Top PDF Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers

Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers

Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers

The aim of this work is to present some cases of aggregation operators with intuitionistic trapezoidal fuzzy numbers and study their desirable properties. First, some operational laws of intuitionistic trapezoidal fuzzy numbers are introduced. Next, based on these oper- ational laws, we develop some geometric aggregation operators for aggregating intuition- istic trapezoidal fuzzy numbers. In particular, we present the intuitionistic trapezoidal fuzzy weighted geometric (ITFWG) operator, the intuitionistic trapezoidal fuzzy ordered weighted geometric (ITFOWG) operator, the induced intuitionistic trapezoidal fuzzy ordered weighted geometric (I-ITFOWG) operator and the intuitionistic trapezoidal fuzzy hybrid geometric (ITFHG) operator. It is worth noting that the aggregated value by using these operators is also an intuitionistic trapezoidal fuzzy value. Then, an approach to multi- ple attribute group decision making (MAGDM) problems with intuitionistic trapezoidal fuzzy information is developed based on the ITFWG and the ITFHG operators. Finally, an illustrative example is given to verify the developed approach and to demonstrate its prac- ticality and effectiveness.
Show more

10 Read more

Interval-valued Trapezoidal Intuitionistic Fuzzy Generalized Aggregation Operators and Application to Multi-attribute Group Decision Making

Interval-valued Trapezoidal Intuitionistic Fuzzy Generalized Aggregation Operators and Application to Multi-attribute Group Decision Making

In a similar way to TIFNs, Wang [35] dened the Trapezoidal IFN (TrIFN) and Interval-Valued Trape- zoidal IFN (IVTrIFN). Both TrIFN and IVTrIFN are extensions of TIFNs. Wang and Zhang [36] investi- gated the weighted arithmetic averaging operator and weighted geometric averaging operator on TrIFNs and their applications to MADM problems. Wei [37] in- vestigated some arithmetic aggregation operators with TrIFNs and their applications to MAGDM problems. Du and Liu [38] extended the fuzzy VIKOR method with TrIFNs. Wu and Cao [39] developed some fam- ilies of geometric aggregation operators with TrIFNs and applied them to MAGDM problems. Wan and Dong [40] dened the expectation and expectant score, ordered weighted aggregation operator and hybrid aggregation operator for TrIFNs and employed them for MAGDM. Ye [41] developed the expected value method for intuitionistic trapezoidal fuzzy multicrite- ria decision-making problems. Ye [42] proposed the MAGDM method using vector similarity measures for TrIFNs. Wan [43] developed four kinds of power av- erage operator of TrIFNs, involving the power average operator, weighted power average operator of, power order weighted average operator of, and power hybrid average operator of TrIFNs. Wan [44] rstly dened some operational laws and the weighted arithmetical average operator of IVTrIFNs. Based on the score function and accurate function, an approach is pre- sented to rank IVTrIFNs. The MAGDM method using IVTrIFNs is then proposed. Wan [45] constructed non- linear fractional programming models to estimate the alternative's relative closeness. After transformation into linear programming models, the interval of the
Show more

14 Read more

A robust aggregation operators for multi-criteria decision-making with intuitionistic fuzzy soft set environment

A robust aggregation operators for multi-criteria decision-making with intuitionistic fuzzy soft set environment

Abstract. Soft set theory acts as a fundamental tool for handling the uncertainty in the data by adding a parameterized factor during the process unlike fuzzy as well as intuitionistic fuzzy set theory. In this manuscript, an attempt has been made to compare two Intuitionistic Fuzzy Soft Numbers (IFSNs) and then weighted averaging and geometric aggregation operators for aggregating the dierent input arguments have been presented. Further, their various properties have been established. The eectiveness of these operators has been demonstrated through a case study.
Show more

12 Read more

Some Generalized Einstein Aggregation Operators Based on the Interval-Valued Intuitionistic Fuzzy Numbers and Their Application to Group Decision Making

Some Generalized Einstein Aggregation Operators Based on the Interval-Valued Intuitionistic Fuzzy Numbers and Their Application to Group Decision Making

All the above aggregation operators are based on the algebraic operational rules of IVIFNs, and the keys of the algebraic operations are Algebraic product and Algebraic sum, which are one type of operations that can be chosen to model the intersection and union of IVIFNs. In general, a general T -norm and T - conorm can be used to model the intersection and union of IVIFNs [32,33]. Wang and Liu [34] proposed the intuitionistic fuzzy Einstein aggregation operators based on Einstein operations which meet the typical T -norm and T -conorm and have the same smooth approximations as the algebraic operators such as the Intuitionistic Fuzzy Einstein Weighted Geometric op- erator (IFEWG) and the Intuitionistic Fuzzy Einstein Ordered Weighted Geometric operator (IFEOWG), and established some general properties of these oper- ators such as idempotency, commutativity, and mono- tonicity. Wang and Liu [35] proposed the Intuitionistic Fuzzy Einstein Weighted Averaging operator (IFEWA) and the Intuitionistic Fuzzy Einstein Ordered Weighted Averaging operator (IFEOWA), and studied various properties of these operators and analyzed the relations between the existing intuitionistic fuzzy aggregation operators and them. Maris and Iliadis [36] further explained the advantages of Einstein operations by using some T -norms to unify the risk indices and to produce a unied means of risk measure. The algebraic T -norm estimated the risky areas under average rainfall conditions, and the Einstein T -norm oered a good approach for an overall evaluation. The computer system has proven its ability to work more eectively compared to the older methods.
Show more

