scholarly journals Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2196
Author(s):  
Hui Li ◽  
Junyang Cai
Keyword(s):  
Fuzzy Variable ◽  
Fuzzy Arithmetic ◽  
Computation Complexity ◽  
Arithmetic Operations ◽  
Fuzzy Variables ◽  
Expected Value Operator ◽  
Interval Type ◽  
High Degree ◽  
Mutually Independent

High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs having the greatest membership degrees of 1. Firstly, by defining the medium of an RSTIT2-FV, its membership function, credibility distribution, and inverse distribution are analytically and explicitly expressed. Secondly, an operational law for fuzzy arithmetic operations regarding mutually independent RSTIT2-FVs is proposed, which can simplify the calculations and directly output the inverse credibility of the functions. Afterwards, the operational law is applied to define the expected value operator of the IT2-FV and prove the linearity of the operator. Finally, some comparative examples are provided to verify the efficiency of the proposed operational law.

Modeling pricing decision problem based on interval type-2 fuzzy theory

2021 ◽  
pp. 1-16
Author(s):  
Huili Pei ◽  
Hongliang Li ◽  
Yankui Liu
Keyword(s):  
Decision Making ◽  
Level Sets ◽  
Fuzzy Variable ◽  
Possibility Distribution ◽  
Fuzzy Variables ◽  
Pricing Decision ◽  
Selection Variable ◽  
Interval Type ◽  
Analytical Expressions

In practical decision-making problems, decision makers are often affected by uncertain parameters because the exact distributions of uncertain parameters are usually difficult to determine. In order to deal with this issue, the major contribution in this paper is to propose a new type of type-2 fuzzy variable called level interval type-2 fuzzy variable from the perspective of level-sets, which is a useful tool in modeling distribution uncertainty. With our level interval type-2 fuzzy variable, we give a method for constructing a parametric level interval (PLI) type-2 fuzzy variable from a nominal possibility distribution by introducing the horizontal perturbation parameters. The proposed horizontal perturbation around the nominal distribution is different from the vertical perturbation discussed in the literature. In order to facilitate the modeling in practical decision-making problems, for a level interval type-2 fuzzy variable, we define its selection variable whose distribution can be determined via its level-sets. The numerical characteristics like expected value and second order moments are important indices in practical optimization and decision-making problems. With this consideration, we establish the analytical expressions about the expected values and second order moments of the selection variables of PLI type-2 trapezoidal, normal and log-normal fuzzy variables. Furthermore, in order to derive the analytical expressions about the numerical characteristics of the selection variable for the sums of the common PLI type-2 fuzzy variables, we discuss the arithmetic about the sums of common PLI type-2 fuzzy variables. Finally, we apply the proposed optimization method to a pricing decision problem to demonstrate the efficiency of our new method. The computational results show that even a small perturbation of the nominal possibility distribution can affect the quality of solutions.

scholarly journals A FUZZY BASED APPROACH FOR EARLY REQUIREMENT PRIORITIZATION

2015 ◽  
Vol 15 (2) ◽  
pp. 6480-6490
Author(s):  
Mohd Muqeem ◽  
Dr. Md. Rizwan Beg
Keyword(s):  
Software Development ◽  
Early Phase ◽  
Fuzzy Variable ◽  
Requirement Engineering ◽  
Expected Value ◽  
Inference System ◽  
Complex Time ◽  
Fuzzy Variables ◽  
Expected Value Operator ◽  
Requirement Prioritization

The importance of the prioritization in commercial software development has been analyzed by many researchers. The gathered requirements are required to be put into an order of some priority. In other words we can say that there is a need to prioritize the requirements. It is evident that most of the approaches and techniques proposed in recent research to prioritize the requirements have not been widely adopted. These approaches are too complex, time consuming, or inconsistent and difficult to implement In this paper we propose a fuzzy based approach for requirement prioritization in which  requirement are prioritized in early phase of requirement engineering as post elicitation step. This category of prioritization is known as early requirement prioritization. The proposed fuzzy based approach considers the nature of requirements by modeling their attributes as fuzzy variables. As such, these variables are integrated into a fuzzy based inference system in which the requirements represented as input attributes and ranked via the expected value operator of a fuzzy variable.

