Decision on the Selection of Tourist Hotels for an Hotelier Using the Concept of Fuzzy Inference System

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1 Decision on the Selection of Tourist Hotels for an Hotelier Using the Concept of Fuzzy Inference System Gunjan Gupta 1, Manish K. Srivastava 2 and S. Kumar 3 1. Mewar University, Mewar, Rajasthan 2. Lecturer of Maths, Boy s Anglo Bengali I/C, Sunderbagh, Lucknow 3. Dept. of Maths, IBS, Khandari Campus, Agra Location of a tourist hotel is always a super criterion for the tourist, and this is a typical task for the hotelier to take a decision on it. Therefore the main aim of this work is to design a fuzzy inference system to take a decision for the section of tourist hotel. Here the method of fuzzy set theory and fuzzy logic process are used to consolidate decisionmakers assessments about criteria weighting. An empirical study is made for indentifying the international tourist hotel location in India and also to highlight the effectiveness of fuzzy model proposed. Thus, this work proposes a simple and practical decision model that will provide significant managerial insights to evaluation committees when making location selection. It will also help committee members to understand the organizational goal and decision process. Key words: Hotel, tourist, hotelier, fuzzy logic, membership function. 1. Introduction In recent years, e-commerce has had great impacts on various industries by developing new approaches. Its benefits include faster and easier access to information and the possibility to coordinate for any task before attempting it. In the tourism sector, e-commerce is playing a great role to develop this industry and improve services. On the other hand, combining e-commerce technology with mathematics and the other basic sciences has provided special facilities and flexibility in complying human needs. Nowadays hotel industry is fighting with a major issue and that is how to attract tourist, further other issues which are related above are reducing the rent, operational performance, hotel location and some more. Geographical location of any hotel is always paid attention not only to the tourist but also a research attraction for academician. We can collect the influential factors for hotels to achieve successes for reputation, marketing building style, staff quality etc., but location is the most significant factor influence operational performance [Aikens (1985)]. Moreover, in the age of customer-based service, the convenience of customer longing will directly raise customer loyalty. As far as the interest of academician is concerned, Chen (1996) worked on a mathematical model to build a location choice model for distribution centers, based on mathematical programming. Chan (1997) again worked on a fuzzy multi-objectives facility location programming to search for an airport fire station. Teng (2000) used the concept of multi-criteria decision-making to deal with the site selection of restaurant. As far as other industries are concern, Chang et al (1997) worked for aviation industry, Kno et al (2002) for retail business, Aberbakh and Berman (1995) worked for sales-delivery facility location. Treng et al (2002) evaluated the alternative locations to the restaurant using AHP (analytic hierarchy process, which is a popular method used in finding a solution to the problem of location selection. Hadavandi et al. (2011) design a fuzzy model for the tourist arrival forecasting and solved this problem by evolutionary fuzzy system, while Jowkar et al. (2011) worked for fuzzy risk analysis model for e-tourism investment. As we know that, due to the availability and uncertainly of information as well as the vagueness of human feeling and recognition, it is difficult to make an exact evaluation and convey the feeling and recognition of objects for decision maker. Therefore it is better to use the concept of fuzzy logic to design the modeling of such problem which contains the vagueness and uncertainty. Thus a fuzzy based decision model for tourist hotel location selection is more appropriate and effective than traditional precision-based 63 Gunjan Gupta, Manish K. Srivastava and S. Kumar

