzzy topological spaces. We study some relationships connecting the closures and interiors of an intuitionistic fuzzy set in an intuitionistic fuzzy topological space and the closures and interiors of its co- ordinate fuzzy sets in its corresponding fuzzy topological spaces. .

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Intuitionistic Fuzzy Soft Graph

Intuitionistic Fuzzy Soft Graph

Molodtsov [13] introduced the concept of soft set that can be seen as a new mathematical theory for dealing with uncertainties. Molodtsov applied this theory to several directions [13, 14, 15] and then formulated the notions of Soft number, Soft derivative, Soft integral, etc. in [16]. The soft set theory has been applied to many different fields with greatness. Maji [11] worked on theoretical study of soft sets in detail. The algebraic structure of soft set theory dealing with uncertainties has also been studied in more detail. Aktas and Cagman [2] introduced definition of soft groups, and derived their basic properties. The most appreciate theory to deal with uncertainties is the theory of fuzzy sets, developed by Zadeh [22] in 1965. But it has an inherent difficulty to set the membership function in each particular cases. The generalization of Zadeh’s fuzzy set called intuitionistic fuzzy set was introduced by Atanassov [4] which is characterized by a membership function and a non-membership function. In Zadeh’s fuzzy set, the sum of membership degree and non- membership degree is equal to one. In Atanassov’s intuitionistic fuzzy set the sum of membership degree and non- membership degree does not exeed one.

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On Intuitionistic Fuzzy R0-Spaces

On Intuitionistic Fuzzy R0-Spaces

Definition 1.6. [3] Let X be a non-empty set and I be the unit interval #0, 1&. An intuitionistic fuzzy set A (IFS, in short) in X is an object having the form A = '(x, µ * x , ν * x ,, x X- , where µ * : X / I and ν * : X / I denote the degree of membership and the degree of non-membership respectively, and µ * x 0 ν * x 1 1. Let IX denote the set of all intuitionistic fuzzy sets in X . Obviously every fuzzy set µ * in X is an intuitionistic fuzzy set of the form µ * , 1 µ * .

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Matrix Representations of Intuitionistic Fuzzy Graphs

Matrix Representations of Intuitionistic Fuzzy Graphs

Graphs can be sometimes very complicated. So one needs to find more practical ways to represent them. Matrices are a very useful way of studying graphs, since they turn the picture into numbers. Networks can represent all sorts of systems in the real world. As computers are more adept at manipulating numbers than at recognizing pictures, it is standard practice to communicate the specification of a graph to a computer in matrix form. Matrices play an important role in the broad area of science and engineering. However, the classical matrix theory sometimes fails to solve the problems involving uncertainties, occurring in an imprecise environment. Sometimes it seems to be more natural to describe imprecise and uncertain opinions not only by membership functions and also by non membership function.So an Intuitionistic fuzzy matrix is the appropriate choice when exhibiting the membership degree and non- membership degree. In 1975, Rosenfeld [17] discussed the concept of fuzzy graphs whose basic idea was introduced by Kauffmann [12] in 1973. The fuzzy relations between fuzzy sets were also considered by Rosenfeld and he developed the structure of fuzzy graphs, obtaining analogs of several

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Point Set Domination of Intuitionistic Fuzzy Graphs

Point Set Domination of Intuitionistic Fuzzy Graphs

Proof: Suppose there exist vertices u and v belonging to two different components of G. Since D is an intuitionistic fuzzy psd-set of G, there much exist w D such that <{u,v,w}> is stongly connected IFG.Which is contradiction to our assumption, i.e. V– D ⊆ V(H) for some component H of G. Further D 5 V(H) ≠ 6 which implied <V – D > is a proper sub graph of H. Hence the proof.