ANALYSIS AND ALGORITHMS OF BIFUZZY SYSTEMS

2004 ◽  
Vol 12 (03) ◽  
pp. 357-376 ◽  
Author(s):  
JIAN ZHOU ◽  
BAODING LIU
Keyword(s):  
Numerical Experiments ◽  
Fuzzy Variable ◽  
Expected Value ◽  
Real Numbers ◽  
Fuzzy Variables ◽  
Chance Distribution ◽  
Expected Value Operator ◽  
Possibility Space ◽  
Bifuzzy Variable

A fuzzy variable is a function from a possibility space to the set of real numbers, while a bifuzzy variable is a function from a possibility space to the set of fuzzy variables. In this paper, a concept of chance distribution is originally presented for bifuzzy variable, and the linearity of expected value operator of bifuzzy variable is proved. Furthermore, bifuzzy simulations are designed and illustrated by some numerical experiments.

An Interval Type-2 Fuzzy Number Based Approach for Multi-Criteria Group Decision-Making Problems

2015 ◽  
Vol 23 (04) ◽  
pp. 565-588 ◽  
Author(s):  
Jian-Qiang Wang ◽  
Su-Min Yu ◽  
Jing Wang ◽  
Qing-Hui Chen ◽  
Hong-Yu Zhang ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Weighted Averaging ◽  
Ranking Methods ◽  
Arithmetic Operations ◽  
New Approach ◽  
Interval Type

In this paper, a new approach is presented for solving multi-criteria group decision-making (MCGDM) problems, which is based on new arithmetic operations and the ranking rules of trapezoidal interval type-2 fuzzy numbers (IT2FNs). Firstly, the shortcomings of some existing arithmetic operations of trapezoidal IT2FNs are discussed along with their ranking methods, before some new arithmetic operations and ranking rules are proposed. Secondly, some new aggregation operators including the arithmetic averaging aggregation operator, the ordered weighted averaging aggregation operator and the hybrid weighted averaging aggregation operator for trapezoidal IT2FNs are also developed. Thirdly, a new approach for MCGDM problems is developed based on the proposed operators and ranking rules. Finally, an example is provided to illustrate the feasibility and validity of this new approach, and a comparison analysis referring to the same example is also presented.

scholarly journals A Combined Interval Type-2 Fuzzy MCDM Framework for the Resilient Supplier Selection Problem

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 44
Author(s):  
Seyed Amirali Hoseini ◽  
Sarfaraz Hashemkhani Zolfani ◽  
Paulius Skačkauskas ◽  
Alireza Fallahpour ◽  
Sara Saberi
Keyword(s):  
Distance Measure ◽  
Hamming Distance ◽  
Real Life ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Order Preference ◽  
Simple Additive Weighting ◽  
Interval Type ◽  
High Degree

Selecting the most resilient supplier is a crucial problem for organizations and managers in the supply chain. However, due to the inherited high degree of uncertainty in real-life projects, developing a decision-making framework in a crisp or fuzzy environment may not present accurate or reliable results for the managers. For this reason, it is better to evaluate the potential suppliers in an Interval Type-2 Fuzzy (IT2F) environment for better dealing with this ambiguity. This study developed an improved combined IT2F Best Worst Method (BWM) and IT2F technique for Order Preference by Similarity to Ideal Solution (TOPSIS) model “Atieh Sazan” Co. as a case study, such that the IT2FBWM was employed for obtaining the weight of criteria. The IT2FTOPSIS was utilized for ranking the potential suppliers based on Hamming distance measure. In both phases, the opinions of experts as IT2F linguistic terms were employed for weighting the criteria and obtaining the relative importance of the alternatives in terms of the evaluative criteria. After obtaining the final results, the proposed model was validated by replacing Analytical Hierarchy Process (AHP) and Simple Additive Weighting (SAW) approaches separately instead of BWM for weighting the criteria. After executing both new models, it was found that the final ranking was similar to the final ranking of the proposed model, representing the reliability and accuracy of the obtained results. Moreover, it was concluded that the resilient criteria of “Reorganization” and “Redundancy” are the most determinant measures for selecting the best supplier rather than measures in the Iranian Construction Industry.