2 models. On the basis of available information we try to design a fuzzy logic based model for the decision on selection of tourist hotels. This model is subdivided as follows. In section 2, we introduce the criteria of tourist hotel location selection while in section 3; the basic concepts and research method are discussed. Section 4 presents the empirical study by the decision model, finally, conclusions are highlighted. 2. Tourist Hotel During the decision-making process of selecting the tourist hotel location, the objective of synergy can be accomplished if facilities such as commercial areas, conventional centers, and airports can be taken into consideration. Gray and Liguori (1998) in a feasibility study of hotel establishment, suggested several considerations for location selection: local economic environment, regional or zone regulations, height limit of buildings, car park facilities, public facilities, traffic convenience and accessibility, geographic factors, natural resources, and the size of the location. Further, Pan (2002) categorized tourist hotel location selection factors according to base station suitability, traffic convenience and fine visual perception, public facilities and other services, application of certain regulations, and flexible space. The basis of these discussions is focused on the overall facilities surrounding the hotel, traffic conditions, and future considerations for expandability. Some scholars have also utilized the issues of location theory such as central place theory, principle of minimum differentiation, and bid rent theory as the basis for making decisions on tourist hotel locations [Hsieh and Huang (1998), Lee et al., (2000)]. From the standpoint of the central place theory, two primary concepts of service scope and demand threshold are survived for the hotel operator. Given these two concepts, we can theorize that the consumer characteristics and scope covered under the overall market conditions include factors such as consumption standard and number of consumers. Factors attributed to the principle of minimum differentiation mainly emphasized on the concept of cluster effect, which is a result of the consumer behavior of asking for quotations. In order to minimize the cost of transportation during the process in which consumers are seeking price information, companies will engage in cluster activities. According to Lee et at. (2000) and Hsieh and Huang (1998), the number of competitive store locations is an important factor for location selection, where competitiveness is demonstrated by market share in commercial circles. The degree of proximity to competitor locations is also an indicator of competitiveness. Therefore, when businesses are making location selection decisions, future development potential is an important consideration in addition to projecting the competitiveness of the new location. From the perspective of surrounding environment, public order issues such as the outbreak of theft, fire, and robbery are also major concerns in location selection. Tzeng et al. (2002) noted that car parking conditions should also be included into location selection factors, as additional numbers of parking spaces will attract more customers. Meanwhile, other base station traffic accessibility or convenience is one of consumers primary concerns in selecting a tourist hotel location. Hotel s unique core ability is also one of customer s main considerations for selecting a tourist hotel. Entertainment facilities, food and beverage services, and environmental conditions are major attributes in hotel selection. Also, developing hotel genre, amalgamating with local culture, and using decorative styles to create competitive advantage are all prime components influencing customer choice of hotels. Furthermore, the quality and quality of local human resources is also a focal point for enterprises when making decisions on the establishment of international tourist