18 Read more

Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment

Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment

Multiple Criteria Group Decision Making Problems (MCGDM) are important parts of modern decision theory due to rapid development of economic and social uncertainties. Today, Decision-Maker (DM) wants to attain more than one goal by satisfying dierent constraints. But, due to the complexity of management environments and decision problems themselves, DMs may provide their rating or judgment in the form of crisp numbers without considering the degree of fuzziness or vagueness of the data in the domain of the problem [1]. However, in these days, uncertainties play a dominant role during the decision-making process, and the decision-maker cannot give their preferences to an accurate level without being proper handled. The main objective during an analysis is to handle the proper data so as to minimize the uncertainties level. To handle this, a fuzzy set theory [2] has been
Show more

17 Read more

A Ranking Approach for Intuitionistic Fuzzy Numbers and its Application

A Ranking Approach for Intuitionistic Fuzzy Numbers and its Application

Concerning ranking IF numbers some work has been reported in the literature. Grzegorzewski [12] defined two families of metrics in the space of IF numbers and proposed a method for comparing IF numbers based on these metrics. Mitchell [15] extended the natural ordering of real numbers to triangular intuitionistic fuzzy (TrIF) numbers by adopting a statistical view point and interpreting each IF number as ensemble of ordinary fuzzy numbers. Nayagam et al. [19] introduced TrIF numbers of special type and described a method to compare them. Although their ranking method appears to be attractive, the definition of TrIF number seems unrealistic. This is because the triangular nonmembership function is defined to geometrically behave in an identical manner as the membership function. Nan and Li [16] proposed a method for comparing TrIF number using lexicographic technique. Nehi [20] proposed a new method for comparing IF numbers in which two characteristic values for IF numbers are defined by the integral of the inverse fuzzy membership and nonmembership functions multiplied by the grade with powered parameter. Almost in parallel, Li [13] introduced a new definition of the TrIF number which has an appealing and logically reasonable interpretation. He defined two concepts of the value and the ambiguity of a TrIF number similar to those for a fuzzy number introduced by Delgado et al. [4]. Dubey and Mehra [5] defined a TrIF number which is more general than the one defined in [13, 16]. They extended the definitions of the value and the ambiguity index given by Li [13] to the newly defined TrIF numbers and proposed an approach to handle linear programming problems with data as IF numbers.
Show more

16 Read more

A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers

A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers

The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones.
Show more

25 Read more

Interpretations on Quantum Fuzzy Computing: Intuitionistic Fuzzy Operations × Quantum Operators

Interpretations on Quantum Fuzzy Computing: Intuitionistic Fuzzy Operations × Quantum Operators

This work is mainly focussed on the interpretation of Atanassov’s intuitionistic fuzzy logic via QC , where not only the intuitionistic fuzzy sets but also complement, inter- section, union, difference and codifference operations are interpreted based on the quantum circuit model, including IFSs obtained by representable (co)implications. Further work aims to consolidate this specification including not only other fuzzy connectives but also constructors (e.i. automorphisms and reductions) and the corresponding extension of (de)fuzzyfication methodology from formal structures provided by QC .
Show more

16 Read more

New Operators over the Generalized Intuitionistic Fuzzy Sets

New Operators over the Generalized Intuitionistic Fuzzy Sets

The concept of fuzzy set was introduced by Lotfi.A.Zadeh[1]. It is an extension of the classical sets. Many authors extended the idea of fuzzy set in different directions. In [2] and [3], Atanassov introduced the concept of intuitionistic fuzzy set(IFS), using a degree of membership and a degree of non-membership, under the constraint that the sum of the two degrees does not exceed one. IFS is one of the most successful extension of fuzzy set used for handling the uncertainties in the data. Modal operators, topological operators, level operators, negation operators and aggregation operators are different groups of operators over the IFS due to Atanassov[2]. In [4], T.K.Mondal and S.K.Samanta introduced the concept of generalized intuitionistic fuzzy set (GIFS)𝑆 = { 𝑥, 𝜇 𝑆 𝑥 , 𝜈 𝑆 (𝑥) : 𝑥 ∈ 𝐸} where 𝜇 𝑆 : 𝐸 → 𝐼 and 𝜈 𝑆 : 𝐸 → 𝐼 satisfy the condition 𝜇 𝑆 𝑥 ∧ 𝜈 𝑆 𝑥 ≤ 0.5, ∀ 𝑥 ∈
Show more

