DECISION MAKING BASED ON STATISTICAL DATA, SIGNED DISTANCE AND COMPOSITIONAL RULE OF INFERENCE

2004 ◽  
Vol 12 (02) ◽  
pp. 161-190 ◽  
Author(s):  
JING-SHING YAO ◽  
MING-MIIN YU
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Statistical Data ◽  
Fuzzy Decision Making ◽  
Seamless Integration ◽  
Transit System ◽  
Signed Distance ◽  
Decision Making Problem ◽  
Interval Valued

An assessment of a set of alternatives under certain evaluation criteria has difficulty in dealing with the priority of these alternatives, especially with a lack of precise information in an uncertain environment. Fuzzy numbers are usually applied to represent the imprecise numerical measurements of different alternatives. In this study statistical data are used to derive level (1-α,1-β) interval-valued fuzzy numbers to represent unknown alternative effectiveness scores, after which, by using the compositional rule of inference and signed distance to transform the fuzzy decision making problem into crisp one, one can conveniently obtain the order of these different alternatives and subsequently obtain the best alternative. The approach presented is computationally efficiency, and its underlying concepts are simple and comprehensible. By using this extended generalized method, two cases of an organizational type of rapid-transit-system selection problem are presented as examples to illustrate the applicability of the interval-valued fuzzy numbers and ranking system for decision making. The key contribution of the method is the seamless integration of the statistical data, interval-valued fuzzy number and signed distance to analyze multicriteria decision making problem. The innovation introduced in the model concerns interval-valued fuzzy number which is recognized as a determinant of the effectiveness score in fuzzy relation matrix.

A multi-criteria decision-making method based on triangular interval-valued fuzzy numbers and the VIKOR method

2021 ◽  
Vol 40 (1) ◽  
pp. 221-233
Author(s):  
Xingang Wang ◽  
Ke Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Fuzzy Theory ◽  
Research Direction ◽  
Vikor Method ◽  
Connection Number ◽  
Criterion Weight ◽  
Decision Making Problem ◽  
Electre Method ◽  
Interval Valued

In many cases, complex problems cannot be accurately described by precise numerical values. Fuzzy theory provides a suitable tool for solving these problems. However, if decision makers cannot reach an agreement on the method for defining linguistic variables based on fuzzy sets, TIVFNs (triangular interval-valued fuzzy numbers) can provide more accurate modeling. Therefore, solving fuzzy MCGDM (multiple criteria group decision-making) problem with an unknown expert weight and criterion weight in TIVFNs has become an important research direction. In this paper, TIVF-VIKOR (triangular interval-valued fuzzy VIKOR) method, which is suitable for the environment of TIVFNs, is proposed to solve the problem of fuzzy MCGDM. To achieve this goal, the TIVF-VIKOR method is innovatively adopted similarity and coefficient of variation are combined to calculate expert weight, and deviation maximization method based on divergence matrix is used to calculate criterion weight. VIKOR method is used to find the compromise solutions, which are converted into the form of binary connection number, and the optimal compromise solution is obtained after ranking. The proposed method is applied to the problem of machine fault detection, and the validity and feasibility of the method are illustrated. Compared with the TOPSIS∖ELECTRE method, the ranking results of the three methods are equivalent, and the fluctuation of the TIVF-VIKOR method is more distinct.

A QUANTITY PROPERTY-BASED FUZZY NUMBER RANKING METHOD FOR DECISION MAKING WITH UNCERTAINTY

2012 ◽  
Vol 20 (supp01) ◽  
pp. 133-145 ◽  
Author(s):  
FACHAO LI ◽  
FEI GUAN ◽  
CHENXIA JIN
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Ranking Method ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Interval Numbers ◽  
Interval Representation ◽  
Ranking Model ◽  
Key Issues

One of the key issues for support fuzzy decision-making is fuzzy number ranking. The existing ranking methods either do not provide a total ordering or cannot be effectively applied to decision-making processes. In this paper, we first give five basic principles that interval number ranking must satisfy, and construct a quantitative ranking model of interval numbers based on the synthesis effects of each index. We then propose a new constructions method of synthesis effect function systematically. Third, we also develop a new fuzzy numbers ranking model based on numerical characteristics, combining with the interval representation theorem of fuzzy numbers, and analyze the performance and characteristics of this ranking method by a case-based example. The results indicate that this proposed ranking method has good operability and interpretability, which can integrate the decision consciousness into decision process effectively and serve as a guideline for constructing different fuzzy decision methods.

