# New Order On Type 2 Fuzzy Numbers

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### Fault Diagnosis of Power Systems Using Fuzzy Reasoning

model the fuzzy production rule of type 2, shown in Fig. 1(c). When the or -type rule neuron receives spikes with pulse values 1; 2;:::; k 1 from other proposition neurons, it will re and produce a spike with pulse value = ( 1 6 2 6:::6 k 1) c. 2.3. Fuzzy reasoning algorithm based on ivFRSN P systems

### Uncertainty Prediction for Tool Wear Condition Using Type-2

type-2 fuzzy logic theory with the handling of uncertainties [14]. For the most general type-2 fuzzy model, antecedents are type-2 fuzzy sets and consequents are type-1 fuzzy sets, then consequent parameter are assumed as convex and normal type-1 fuzzy number subsets of the real numbers, so that they are fuzzy numbers.

### A new approach to evaluate linear programming problem in

Pal [11]oduced a pentagonal fuzzy number method and appied in fuzzy matrix theory. Pathinathan and Ponnivalavan [12]oduced the reverse order linear membership func-tion and deﬁne arithmetic operation on pentagonal fuzzy numbers. Garcia and Hernandez [48]oposed a interval type-2 fuzzy constraints applied in LP. A degree of satisfac-

### An extended TOPSIS method based on ordered fuzzy numbers for

2102 D.Kacprzak fuzzy extension based on ordered fuzzy numbers are presented. The proposed approach and a numerical example are described in Sects. 4 and 5, respectively.

### New Order on Type 2 Fuzzy Numbers - MDPI

type 2 fuzzy numbers, which are a subset of type 2 generalized fuzzy numbers. Keywords: type 2 fuzzy sets; fuzzy numbers; partial order 1. Introduction In the framework of fuzzy systems, in order to give a response or to make a decision, fuzzy numbers (FNs) and fuzzy quantities (FQs) need to be compared, i.e., to be ranked. In a sense, fuzzy

### Genetically Tuned Interval Type- 2 Fuzzy Logic for Fault

ABSTRACT: This paper presents study of tune Fuzzy based Fault Diagnosis Model of Induction Motor using GA. Interval Type-2 Fuzzy Logic Controller (IT2FLC) where the fuzzy parameter s, e.g. Fuzzy Membership Functions and Fuzzy Rule Bases are tuned by Genetic Algorithm (GAs) known as Genetic Interval Type2 Fuzzy System (GIT2FS).

### A New Method for Fuzzy Critical Path Analysis in Project

In this section addition and multiplication operations between two triangular fuzzy numbers are reviewed. 2.3.1. Arithmetic Operations between a, b, c Type Triangular Fuzzy Numbers (Kaufmann and Gupta, 1985) Let 1 1, 1, 1 ~ A a b c and 2 2, 2, 2 ~ A a b c be two triangular fuzzy numbers, then (i) 1 2

### An Interval Type-2 Fuzzy Similarity-Based MABAC Approach for

numbers, interval type-2 fuzzy sets, etc. The concept of linguistic variables can effectively be applied to deal with complicated or unexplained situations and are frequently represented by type-2 fuzzy sets [19]. The general type-2 fuzzy numbers (GT2FNs) have been around for decades as one of the major areas in the ﬁeld of fuzzy sets [20].

### A NOVEL TRIANGULAR INTERVAL TYPE-2 INTUITIONISTIC FUZZY SETS

the interval type-2 fuzzy sets [8] are usually taken in some simpliﬁed formations in applications in which the upper membership function (UMF) and the lower membership function (LMF) are represented by the triangular fuzzy numbers. Deﬁnition 2.4. Let α = [a,b],c,[d,e] be a triangular interval type-2 fuzzy set

### An Extended VIKOR Method for Multi Attribute Decision Making

new raking value method to convert the interval type-2 trapezoidal fuzzy numbers(IT2TrFNs) to real numbers and obtained the final rank order based on the integrated ranking value. In [5], the notion of trapezoidal interval type-2 fuzzy soft sets was presented based on interval type-2 trapezoidal fuzzy sets (IT2TrFSs) and soft sets.

### Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of

the concept of linguistic variable and the induced concept of type-2 (type-n) fuzzy sets [3, 27 30]. Other notable extensions to the theory offuzzy sets and fuzzy logic include complex fuzzy numbers [31], and Z-numbers [32]. Many natural phenomena are complex and cannot be modelled using one-dimensional classes and/or one-dimensional variables.

### Some New Results On Semi Fully Fuzzy Linear Programming Problems

de nition of multiplication involving symmetric trapezoidal fuzzy num-bers. 2.3. Order on fuzzy numbers. Ranking of fuzzy numbers is an important issue in the study of fuzzy set theory. Ranking procedures are also useful in various applications and one of them will be in the study of fuzzy mathematical programming in later sections.

### A Novel Hybrid Fuzzy Weighted Average for MCDM with Interval

type-2 fuzzy sets (in Section 2.1) and weighted average (in Section 2.2) are presented. 2.1 Interval Triangular Type-2 Fuzzy Sets We do some modification on the existed type-2 fuzzy sets by building up an interval triangular type-2 fuzzy sets (ITT2FS). This ITT2FS is described from Definition 2 till 6.

### A Study on Triangular Type 2 Triangular Fuzzy Matrices

A type-2 triangular fuzzy number # is said to be a type-2 unit-equivalent triangular fuzzy number if Ř ( # ) = 1. It is denoted by 1 è è. 3. TYPE-2 TRIANGULAR FUZZY MATRICES (T2TFMS) [9] 3.1. Definition: Type-2 triangular fuzzy matrix (T2TFM) A type-2 triangular fuzzy matrix (T2TFM) of order m×n is defined as A = ( = ä è Ü Ý)mxn

### PAPER OPEN ACCESS Ranking fuzzy numbers based on weighted

2. Fuzzy numbers and weighted distance d q φψ This section reviews some elementary concepts about fuzzy number and introduces a type of weighted distances. d q φψ between fuzzy numbers. The readers can find further details on fuzzy numbers in [3, 7]. We use F(i) to represent all fuzzy sets on i, where i is the set of all real numbers.

### Fuzzy Bayesian Classification of LR Fuzzy Numbers

A. Definition of fuzzy numbers Consider A ~ as a fuzzy number, then Alpha-cut of A ~ is shown by D ^ P t D ` A A x: ~ ~ which is a closed interval and is denoted to > LA U @ D D, D ~, where D > 0,[email protected] In order to compute the distance of two fuzzy numbers, several formulas are proposed. One is Hausdorff distance described below: For any two fuzzy

### A New Hendecagonal Fuzzy Number for Optimization Problems

existing fuzzy numbers by C.B.Chen and C.M.Klein,T.S.Liou and M.J.Wang [6],[11]. When the vagueness arises in eleven different points it is difficult to represent the fuzzy number. In this paper a new type of fuzzy number named as hendecagonal fuzzy number is defined with its membership function.

### Fuzzy Bayesian Classification of LR Fuzzy Numbers

A. Definition of fuzzy numbers Consider A ~ as a fuzzy number, then Alpha-cut of A ~ is shown by { m a} a = ≥ A A x: ~ ~ which is a closed interval and is denoted to A [AL AU] a a, a ~ =, wherea ∈[0,1]. In order to compute the distance of two fuzzy numbers, several formulas are proposed. One is Hausdorff distance described below: For any

### A New Approach for Ranking Shadowed Fuzzy Numbers and its

2.3.1. Shadowed Fuzzy Numbers Shadowed fuzzy numbers (SFNs) are induced from fuzzy numbers [26]. The author proposed an improved approach to create SFN that preserves uncertainty characteristics of fuzzy number and can be deduced from type-1 fuzzy numbers and higher type of them e.g., intuitionistic fuzzy sets (IFS) [4].

### Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control

Fuzzy control methods and algorithms, including many specialized software and hardware available on the market today, may be classified as one type of intelligent control. This is because fuzzy systems modeling, analysis, and control incorporate a certain amount of human knowledge into its components (fuzzy sets, fuzzy logic, and fuzzy rule base).

### Fuzzy Solutions to Second Order Three Point Boundary Value

Dec 11, 2020 work to establish our existence result for second order three point boundary value problem. Fuzzy numbers play a particularly important role in this regard as a special type of fuzzy sets. In many respects, fuzzy numbers more realistically depict the physical world than single-valued numbers.

### Type-Reduction of General Type-2 Fuzzy Sets: The Type-1 OWA

Type-2 fuzzy sets initially proposed by Zadeh in 19751 o er the advantage of modelling higher level uncer-tainty in human decision making process than using type-1 fuzzy sets. In a type-2 fuzzy inference system (FIS), type-2 fuzzy sets are used in the antecedent and/or consequent parts of all or some of its fuzzy rules.

### Multi-Criteria Decision-Making Method Based on Type-2 Fuzzy Sets

type-2 fuzzy numbers (TT2FNs) are deﬁned on the basis of interval type-2 trapezoidal fuzzy numbers (IT2TFNs), and they can convey more uncertainty information than T1FSs and IT2FSs. Moreover, the drawbacks of the existing computational models of generalized fuzzy numbers are analyzed, and a new

### Fuzzy Hungarian Method for Solving Intuitionistic Fuzzy

respectively. Hence every triangular Intuitionistic fuzzy I '' a (a , a , a ;a ,a ,a ) = 1 2 3 12 3 can also be represented I ( * ' '* ) a a ,a ,a ;a ,a ,a = 0* 0 * 2.1. Arithmetic operation on triangular intuitionistic fuzzy numbers: Ming Ma et al. [16] have proposed a new fuzzy arithmetic based upon both location index and fuzziness index

### New Product Development Process Valuation using Compound

Type-1 fuzzy set is an extension of the concept of an ordinary set. Whereupon Type-2 fuzzy set is an extension of Type-1 fuzzy set that has grade of membership which is itself fuzzy also. In Type-2 fuzzy set the membership function is three-dimensional, and the third one is for coping with new degrees of freedom. In vague computing Type-2

### Fuzzy Transportation problem of Trapezoidal Fuzzy numbers

is a fuzzy numbers defined on s et of real numbers, which maps each fuzzy number into a real number, where natural order exists. Wang [9 ] used a centroid based distance approach to rank fuzzy numbers. For trapezoidal fuzzy number ( , , , ; ) ~ A a 1 a 2 a 3 a 4 , the ranking function is defined as Where ) ~ x 0 (A =

### A novel interval type-2 fuzzy AHP-TOPSIS approach for ranking

the need for type-2 fuzzy sets for the existing studies. According to their research, there are several di erent domains to which type-2 FSs can be applied in order to provide a better solution. Currently, interval type-2 fuzzy sets have been successfully applied to the design of intrusion detection system [29], technology

### Ordering L-R type Generalized Trapezoidal Fuzzy Numbers

where a natural order exists. In the fuzzy number literature, there are many proposals for ordering L-R(left and right) type fuzzy numbers. Proposals are based on the strategy of characterization of a fuzzy number by a real number in order to rank fuzzy numbers, which is classified into four main groups [11]. Namely, the first group is based on

### A New Interval Type-2 Fuzzy Decision Method with an Extended

A New Interval Type-2 Fuzzy Decision Method with an Extended Relative Preference Relation and Entropy to Project Critical Path Selection

