Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 301
Author(s):  
Li Huang ◽  
Jian-Zhang Wu ◽  
Rui-Jie Xi
Keyword(s):  
Generation Process ◽  
Random Generation ◽  
Decision Criteria ◽  
Interaction Index ◽  
Decision Aiding ◽  
Satisfactory Performance ◽  
Complex Constraints ◽  
Interaction Phenomenon

The capacity is a powerful tool with exponential coefficients to represent the interaction phenomenon among decision criteria, but its random generation becomes a tough issue for dealing with the monotonicity with all inclusion subsets as well as the complex constraints of decision preference. In this paper, we adopt a kind of explicit interaction index, the nonadditivity index, to construct two types of quasi-random generation methods of capacity under a given decision interaction preference. Compared to the existing random generation algorithms, the methods have relatively satisfactory performance on the statistics characteristic of generated capacities but need rather less calculation effort on the generation process. We also show the effectiveness of proposed quasi-random generation methods by an illustrative decision example.

Multicriteria correlation preference information (MCCPI) with nonadditivity index for decision aiding

2020 ◽  
Vol 39 (3) ◽  
pp. 3441-3452
Author(s):  
Li Huang ◽  
Jian-Zhang Wu ◽  
Gleb Beliakov
Keyword(s):  
Decision Aid ◽  
Pairwise Comparison ◽  
Random Generation ◽  
Decision Criteria ◽  
Preference Information ◽  
Decision Aiding ◽  
Dominance Relationships ◽  
Decision Scheme ◽  
Internal Interaction ◽  
Decision Alternatives

MCCPI (Multiple Criteria Correlation Preference Information) is a kind of 2 dimensional decision preference information obtained by pairwise comparison on the importance and interaction of decision criteria. In this paper, we introduce the nonadditivity index to replace the Shapley simultaneous interaction index and construct an undated MCCPI based decision scheme. We firstly propose a diagram to help decision maker obtain the nonadditivity index type MCCPI, then establish transform equations to normalize them into desired capacity and finally adopt a random generation MCCPI based comprehensive decision aid algorithm to explore the dominance relationships and creditable ranking orders of all decision alternatives. An illustrative example is also given to demonstrate the feasibility and effectiveness of the proposed decision scheme. It’s shown that based on some good properties of nonadditivity index in practice, the updated MCCPI model can deal with the internal interaction among decision criteria with relatively less model construction and calculation effort.

scholarly journals Multicriteria Correlation Preference Information (MCCPI)-Based Ordinary Capacity Identification Method

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 300 ◽  
Author(s):  
Jian-Zhang Wu ◽  
Yi-Ping Zhou ◽  
Li Huang ◽  
Jun-Jie Dong
Keyword(s):  
Decision Making ◽  
Decision Aid ◽  
Higher Order ◽  
Decision Criteria ◽  
Preference Information ◽  
Decision Aiding ◽  
Identification Method ◽  
Explicit Information ◽  
Dominance Relationships ◽  
Decision Alternatives

Multicriteria correlation preference information (MCCPI) refers to a special type of 2-dimensional explicit information: the importance and interaction preferences regarding multiple dependent decision criteria. A few identification models have been established and implemented to transform the MCCPI into the most satisfactory 2-additive capacity. However, as one of the most commonly accepted particular type of capacity, 2-additive capacity only takes into account 2-order interactions and ignores the higher order interactions, which is not always reasonable in a real decision-making environment. In this paper, we generalize those identification models into ordinary capacity cases to freely represent the complicated situations of higher order interactions among multiple decision criteria. Furthermore, a MCCPI-based comprehensive decision aid algorithm is proposed to represent various kinds of dominance relationships of all decision alternatives as well as other useful decision aiding information. An illustrative example is adopted to show the proposed MCCPI-based capacity identification method and decision aid algorithm.

Comprehensive nonmodularity and interaction indices for decision analysis

2021 ◽  
pp. 1-15
Author(s):  
Jian-Zhang Wu ◽  
Gleb Beliakov
Keyword(s):  
Decision Analysis ◽  
Decision Criteria ◽  
Internal Interaction ◽  
The Common ◽  
Interaction Phenomenon

Nonmodularity is a prominent property of capacity that deeply links to the internal interaction phenomenon of multiple decision criteria. Following the common architectures of the simultaneous interaction indices as well as of the bipartition interaction indices, in this paper, we construct and study the notion of probabilistic nonmodularity index and also its particular cases, such as Shapely and Banzhaf nonmodularity indices, which can be used to describe the comprehensive interaction situations of decision criteria. The connections and differences among three categories of interaction indices are also investigated and compared theoretically and empirically. It is shown that three types of interaction indices have the same roots in their first and second orders, but meanwhile the nonmodularity indices have involved less amount of subsets and can be adopted to describe the interaction phenomenon in decision analysis.

Motivated Recall of Decision Criteria

2003 ◽  
Author(s):  
Erica Dawson ◽  
Thomas Gilovich ◽  
Dennis Regan
Keyword(s):  
Decision Criteria

DEWARD

Alloy Digest ◽  
1976 ◽  
Vol 25 (12) ◽  
Keyword(s):  
Heat Treatment ◽  
Fracture Toughness ◽  
Wear Resistance ◽  
Compressive Strength ◽  
Physical Properties ◽  
Heat Treating ◽  
Die Steel ◽  
Satisfactory Performance ◽  
Specialty Steel ◽  
Minimum Distortion

Abstract DEWARD is an oil-hardening, non-deforming, manganese die steel that is characterized by uniformity, good machinability and satisfactory performance in service. Its composition permits a relatively low hardening temperature to give minimum distortion after heat treatment and little danger of cracking. It has good wear resistance and gives excellent results when used for all kinds of intricate tools. This datasheet provides information on composition, physical properties, hardness, elasticity, and compressive strength as well as fracture toughness. It also includes information on forming, heat treating, and machining. Filing Code: TS-310. Producer or source: AL Tech Specialty Steel Corporation.

Sign in / Sign up

Export Citation Format

Share Document