Interval Type-2 Fuzzy Application for Diet Journaling

2019 ◽  
Vol 8 (2) ◽  
pp. 34-67
Author(s):  
Joshua M. Krbez ◽  
Adnan Shaout
Keyword(s):  
Model Uncertainty ◽  
Web Application ◽  
Fuzzy Logic Controller ◽  
Fuzzy Arithmetic ◽  
Nutritional Information ◽  
Food Items ◽  
Dietary Reference Intakes ◽  
Interval Type ◽  
Client Side

In this article, an improved system is constructed using interval type-2 fuzzy sets (IT2FS) and a fuzzy logic controller (FLC) with non-singleton inputs. The primary purpose is to better model nutritional input uncertainty which is propagated through the Type-2 FLC. To this end, methods are proposed to (1) model nutrient uncertainty in food items, (2) extend the nutritional information of a food item using an IT2FS representation for each nutrient incorporating the uncertainty in the extension process, (3) accumulate uncertainties for IT2FS inputs using fuzzy arithmetic, and (4) build IT2FS antecedents for FLC rules based on dietary reference intakes (DRIs). These methods are then used to implement a web application for diet journaling that includes a client-side Type-2 non-singleton Interval Type-2 FLC. The produced application is then compared with the previous work and shown to be more suitable. This is the first known work on diet journaling that attempts to model uncertainty for all anticipated measurement error.

scholarly journals Minimum Risk Facility Location-Allocation Problem with Type-2 Fuzzy Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xuejie Bai ◽  
Ying Liu
Keyword(s):  
Facility Location ◽  
Value At Risk ◽  
Structural Characteristics ◽  
Fuzzy Variable ◽  
Mixed Integer ◽  
Minimum Risk ◽  
Fuzzy Variables ◽  
Location Allocation ◽  
The Impact

Facility location decision is basically viewed as a long-term strategy, so the inherited uncertainty of main parameters ought to be taken into account in order to make models applicable. In this paper, we examine the impact of uncertain transportation costs and customers’ demands on the choice of optimal location decisions and allocation plans. This leads to the formulation of the facility location-allocation (FLA) problem as a fuzzy minimum risk programming, in which the uncertain parameters are assumed to be characterized by type-2 fuzzy variables with known type-2 possibility distributions. Since the inherent complexity of type-2 fuzzy FLA may be troublesome, existing methods are no longer effective in handling the proposed problems directly. We first derive the critical value formula for possibility value-at-risk reduced fuzzy variable of type-2 triangular fuzzy variable. On the basis of formula obtained, we can convert original fuzzy FLA model into its equivalent parametric mixed integer programming form, which can be solved by conventional numerical algorithms or general-purpose software. Taking use of structural characteristics of the equivalent optimization, we design a parameter decomposition method. Finally, a numerical example is presented to highlight the significance of the fuzzy FLA model. The computational results show the credibility and superiority of the proposed parametric optimization method.

A New Method for Solving Multi-Criteria Multi-Attributes Decision Making Based on the Ranking of Type-2 Fuzzy Variables

2021 ◽  
Vol 10 (1) ◽  
pp. 20-42
Author(s):  
Dhiman Dutta ◽  
Mausumi Sen ◽  
Ashok Deshpande ◽  
Biplab Singha
Keyword(s):  
Decision Making ◽  
Decision Makers ◽  
Ranking Method ◽  
Ranking Methods ◽  
Fuzzy Variables ◽  
Decision Making Problem ◽  
Criteria Weights ◽  
Interval Type ◽  
Very High

In this paper, the authors have proposed the concept of interval type-2 triangular fuzzy variables. Then, they studied the concepts of value and ambiguity of interval type-2 triangular fuzzy variables and interval type-2 trapezoidal fuzzy variables. They introduced the concept of value and ambiguity in order to define the ranking method for the interval type-2 fuzzy variables. A comparative result of the various other ranking methods is also given in the tabular form. A multi-criteria multi-attributes decision-making problem is provided to explain the ranking method in which the evaluation ratings of the alternatives on the attributes, and the criteria weights as provided by the decision makers are expressed as linguistic terms (e.g., very high, medium, fair, and good). The multi-criteria multi-attributes decision-making problem is then worked out by applying the proposed algorithm.

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