5 Read more

Intuitionistic Fuzzy Set with New Operators in Medical Diagnosis

Intuitionistic Fuzzy Set with New Operators in Medical Diagnosis

In this paper we propose a new approach for Medical diagnosis with the symptoms of disease using IFS with new operators. This operators apply to identified the disease of the patient with symptoms in the data. The membership and non-membership values are not always possible upto our satisfaction, but in deterministic(hesitation) part has more important role here, the fact that in decision making, particularly in case of medical diagnosis, there is a fair chance of the existence of a non-zero hesitation part at each moment of evaluation .
Show more

5 Read more

Aggregation operators on type-2 fuzzy sets

Aggregation operators on type-2 fuzzy sets

In this paper, we introduce a more general set of operators on M than were given by Taká cˇ, and we study, among other properties, the conditions required to satisfy the axioms of the [r]

17 Read more

Multi-objective Assignment Problem with Generalized Trapezoidal Fuzzy Numbers

Multi-objective Assignment Problem with Generalized Trapezoidal Fuzzy Numbers

In this paper priority based fuzzy goal programming with generalized trapezoidal fuzzy numbers has been proposed. Euclidean distance is used for selecting proper priority structure for obtaining compromise optimal solution. The concept presented, in this paper, is illustrated with multi- objective assignment problems involving generalized trapezoidal fuzzy numbers to check the effectiveness of the proposed method. The proposed method is simple and easy to implement. It may be hoped that proposed method can be applied to solve realistic optimization problems involving generalized trapezoidal fuzzy numbers.
Show more

8 Read more

A fuzzy linear fractional programming problem with fuzzy homogeneous constraints in trapezoidal fuzzy numbers

A fuzzy linear fractional programming problem with fuzzy homogeneous constraints in trapezoidal fuzzy numbers

transforms the given problem in to another FLFPP with fewer fuzzy constraints. A relationship between these two problems, which ensure that the solution of the original problem can be recovered from the solution of the transformed problem. A simple numerical example explains the procedure of the proposed method.

5 Read more

Level Operators on Generalized Intuitionistic Fuzzy Sets

Level Operators on Generalized Intuitionistic Fuzzy Sets

E.BalouiJamkhaneh and Nadarajah[8] defined an extension of generalized intuitionistic fuzzy set. In 2017, BalouiJamkhaneh[9] defined level operators 𝑃 𝛼,𝛽 and 𝑄 𝛼,𝛽 over GIFS.BalouiJamkhaneh and NadiGhara[10] defined four new level operators over GIFS and established some of their properties.In this paper, we introduce new level operators 𝑃 𝛼,𝛽 ∗ and 𝑄

6 Read more

New Approaches to Find the Solution for the Intuitionistic Fuzzy Transportation Problem with Ranking of Intuitionistic Fuzzy Numbers

New Approaches to Find the Solution for the Intuitionistic Fuzzy Transportation Problem with Ranking of Intuitionistic Fuzzy Numbers

ABSTRACT: In this paper, we investigate Intuitionistic Fuzzy Transportation Problem with the Trapezoidal Intuitionistic fuzzy numbers. Methods are proposed to find the initial solution of Intuitionistic Fuzzy Transportation Problem and a method to find the optimal solution of Intuitionistic Fuzzy Transportation Problem is developed. Ranking method based on the magnitude of membership function and non-membership function of a Intuitionistic Fuzzy Number is utilized to order the Intuitionistic fuzzy numbers. Numerical example is provided to illustrate the new approaches.
Show more

9 Read more

Extended TODIM Method for MADM Problem under Trapezoidal Intuitionistic Fuzzy Environment

Extended TODIM Method for MADM Problem under Trapezoidal Intuitionistic Fuzzy Environment

In recent years, with the increasing complexity of the managerial decision making envi- ronment, many managerial decision-making problems contain qualitative properties which are difficult to quantify. Zadeh’s fuzzy sets have been greatly successful in dealing with fuzzy manage- ment decision making problems [3,4,18,20,22,35]. Zadeh’s fuzzy set is characterized by a single scale (membership), which can only characterize the support and opposition of the two aspects of the evidence. But some decision making problems have ambiguous hesitant phenomenon with respect to evaluation of information, and Zadeh’s fuzzy set is hard or difficult to depict these sit- uations. Therefore, many scholars developed Zadeh’s fuzzy set, and intuitionistic fuzzy (IF) set is one of the most famous fuzzy sets among them. Originally proposed by Atanassov in 1986 [1], IF sets can well describe the hesitation and uncertainty of judgment through the addition of a non-membership parameters, which can describe the vague characters of things comprehensively. Then IF sets have become a powerful and effective tool in dealing with uncertain or vague in- formation in actual applications. In dealing with ambiguity and uncertainty, IF sets are more flexible and practical than fuzzy sets, and thus they have been applied widely in decision making. Because of the complexity and uncertainty of objective things and the limitation of decision maker’s knowledge, membership and non-membership functions are sometimes difficult to repre- sent by using the precise numbers. But interval number can be very useful to describe this kind
Show more