hotels. As far as the application of fuzzy logic in other areas are concerned then, Kumar et. al, (2010) worked for fuzzy based bonus malus system to calculate the premium of car insurance, and another application by Kumar et. al, (2012) about a fuzzy approach to calculate the health insurance premium of a person having cardiovascular disease. Kumar and Saxena (2014) developed an intelligent traffic light control system using fuzzy logic and edge detection, while Yang et al (2014) worked for theoretical, empirical, and operational models in hotel location research. Combining the criteria of selecting the hotel location reported in the above literature review and considering the characteristics of Indian hotel industry and comments from expert academics as well as 64 Gunjan Gupta, Manish K. Srivastava and S. Kumar

3 known hotel managers in India, 21 criteria were selected to assess the superiority of an international tourist hotel location. The results are shown through Table Research Method AHP (Saaty, 1980) is used to solve multiple criteria decision problems. By means of a systematic hierarchy structure, complex estimation criteria can be clearly and distinctly presented. Ratio scales are utilized to make reciprocal comparisons for each element and layer. After completing the reciprocal matrix, the comparative weights for each element can be obtained. The AHP is widely used for tackling multi-criteria decision-making problems in real situations. In spite of its popularity and simplicity in concept, this method is often criticized for its inability to adequately handle the inherent uncertainly and imprecision associated with the mapping of the decision-maker s perception to crisp values. In the traditional formulation of the AHP, human judgments are represented as crisp values. However, in many practical cases the human preference model is uncertain and decision makers might be reluctant of unable to assign crisp vales to the comparison judgments. The use of fuzzy set theory allows the decision-makers to incorporate unquantifiable information, incomplete information, non-obtainable information, and partial facts into the decision model (Werthner et al., 1999). Although fuzzy AHP requires tedious computations, it is capable of capturing a human s appraisal of ambiguity when complex multi-criteria decision-making problems are considered (Erensal et al., 2006). 4. Fuzzy set theory and fuzzy number The fuzzy set theory introduced by Zadeh (1965) is suitable for handling problems involving the absence of sharply defined criteria. In a universal set of discourse X, a fuzzy subset A of X is defined by a membership function f A (x) which maps each element x in A to a real number in the interval [0, 1]. The function value f A (x) represents the grade of membership of x in A. The larger the f A (x), the stronger is the grade of membership for x in A. A fuzzy number A in R (real line) is a triangular fuzzy number if its membership function f A : R [0, 1] is defined as: f A (x) = ( x c) /( a c) c x a, ( x b) /( a b) a x b 0 otherwise with c a b. The triangular fuzzy number A can be denoted by (c, a, b). The parameter a gives the maxima grade of f A (x), i.e. 1 and it is the most possible value of the evaluated data. c and b are the lower and upper bounds of the available area for the evaluated data. They are used to reflect the fuzziness of the evaluation data. The narrower the interval [c, b], the lower is the fuzziness of the evaluated data. 5. Linguistic Value The concept of linguistic values (Zadeh, 1975) is very useful in handling situations that are too complex or ill-defined to be reasonably described in conventional quantitative expressions. The triangular fuzzy numbers defined on [0, 1] and/or the linguistic values characterized by triangular fuzzy numbers defined on [0, 1] are utilized to convey the suitability evaluation of alternatives versus criteria. For example, S = {VG, G, M, B, VB}, where VB is very bad, B is bad, M is medium, G is good, VG is very good. The membership functions of those linguistic values are VB = (0, 0, 0.2), B = (0, 0.2, 0.4), M = (0.3, 0.5, 0.7), G = (0.6, 0.8, 1), VG = (0.8, 1, 1). Here we can determine the weights of the criteria and sub-criteria by using pair-wise comparison matrices. The fuzzy scale regarding relative importance to measure the relative weights is given through Table 1. This scale is proposed by Kahraman et al. (2006) and used for solving fuzzy decision-making problems. 65 Gunjan Gupta, Manish K. Srivastava and S. Kumar

