Decision Analysis Methods Combining Quantitative Logic and Fuzzy Soft Sets
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Decision Analysis Methods Combining Quantitative Logic and Fuzzy Soft Sets Jialu Zhang1 • Xia Wu1 • Ruhua Lu2
Received: 21 February 2019 / Revised: 28 June 2019 / Accepted: 26 May 2020 Taiwan Fuzzy Systems Association 2020
Abstract In this paper we propose a new decision analysis method combining quantitative logic and fuzzy soft set theory. Firstly, we transform a fuzzy information system into a fuzzy soft set, and then establish a formal language based on the fuzzy soft set, in which the parameters of fuzzy soft set are regarded as atomic formulas, some atomic formulas are connected by the logical connectives and then a logical formula is formed, and a implicative type of formula is interpreted as a soft decision rule (SDR). Secondly, various types of measures to evaluate the SDR are introduced and then the soft metric between two logical formulas is established. Thirdly, we apply the soft metric to the soft decision analysis, a SDR extraction algorithm for fuzzy decision information system and a corresponding recommendation algorithm are proposed. Finally, some attribute analysis examples, including the example as shown in rough sets and the practical credit card application example, are given to illustrate the newly proposed method and related concepts. Keywords Fuzzy soft set Fuzzy information system Soft fuzzy semantic Soft truth degree Soft metric Soft decision rule
& Xia Wu [email protected] 1
College of Mathematics and Finance, Xiangnan University, Chenzhou 426000, China
2
College of Software and Communication Engineering, Xiangnan University, Chenzhou 423000, China
1 Introduction In modern decision analysis, multi-attribute and continuous-valued decision-making phenomenon plays a key role to resolve the problems of evaluation of management and project, investment decision-making and many more. As we all known, the classical decision analysis is based on the two-valued logic and the evaluation of alternatives is then absolutely known [1]. However, because the human thinking and preferences may be fuzzy and the naturally existing objects may be uncertain, the attribute valuations associated in decision-making problem are not always accurate. Thus, these attributes involved in decision analysis are well appropriate to be identified by using mathematical methods of uncertainty, including random mathematics, rough sets, interval analysis, fuzzy sets and hesitant fuzzy sets, etc [2–5]. Soft set is one of mathematical theories proposed by Molodtsov to describe and deal with the uncertainty in the real world [6–8]. The application of soft set theory in uncertain decision-making is one of the most active research directions [9–14]. Maji et al. [9] concentrated on the ‘‘optimal alternative selection problem’’, which select the object with the maximum selection value as the best choice, the applications of soft sets in decision-making have almost always followed the thinking of Maji. On the other hand, in the sense of data analysis, we must pay more attention to attributes (i.e., parameters) themse
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