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A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces

A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces

such that and (i, j)-πgβcl{x} ≠ (i, j)-πgβcl{y}then there exists z∈ and (i, j)-πgβcl{x} such that z ∉ (i, j)-πgβcl{y}, Therefore, there exists V∈ and (i, j) πgβ open set (X) such that y ∉ V and z ∈ V and hence x ∈V. Thus we get x ∉ (j,i) πgβ-Cl{y} and therefore, x ∈X\(j,i) πgβ-Cl{y}. This implies that (i,j) πgβ-Cl{x}⊂X\(i,j) πgβ-Cl{y}, and therefore, (j,i)- πgβ-Cl{x}∩(j,i)-πgβ-Cl{y}=ϕ

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The operators over the GIFS

The operators over the GIFS

intuitionistic fuzzy operators applied in contracting a classifier recognizing imbalanced classes, image recognition, image processing, multi-criteria decision making, deriving the similarity measure, sales analysis, new product marketing, medical diagnosis, financial services, solving optimization problems and etc. Baloui Jamkhaneh and Nadarajah [7] considered a new generalized intuitionistic fuzzy sets (GIF S B ) and introduced some operators over GIF S B . By analogy we shall introduce the some of

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Intuitionistic Heuristic Prototype-based Algorithm of Possibilistic Clustering

Intuitionistic Heuristic Prototype-based Algorithm of Possibilistic Clustering

In the eighth place, an intuitionistic fuzzy possibilistic c - means algorithm to clustering intuitionistic fuzzy sets is proposed in [21]. The corresponding IFPCM-algorithm is developed by hybridizing concepts of the FPCM clustering method [22], intuitionistic fuzzy sets and distance measures. The IFPCM-algorithm resolves inherent problems encountered with information regarding membership values of objects to each cluster by generalizing membership and non- membership with hesitancy degree. Moreover, the IFPCM- algorithm is extended in [21] for clustering interval-valued intuitionistic fuzzy sets leading to interval-valued intuitionistic fuzzy possibilistic c -means algorithm. So, the IVIFPCM-algorithm has membership and non-membership degrees as intervals.

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Intuitionistic Fuzzy β Generalized Continuous Mappings

Intuitionistic Fuzzy β Generalized Continuous Mappings

The concept of fuzzy sets was introduced by Zadeh [11] and later Atanassov [1] generalized this idea to intuitionistic fuzzy sets using the notion of fuzzy sets. On the other hand Coker [4] introduced intuitionistic fuzzy topological spaces using the notion of intuitionistic fuzzy sets. In this paper, we introduced intuitionistic fuzzy 𝜷 generalized continuous mappings and studied some of their basic properties. We arrived at some characterizations of intuitionistic fuzzy 𝜷 generalized continuous mappings.

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Ordering Of Intuitionistic Fuzzy Numbers Using Centroid Of Centroids Of Intuitionistic Fuzzy Number

Ordering Of Intuitionistic Fuzzy Numbers Using Centroid Of Centroids Of Intuitionistic Fuzzy Number

This is a novel method of ascertaining the ranking of the Trapezoidal Intuitionistic Fuzzy Number (TIF) and Triangular Intuitionistic Fuzzy Number (TrIF) applying the mean of centroids. A comparative study is conducted about the proposed ranking and other methods of ranking for the Trapezoidal as well as Triangular Intuitionistic Fuzzy Numbers (TIF and TrIF).

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Connectedness In Pythagorean Fuzzy Topological Spaces

Connectedness In Pythagorean Fuzzy Topological Spaces

Proposition 3.11. Let , be two Pythagorean fuzzy topological spaces and let f :X→Y be a Pythagorean fuzzy continuous surjection. If is Pythagorean fuzzy connected, , then so is . Proof. On the contrary, suppose that is Pythagorean fuzzy disconnected. Then there exist Pythagorean fuzzy open sets A≠0 Y ,B≠0 Y in Y such that AUB=1 y , A∩B=0 Y . Now, we see that U=f -1 (A), V= f -1 (B) are

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Browder's Fixed Point Theorem and Some Interesting Results in Intuitionistic Fuzzy Normed Spaces

Browder's Fixed Point Theorem and Some Interesting Results in Intuitionistic Fuzzy Normed Spaces

We define and study Browder’s fixed point theorem and relation between an intuitionistic fuzzy convex normed space and a strong intuitionistic fuzzy uniformly convex normed space. Also, we give an example to show that uniformly convex normed space does not imply strongly intuitionistic fuzzy uniformly convex.

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