Abstract
A series of new concepts including interval entropy, interval similarity measure, interval distance measure, and interval inclusion measure of fuzzy sets are introduced. Meanwhile, some theorems and corollaries are proposed to show how these definitions can be deduced from each other. And then, based on interval entropy, a fuzzy multiple attribute decision making (FMADM) model is set up. In this model, interval entropy is used as the weight, by which the evaluation values of all alternatives can be obtained. Then all alternatives with respect to each criterion can be ranked as the order of the evaluation values. At last, a practical example is given to illustrate an application of the developed model and a comparative analysis is made.
Highlights
Multiple attribute decision making (MADM) problems existed in the economic, management, and various social fields
Most of the literatures pertaining to MADM analysis have been published using entropy weights
The concept of interval entropy is proposed and the relationships among other conceptions such as interval entropy, interval similarity measure, interval distance measure, and interval inclusion measure are investigated in detail
Summary
Multiple attribute decision making (MADM) problems existed in the economic, management, and various social fields. Bellman and Zadeh [1] put forward a fuzzy model based on MADM method by combining fuzzy set and decision making. For MADM problems, when the weight of alternative is defined, results of decision making depended on the values. In terms of determining objective alternative weights, one of the most famous approaches is the entropy method, which expresses the relative intensities of alternative importance to signify the average intrinsic information transmitted to the decision maker. Zhang et al [26] investigated the MADM problem with completely unknown attribute weights in the framework of interval value intuitionistic fuzzy sets. Using a new definition of interval value intuitionistic fuzzy entropy and some calculation methods for interval value intuitionistic fuzzy entropy, an entropy-based decision making method to solve interval value intuitionistic FMADM problems with completely unknown attribute weights is proposed.
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