### Research Article A New Method for Defuzzification and Ranking

trapezoidal fuzzy numbers. In , Asady and Zendehnam [] presented a method for ranking fuzzy numbers by distance minimization. e fuzzy number ranking method proposedinbyChenandWang[] used -cutsforthis purpose. is paper aims to use statistical Beta distribution for defuzzifying and ranking fuzzy numbers, since it is the only

### A New Approach For Triangular Intuitionistic Fuzzy Number in

with fuzzy numbers. 2.4 Topsis for intuitionistic fuzzy number There are many extensions of topsis in literature [ [36], [37], [38], [46] ] to deal with fuzzy numbers. One of the most classical and widely-used MADM method is TOPSIS (Tech-nique of Order Preference Similarity to the Ideal Solution) [ [22], [33]] In

### Group Decision Analysis with Interval Type-2 Fuzzy Numbers

In order to compare normal fuzzy is an area of active research today [12, 17, 22]. Interval Type-2 Fuzzy Numbers (IT2 FNs) suitably reflect subjective opinion and present a richer perception

### A new model for solving fuzzy linear fractional programming

problems with trapezoidal fuzzy numbers where the objective functions are fuzzy numbers and the constraints are real numbers. In this study, in order to obtain the fuzzy optimal solution with unrestricted variables and parameters, a new efficient method for FLFP problem has been proposed. These proposed

### R-sets, Comprehensive Fuzzy Sets Risk Modeling for Risk-based

Therefore, in order to implement fuzzy sets, it is crucial to determine the reliability of the available data. So far, the fuzzy sets have been extended to different innovative approaches such as type 2 fuzzy sets [7], interval-valued fuzzy sets (IVFSs) [8], Z-numbers [9], intuitionistic fuzzy sets (IFSs)

### A Generalized Model for Fuzzy Linear Programs with

a new method to find the fuzzy optimal solution of the same type of fuzzy linear programming problems. Ganesan and Veeramani [4] introduced a new type of fuzzy arithmetic for symmetric trapezoidal fuzzy numbers and proposed a method for solving FLP

### Contents lists available at GrowingScience Uncertain Supply

aa aabbb1 234 1 2 3 , , and b4 be non-zero positive real numbers 2.4. Linguistic variables and fuzzy numbers Table 1 shows the linguistic variables representing by generalized triangular fuzzy number s of the ratings of alternatives and the importance weights of criteria. Table 1 Ratings of alternatives and importance weights of criteria

### Expert Systems with Applications - ISI Articles

This study proposes the integration of fuzzy AHP and interval type-2 fuzzy DEMATEL (IT2 fuzzy DEMATEL) where the interval type-2 trapezoidal fuzzy numbers are used predominantly. This new integration model includes linguistic variables in inter-val type-2 fuzzy sets (IT2 FS) and expected value for normalizing upper and lower memberships of IT2 FS.

### TOPSIS Modification with Interval Type-2 Fuzzy Numbers

3.1. Interval type-2 fuzzy sets The disadvantages of classic fuzzy sets such as difficulties in aggregation of alternative s evaluations, working with noisy data and natural language estimates, catalyzed the creation of type-2 fuzzy sets. A type-2 fuzzy set 𝐴̃̃ can be represented by a type-2 membership function 𝜇

### A comprehensive study of an economic order quantity model

angular fuzzy number A~ ¼ a 1;a 2;a 3; then the following situations may arise. Figure 3a c indicates the converging, diverging and natural tunnel type curves of the fuzzy objective functions with respect to the fuzzy set A~. 2.5 The conventional left fuzzy (L-fuzzy) number Let a fuzzy number b~ have U and L as upper and lower bounds.

### Extended VIKOR Method and its Application to Farming using

Pentagonal Fuzzy Numbers (PFNs). Pentagonal Fuzzy Numbers is a new type of fuzzy number introduced by T. Pathinathan and K. Ponnivalavan in the year 2014 [13]. Using this number we examine the information given by the Experts in a more exact way and the opinions are observed to be 5-tuple fuzzy values. VIKOR decision making