scholarly journals Disjunctive Representation of Triangular Bipolar Neutrosophic Numbers, De-Bipolarization Technique and Application in Multi-Criteria Decision-Making Problems

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 932 ◽  
Author(s):  
Avishek Chakraborty ◽  
Sankar Prasad Mondal ◽  
Shariful Alam ◽  
Ali Ahmadian ◽  
Norazak Senu ◽  
...  
Keyword(s):  
Decision Making ◽  
Real Number ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Research Paper ◽  
Frame Of Reference ◽  
Multi Criteria Decision Making ◽  
Membership Functions ◽  
Decision Making Problem ◽  
Neutrosophic Number

This research paper adds to the theory of the generalized neutrosophic number from a distinctive frame of reference. It is universally known that the concept of a neutrosophic number is generally associated with and strongly related to the concept of positive, indeterminacy and non-belongingness membership functions. Currently, all membership functions always lie within the range of 0 to 1. However, we have generated bipolar concept in this paper where the membership contains both positive and negative parts within the range −1 to 0 and 0 to 1. We describe different structures of generalized triangular bipolar neutrosophic numbers, such as category-1, category-2, and category-3, in relation to the membership functions containing dependency or independency with each other. Researchers from different fields always want to observe the co-relationship and interdependence between fuzzy numbers and crisp numbers. In this platform, we also created the perception of de-bipolarization for a triangular bipolar rneutrosophic number with the help of well-known techniques so that any bipolar neutrosophic fuzzy number of any type can be smoothly converted into a real number instantly. Creating a problem using bipolar neutrosophic perception is a more reliable, accurate, and trustworthy method than others. In this paper, we have also taken into account a multi-criteria decision-making problem (MCDM) for different users in the bipolar neutrosophic domain.

scholarly journals A Novel Method for Dynamic Multicriteria Decision Making with Hybrid Evaluation Information

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Shihu Liu ◽  
Tauqir Ahmed Moughal
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Ideal Solutions ◽  
Interval Valued ◽  
Evaluation Information

How to select the most desirable pattern(s) is often a crucial step for decision making problem. By taking uncertainty as well as dynamic of database into consideration, in this paper, we construct a dynamic multicriteria decision making procedure, where the evaluation information of criteria is expressed by real number, intuitionistic fuzzy number, and interval-valued intuitionistic fuzzy number. During the process of algorithm construction, the evaluation information at all time episodes is firstly aggregated into one, and then it is transformed into the unified interval-valued intuitionistic fuzzy number representational form. Similar to most multicriteria decision making approaches, the TOPSIS method is applied in the proposed decision making algorithm. In particular, the distance between possible patterns and the ideal solutions is defined in terms of cosine similarity by considering all aspects of the unified evaluation information. Experimental results show that the proposed decision making approach can effectively select desirable pattern(s).

Possibility belief interval-valued soft set and its application in decision making

2021 ◽  
pp. 1-19
Author(s):  
Wenqing Fu ◽  
Ahmed Mostafa Khalil ◽  
Ahmed Mohamed Zahran ◽  
Rehab Basheer
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Soft Sets ◽  
Numerical Example ◽  
Decision Making Problem ◽  
Interval Valued

The aim of this article is to present the concept of restricted union and extended intersection of belief interval-valued soft sets, along with its properties. In addition, we propose the concept of possibility belief interval-valued soft set theory and investigate their properties. For suitability of possible applications, there are seven kinds of operations (e.g., union, intersection, restricted union, extended intersection, complement, soft max-AND, and soft min-OR) on the possibility belief interval-valued soft sets are defined and their basic theoretical are given. Then, we construct two algorithms by using soft max-AND and soft min-OR operations of possibility interval-valued soft sets for fuzzy decision-making problem. Lastly, we introduce an algorithm using a possibility interval-valued soft set to solve the decision-making problems and clarify its applicability by a numerical example.

scholarly journals Generalised Interval-Valued Fuzzy Soft Set

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.

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