CHARACTERIZATIONS OF THE BOREL -FIELDS OF THE FUZZY NUMBER SPACE

2017 ◽  
Vol 58 (3-4) ◽  
pp. 265-275
Author(s):  
TAI-HE FAN ◽  
MENG-KE BIAN
Keyword(s):  
Approximation Method ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Hausdorff Metric ◽  
Measurable Space ◽  
Borel Field ◽  
Applied Fields ◽  
Supremum Metric

In this paper, we characterize Borel $\unicode[STIX]{x1D70E}$-fields of the set of all fuzzy numbers endowed with different metrics. The main result is that the Borel $\unicode[STIX]{x1D70E}$-fields with respect to all known separable metrics are identical. This Borel field is the Borel $\unicode[STIX]{x1D70E}$-field making all level cut functions of fuzzy mappings from any measurable space to the fuzzy number space measurable with respect to the Hausdorff metric on the cut sets. The relation between the Borel $\unicode[STIX]{x1D70E}$-field with respect to the supremum metric $d_{\infty }$ is also demonstrated. We prove that the Borel field is induced by a separable and complete metric. A global characterization of measurability of fuzzy-valued functions is given via the main result. Applications to fuzzy-valued integrals are given, and an approximation method is presented for integrals of fuzzy-valued functions. Finally, an example is given to illustrate the applications of these results in economics. This example shows that the results in this paper are basic to the theory of fuzzy-valued functions, such as the fuzzy version of Lebesgue-like integrals of fuzzy-valued functions, and are useful in applied fields.

Research on Post Evaluation System of Scenic Highway and Quantitative Evaluation with Interval Approximation Method

2014 ◽  
Vol 505-506 ◽  
pp. 637-644
Author(s):  
Chun Yi Yuan ◽  
Wen Yu Li ◽  
Le Yi Zhao
Keyword(s):  
Quantitative Evaluation ◽  
Approximation Method ◽  
Evaluation System ◽  
Evaluation Method ◽  
Post Evaluation ◽  
Interval Approximation

To promote the demonstration and guidance effect of scenic highway with the project post evaluation, this paper studied the concept of harmony scenic highway and built a Scenic Highway harmony evaluation system which takes highway road area harmony, human road harmony and highway external environmental harmony as core indexes. Scenic highway harmony evaluation method based on interval approximation was adopted to post evaluate typical demonstration scenic highway in Hebei. The practicability of the scenic highway harmony evaluation method based on interval approximation was verified.

scholarly journals Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 195
Author(s):  
Haiyi Mao ◽  
Rui Cai
Keyword(s):  
Service Quality ◽  
Fuzzy Number ◽  
Supplier Selection ◽  
Future Market ◽  
Selection System ◽  
Uncertainty Measure ◽  
Good Ability ◽  
Relative Closeness ◽  
The Future ◽  
Market Trends

The Pythagorean fuzzy number (PFN) consists of membership and non-membership as an extension of the intuitionistic fuzzy number. PFN has a larger ambiguity, and it has a stronger ability to express uncertainty. In the multi-criteria decision-making (MCDM) problem, it is also very difficult to measure the ambiguity degree of a set of PFN. A new entropy of PFN is proposed based on a technique for order of preference by similarity to ideal solution (Topsis) method of revised relative closeness index in this paper. To verify the new entropy with a good performance in uncertainty measure, a new Pythagorean fuzzy number negation approach is proposed. We develop the PFN negation and find the correlation of the uncertainty measure. Existing methods can only evaluate the ambiguity of a single PFN. The newly proposed method is suitable to systematically evaluate the uncertainty of PFN in Topsis. Nowadays, there are no uniform criteria for measuring service quality. It brings challenges to the future development of airlines. Therefore, grasping the future market trends leads to winning with advanced and high-quality services. Afterward, the applicability in the service supplier selection system with the new entropy is discussed to evaluate the service quality and measure uncertainty. Finally, the new PFN entropy is verified with a good ability in the last MCDM numerical example.

