Abstract
Non-additive measures and corresponding integrals originally have been introduced by Choquet in 1953 (1) and independently defined by Sugeno in 1974 (2) in order to extend the classical measure by replacing the additivity property to non-additive property. An important feature of non –additive measures and fuzzy integrals is that they can represent the importance of individual information sources and interactions among them. There are many applications of non-additive measures and fuzzy integrals such as image processing, multi-criteria decision making, information fusion, classification, and pattern recognition. This paper presents a mathematical model for discussing an application of non-additive measures and corresponding integrals in tourism management. First, the problem of tourism management is described for one of the tourism companies in Iraq. Then, fuzzy integrals (Sugeno integral, Choquet integral, and Shilkret integral) are applied with respect to non-additive measures to evaluate the grade of the gratification of the tourist of staying in a particular town for determining the best evaluation.
Highlights
Non-additive measures and fuzzy integral theory are an evolution of classical measure theory
Non-additive measures (capacities [1], or fuzzy measures [2]) and fuzzy integral theory are an evolution of classical measure theory
Fuzzy integrals (Sugeno integral, Choquet integral and Shilkret integral) are applied with respect to λ-non additive measures to evaluate the grade of the gratification of the tourist of staying in a particular town for determining the best evaluation
Summary
Non-additive measures (capacities [1], or fuzzy measures [2]) and fuzzy integral theory are an evolution of classical measure theory. This paper discusses an application of non-additive measures and corresponding integrals in Tourism management for the case study. This section, briefly recalls the three most famous fuzzy integrals (i.e., the Sugeno, Choquet, and Shilkret integrals) on [0,1]-valued function. Let us suppose that μ be a non-additive measure defined on C Choquet integral of a function f: C → [0,1] w.r.t a non-additive measure μ is defined as [1]. This section will apply the non-additive model (non- additive measures and fuzzy integrals) on tourism management for one of the tourism companies in Iraq to evaluate the visitation more cities with greater satisfaction to the tourist of staying in a particular town, (i.e. to decide which the most acceptable town for the tourist to indwelling).
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