13 Read more

INTERVAL - VALUED INTUITIONISTIC FUZZY ASSIGNMENT PROBLEM WITH REPLACEMENT BASED ON FUZZY AGGREGATION

INTERVAL - VALUED INTUITIONISTIC FUZZY ASSIGNMENT PROBLEM WITH REPLACEMENT BASED ON FUZZY AGGREGATION

aggregate all individual decision into a collective decision. Since the individuals in the groups may have different capabilities it is necessary to use weighted aggregation. In the present complex socio economic environment and the insufficient knowledge of the problem, under the fuzzy environment, individuals in the group may provide their information over alternatives with interval valued intuitionistic fuzzy number (IVIFN). Chen (1985) introduced a fuzzy assignment model that considers all individuals have same skills. Huang and Zhang (2006) proposed a mathematical model for the fuzzy assignment problem with restriction on qualification. Mukherjee and Basu (2011) proposed intuitionistic fuzzy assignment problem by using similarity measures and score functions. Xu (2007) defined the concept of interval - valued intuitionistic fuzzy number. Xu and Chen (2007) define an interval-valued intuitionistic fuzzy ordered weighted averaging operator and an interval-valued intuitionistic hybrid averaging operator. Lin and Wen (2004) concentrate on the assignment problem where costs are not deterministic numbers but imprecise ones. Gaurav and Bajaj (2014) proposed interval-valued intuitionistic fuzzy assignment problem by using similarity measure and score functions.
Show more

22 Read more

Some improved interactive aggregation operators under interval-valued intuitionistic fuzzy environment and its application to decision making process

Some improved interactive aggregation operators under interval-valued intuitionistic fuzzy environment and its application to decision making process

Thus, the objective of this manuscript is to present some series of averaging aggregation operators in an IVIFSs environment. For it, a new operational law on dierent IVIFNs has been proposed by taking the interaction between the pair of membership and non-membership functions. Based on these new op- erational laws, weighted aggregated operators, namely Interval-Valued Intuitionistic Fuzzy (IVIF) Hamacher Interactive Weighted Aggregation (IVIFHIWA), IVIF Hamacher Interactive Ordered Weighted Aggregation (IVIFHIOWA), and IVIF Hamacher Interactive Hy- brid Weighted Aggregation (IVIFHIHWA), have been proposed by properly handling the shortcoming of the existing operators. The main signicance of these operators is that the inuence of the degree of non-
Show more

24 Read more

A Data Envelopment Analysis Model with Triangular Intuitionistic Fuzzy Numbers

A Data Envelopment Analysis Model with Triangular Intuitionistic Fuzzy Numbers

49 TOPSIS and DEA to select the units with the most efficiency. First, the alternative evaluation problem is formulated by DEA and separately formulates each pair of units. In the second stage, he used the opinion of experts to be applied to a model of group Decision-Making called the Intuitionistic Fuzzy TOPSIS method. Gandotra et al. [53] proposed an algorithm to rank DMUs in the presence of intuitionistic fuzzy weighted entropy. Hajiagha et al. [54] developed a DEA model when input/output data was expressed in the form of IFS. They further extended the model to the case of a weighted aggregated operator for IFS. Puri and Yadav [55] developed optimistic and pessimistic DEA models under intuitionistic fuzzy input data. They also presented the application of their proposed models through a case from the banking sector in India where some of the inputs were represented as triangular intuitionistic fuzzy numbers in the form of A   a a a a a a l , m , u ;  l , m ,  u  .
Show more

12 Read more

A Modified Approach for Ranking Non normal p norm Trapezoidal Fuzzy Numbers

A Modified Approach for Ranking Non normal p norm Trapezoidal Fuzzy Numbers

Ranking fuzzy numbers is a prerequisite for the decision making problem. In order to rank fuzzy quantities many researchers proposed and analyzed different techniques on triangular and trapezoidal fuzzy numbers. However, no one can claim their method is a satisfactory one. In this paper a modified distance based approach called signed distance proposed by Yao and Wu [9] is discussed. This proposed approach is free from computational complexity in the process of decision making, optimization and forecasting problems. Some Numerical examples are used to illustrate the proposed approach.
Show more

5 Read more

Show all 10000 documents...

Related subjects