Elicitation criterions for restricted intersection of two incomplete soft setsby Bang-He Han, Yong-Ming Li, Jie Liu, Sheng-Ling Geng, Hou-Yi Li

Knowledge-Based Systems

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cG c School of Computer Science and Technology, Xidian University, Xi’an 710061, China dCollege of Computer, Qinghai Normal University, Xinin e State Key Laboratory of ISN, School of Telecommunicat a r t i c l e i n f o

Article history:

Received 18 March 2013

Received in revised form 14 January 2014

Accepted 18 January 2014 the two cases with soft set model, we propose the elicitation problems to be dealt with in this paper. tion for hi et of 4 po choices. E ¼ fc1; c2; c3; c4g is the set of parameters describing tions such as air humidity, traffic facilities, price of land price. There are two investigators Alice and Bob. They have their incomplete evaluations which are shown in Table 1, where.  in each bracket: (1) the first value refers to the opinion of Alice and the second value refers to that of Bob. ⇑ Corresponding author. Tel.: +86 29 81891371.

E-mail addresses: bhhan@mail.xidian.edu.cn (B.-H. Han), liyongm@snnu.edu.cn (Y.-M. Li), 835088577@qq.com (J. Liu), qhnugsl@gmail.com (S.-L. Geng), lihouyi2008@ 126.com (H.-Y. Li).

Knowledge-Based Systems 59 (2014) 121–131

Contents lists availab

Knowledge-Ba journal homepage: www.elThis section mainly focuses on the motivations of this paper’s subject. Firstly two cases in practice are given. Then we make an introduction to soft sets. At last by describing the problems in

Case 1: Site Selection

A company leader wants to make a site selec seas branch company. U ¼ fs1; s2; s3; s4g is the shttp://dx.doi.org/10.1016/j.knosys.2014.01.015 0950-7051/ 2014 Elsevier B.V. All rights reserved.s overtential condi, labor madesets by extracting from some practical problems. The concept of expected elicitation times of objects is defined and used for developing one type of elicitation strategy.  2014 Elsevier B.V. All rights reserved. 1. Motivations 1.1. Two cases in real practiceAvailable online 31 January 2014

Keywords:

Elicitation

Incomplete soft set

Restricted intersection

Decision making

Choice valueg 810008, China ions Engineering, Xidian University, Xi’an 710061, China a b s t r a c t

Purpose: This paper aims to develop and compare several elicitation criterions for decision making of incomplete soft sets which are generated by restricted intersection.

Design/methodology/approach: One time elicitation process is divided into two steps. Using the greedy idea four criterions for elicitation of objects are built based on maximax, maximin, minimax regret and combination of expected choice values and elicitation times. Then these initial unknown values which produce incomplete values together with known information are in priority.

Findings: Fast methods for computing possibly and necessarily optimal solutions before or in the elicitation process are invented. As far as the sizes of soft sets used in the simulation experiments, it is found statistically that we should choose the criterion based on the combination of expected choice value and expected elicitation times in the first step of one time elicitation.

Practical implications: The developed methods can be used for decision making of incomplete 0–1 information systems, which are generated by the conjunction of two experts’ incomplete 0–1 evaluation results. Whenever the available information is not enough for choosing a necessarily optimal solution, the elicitation algorithms can help elicitate as few unknown values as possible until an optimal result is found. An elicitation system is made to show that our elicitation methods can potentially be embedded in recommender or decision support systems.

Originality/value: The elicitation problems are proposed for decision making of operation-generated softa School of Mathematics and Statistics, Xidian University, Xi’an 710071, China bCollege of Computer Science, Shaanxi Normal University, Xi’an 710062, ChinaElicitation criterions for restricted interse soft sets

Bang-He Han a,⇑, Yong-Ming Li b, Jie Liu c, Sheng-Lingtion of two incomplete eng d, Hou-Yi Li e le at ScienceDirect sed Systems sevier .com/ locate /knosys asedcommunicating ability; c4, adaptability to changes. The evaluation results of the two interviewers can be given by two 0–1 valued tables, where the rows correspond to the job hunters, the columns correspond to the above four abilities. 1 means good, 0 means not good. The final evaluation matrix is got by min operator simi-number of value 0.5 outside these brackets containing two 0.5 in the row si. When c ¼ 0; c is omitted.

For Table 1, the decision value of s2 is equal to 2. However, the real decision values of the other objects are unavailable due to the incomplete information. In this example all of these 4 choices are possible to one of the optimal solutions under usual additive model and no one of themmust be an optimal solution of the real situation.

If we want to make approximate reasoning, which one should be an approximate solution? If we want to make exact reasoning, which investigator should give evaluation on which unknown value?

Case 2: Finding a best employee

A company wants to employ one person from a lot of graduates.

There are two interviewers to evaluate these job hunters about the following aspects: c1, writing ability; c2, organizing ability; c3,(2) 1 means appropriate (positive) and 0 means a negative answer. (3) 0.5 means incomplete evaluation.  the value outside each bracket is equal to the minimum of the two values inside the bracket. This means that a certain choice is appropriate with respect to a certain condition if and only if the two investigators are both satisfied with that. In the situation when Alice is satisfied with certain condition of one choice and Bob has not given his opinion on this, the integration of their evaluations should be incomplete. Obviously, once Alice says no for a certain condition of one choice, the final integration must be negative no matter what the opinion of Bob is.  the value of form aþ b þ c in the row si (i = 1,2,3,4) and the column r corresponds to the incomplete decision value of si : (4) a equals to the number of value 1 outside brackets in the row si. (5) Definition 1.1. b is defined as the incomplete decision value part marked with one asterisk of si, where b equals to the number of value 0.5 outside these brackets containing only one 0.5 in the row si. When b ¼ 0; b is omitted. (6) Definition 1.2 c is defined as the incomplete decision value part marked with two asterisks of si, where c equals to the