scholarly journals Novel Distance Measure in Fuzzy TOPSIS for Supply Chain Strategy Based Supplier Selection

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
B. Pardha Saradhi ◽  
N. Ravi Shankar ◽  
Ch. Suryanarayana
Keyword(s):  
Supply Chain ◽  
Balanced Scorecard ◽  
Fuzzy Number ◽  
Supplier Selection ◽  
Distance Measure ◽  
Fuzzy Topsis ◽  
Research Area ◽  
Manufacturing Strategy ◽  
Supply Chain Strategy ◽  
Trapezoidal Fuzzy Number

In today’s highly competitive environment, organizations need to evaluate and select suppliers based on their manufacturing strategy. Identification of supply chain strategy of the organization, determination of decision criteria, and methods of supplier selection are appearing to be the most important components in research area in the field of supply chain management. In this paper, evaluation of suppliers is done based on the balanced scorecard framework using new distance measure in fuzzy TOPSIS by considering the supply chain strategy of the manufacturing organization. To take care of vagueness in decision making, trapezoidal fuzzy number is assumed for pairwise comparisons to determine relative weights of perspectives and criteria of supplier selection. Also, linguistic variables specified in terms of trapezoidal fuzzy number are considered for the payoff values of criteria of the suppliers. These fuzzy numbers satisfied the Jensen based inequality. A detailed application of the proposed methodology is illustrated.

scholarly journals Resilient Supplier Selection Based on Fuzzy BWM and GMo-RTOPSIS under Supply Chain Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Jiawu Gan ◽  
Shuqi Zhong ◽  
Sen Liu ◽  
Dan Yang
Keyword(s):  
Supply Chain ◽  
Fuzzy Number ◽  
Supplier Selection ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Triangular Fuzzy Number ◽  
Random Environments ◽  
Triangular Fuzzy Numbers ◽  
Supply Chain Risk ◽  
Research Gap

Resilient suppliers can reduce supply chain risk, effectively avoid supply chain disruption, and bring profits to enterprises. However, there is no united measuring index system to evaluate the resilient supplier under supply chain environment, and the assessment language sets are usually crisp values. Therefore, in order to fill the research gap, this paper proposes a hybrid method, which combines triangular fuzzy number, the best-worst method (BWM), and the modular TOPSIS in random environments for group decision-making (GMo-RTOPSIS) to solve the above problem. Firstly, the weight of decision-maker is calculated by using fuzzy BWM which can deal with triangular fuzzy numbers. Secondly, triangular fuzzy number is introduced into GMo-RTOPSIS, and combined with fuzzy BWM, alternatives are sorted to select the best resilient supply chain partner. Finally, the feasibility and universality of this method are proved by illustrative examples.

MATHEMATICAL PROGRAMMING PROBLEMS WITH SEVERAL FUZZY OBJECTIVE FUNCTIONS

2013 ◽  
Vol 21 (supp01) ◽  
pp. 51-62 ◽  
Author(s):  
LUHANDJULA MONGA KALONDA ◽  
RANGOAGA MOETI JOSEPH
Keyword(s):  
Mathematical Programming ◽  
Fuzzy Number ◽  
Multiobjective Programming ◽  
Fuzzy Numbers ◽  
Main Idea ◽  
Objective Functions ◽  
Mathematical Programming Problems ◽  
Nearest Interval Approximation ◽  
Multiobjective Programming Problems ◽  
Interval Approximation

In this paper we propose an approach for multiobjective programming problems with fuzzy number coefficients. The main idea behind our approach is to approximate involved fuzzy numbers by their respective nearest interval approximation counterparts. An algorithm that returns a nearest interval approximation to a given fuzzy number, plays a pivotal role in the proposed method. Our approach contrasts markedly with those based on deffuzification operators which replace a fuzzy set by a single real number leading to a loss of many important information. A numerical example is also provided for the sake of illustration.

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