4 Table 1: Linguistic scales Linguistic scale for importance Triangular fuzzy scale Triangular fuzzy reciprocal scale Just equal (JE) (1, 1, 1) (1, 1, 1) Equally important (EI) (1/2, 1, 3/2) (2/3, 1, 2) Weakly more important (WMI) (1, 3/2, 2) (1/2, 2/3, 1) Strongly more important (SMI) (3/2, 2, 5/2) (2/5, 1/2, 2/3) Very strongly more important (VSMI) (2, 5/2, 3) (1/3, 2/5, 1/2) Absolutely more important (AMI) (5/2, 3, 7/2) (2/7, 1/3, 2/5) 6. Triangular fuzzy number Obtaining the ideal and anti-ideal values is important and essential, and the ranking method plays a key role. Many fuzzy ranking methods have been developed by many authors viz Chen (1985); Kim and Park (1991) etc. Because the graded mean integration representation (Chen and Hsieh (2000)) not only improves some drawbacks of existing ranking methods but also possesses the advantage of easy implementation and powerfulness of problem solving, it is adopted by this study to find the ideal and antiideal solutions. Further based on the graded mean integration representation method, we can obtain the ci 4ai bi presented and ranking value of triangular fuzzy number A i = (c i, a i, b i ) as: R(A i ) = 6 using R(A i ), i = 1, 2,., n, we can rank the n triangular fuzzy numbers, A 1, A 2, A n. Let A i And A j be two fuzzy numbers and. 7. De-fuzzification It is clear that in system output, suggested accommodations are shown to the users. In addition, system can reply as an e-commercial system with fee. Since the membership functions are not included in the output of fuzzy inference system in our case study, and the output is only a list of suggested accommodation, the output values are constant and no-fuzzy and then, our problem is from Fuzzy-Crisp type and hence there isn t the third step or de-fuzzification. 8. Fuzzy decision-making structure Fig.1. Overall structure of Fuzzy decision-making system 66 Gunjan Gupta, Manish K. Srivastava and S. Kumar

5 Table 2 - The integrated fuzzy weight and weight in each level Item Integrated fuzzy weight Weight S 1 (0.1145, , ) S 2 (0.1346, , ) S 3 (0.1534, , ) S 4 (0.1495, , ) S 11 (0.0366, , ) S 12 (0.0426, , ) S 21 (0.0495, , ) S 22 (0.0489, , ) S 31 (0.0588, , ) S 32 (0.0509, , ) S 41 (0.0522, , ) S 42 (0.0527, , ) S 111 (0.0079, , ) S 112 (0.0126, , ) S 113 (0.0228, , ) S 121 (0.0169, , ) Ss 122 (0.0150, , ) S 211 (0.0068, , ) S 212 (0.0058, , ) S 213 (0.0089, , ) S 214 (0.0088, , ) S 221 (0.0109, , ) S 222 (0.0157, , ) S 223 (0.0309, , ) S 311 (0.0209, , ) S 312 (0.0209, , ) S 321 (0.0113, , ) S 322 (0.0168, , ) S 323 (0.0343, , ) S 411 (0.0216, , ) S 412 (0.0215, , ) S 421 (0.0168, , ) S 422 (0.0232, , ) Gunjan Gupta, Manish K. Srivastava and S. Kumar

6 Table 3 - The average evaluation ratings of each criterion Option a Option b Option c Ideal solution Anti-ideal solution S 111 (0.7, 0.75, 0.7) (0.5, 0.75, 0.9) (0.7, 0.94, 1.0) (0.7, 0.94, 1.0) (0.5, 0.73, 0.9) S 112 (0.6, 0.83, 1.0) (0.7, 0.93, 1.0) (0.4, 0.63, 0.8) (0.7, 0.92, 1.0) (0.4, 0.64, 0.8) S 113 (0.6, 0.83, 1.0) (0.6, 0.83, 1.0) (0.4, 0.64, 0.8) (0.6, 0.83, 1.0) (0.4, 0.64, 0.8) S 121 (0.5, 0.73, 0.9) (0.5, 0.74, 0.9) (0.4, 0.63, 0.8) (0.5, 0.73, 0.9) (0.4, 0.63, 0.8) S 122 (0.6, 0.83, 0.9) (0.4, 0.64, 0.8) (0.5, 0.73, 0.8) (0.6, 0.83, 0.9) (0.4, 0.64, 0.8) S 211 (0.5, 0.72, 0.9) (0.6, 0.83, 0.8) (0.7, 0.93, 1.0) (0.7, 0.92, 1.0) (0.5, 0.73, 0.9) S 212 (0.6, 0.82, 1.0) (0.5, 0.74, 0.9) (0.7, 0.93, 1.0) (0.7, 0.93, 1.0) (0.5, 0.74, 0.9) S 213 (0.5, 0.72, 0.9) (0.3, 0.54, 0.7) (0.4, 0.64, 0.8) (0.5, 0.72, 0.9) (0.3, 0.54, 0.7) S 214 (0.5, 0.72, 0.9) (0.6, 0.84, 0.9) (0.4, 0.64, 0.8) (0.6, 0.82, 0.9) (0.4, 0.64, 0.8) S 221 (0.6, 0.83, 1.0) (0.5, 0.73, 0.9) (0.4, 0.64, 0.8) (0.6, 0.82, 1.0) (0.4, 0.63, 0.8) S 222 (0.4, 0.64, 0.8) (0.6, 0.84, 0.9) (0.5, 0.74, 0.9) (0.6, 0.82, 0.9) (0.4, 0.63, 0.8) S 223 (0.4, 0.64, 0.8) (0.5, 0.73, 0.9) (0.4, 0.64, 0.8) (0.5, 0.73, 0.9) (0.4, 0.63, 0.8) S 311 (0.6, 0.85, 0.9) (0.4, 0.64, 0.8) (0.4, 0.64, 0.8) (0.6, 0.83, 0.9) (0.4, 0.63, 0.8) S 312 (0.7, 0.92, 1.0) (0.6, 0.83, 1) (0.4, 0.65, 0.8) (0.7, 0.92, 1.0) (0.4, 0.64, 0.8) S 321 (0.5, 0.74, 0.9) (0.6, 0.83, 0.9) (0.4, 0.65, 0.8) (0.6, 0.83, 0.9) (0.4, 0.63, 0.8) S 322 (0.7, 0.92, 1.0) (0.6, 0.84, 1) (0.5, 0.73, 0.9) (0.7, 0.93, 1.0) (0.5, 0.73, 0.9) S 323 (0.5, 0.73, 0.9) (0.6, 0.84, 0.9) (0.3, 0.54, 0.7) (0.6, 0.82, 0.9) (0.3, 0.54, 0.7) S 411 (0.5, 0.74, 0.7) (0.6, 0.84, 0.9) (0.5, 0.73, 0.8) (0.6, 0.82, 0.9) (0.5, 0.73, 0.8) S 412 (0.5, 0.74, 0.7) (0.3, 0.54, 0.7) (0.4, 0.64, 0.8) (0.5, 0.73, 0.7) (0.3, 0.54, 0.7) S 421 (0.5, 0.73, 0.9) (0.4, 0.63, 0.8) (0.4, 0.64, 0.8) (0.5, 0.73, 0.9) (0.4, 0.63, 0.8) S 422 (0.7, 0.92, 1.0) (0.7, 0.92, 1.0) (0.7, 0.93, 1.0) (0.7, 0.92, 1.0) (0.7, 0.93, 1.0) We get the distance of options versus the ideal and anti-ideal solutions, to obtain the close index of option k versus the ideal solution and select the best option. Table 4 - The distance between options and the ideal and anti-ideal solution Option a Option b Option c * D k ~ D k Gunjan Gupta, Manish K. Srivastava and S. Kumar

7 * The close index S k of three options was obtained (shown in Table 5), which expressed the final results clearly. Moreover, managers will be able to know the criteria gap between location characteristics and the ideal target and devise the operation strategies for the location they selected. Table 5 - The close index of options versus the ideal solution Option a Option b Option c * S k * The relative approximation value of each option k versus ideal solution S k could be obtained. As Table 5 demonstrated, option a was the best location. As the final result was integrated by the weight of each criterion, managers can therefore trace each criterion in order to understand the superiority or inferiority of the strategies established. For instance, empirical results of this study indicated that the criterion of public security, option c versus S 113, is quite distant from the ideal solution and the weight of S 113 was substantial. Therefore managers could make operation strategies for this criterion, public security, in advance. 9. Conclusion Fuzzy decision-making is applied in this work for e-tourism industry and in order to increase research integrity; we focused on a metropolitan city of India. Because hotel location is directly related to the level of hotel business activity, the hotel budget plan, when settled, will affect future hotel customer quantity as well as access of foreign independent tourists. Therefore, developing a set of integrated tourist hotel location selection system and comparing its suitability to major alternatives are needed for managers to sharpen their competitive edge. In fact a fuzzy multi-criteria decision model for selecting a location for a tourist hotel is designed in this work. The process of deriving the solution is illustrated through an easy-tounderstand empirical study. Results demonstrate that the model can provide a framework to assist decision makers in analyzing location factors and making a dispassionate and objective location selection. At the process of model building, the weights of four perspectives, four factors, and 21 criteria are presented. From the result of weights of perspectives, the S 3 (hotel characteristic) and S 4 (operation management) are the first and second important perspectives in the four perspectives. And the S 31 (internal development) is the most important factor in all factors. In the 21 criteria, we know that criteria S 113 (public security), S 223 (convenience of traffic to tourism scenic spots), and S 321 (amalgamation with local culture) are more important in the evaluation model. From the above results, the managers focus on whether the characteristic of a hotel can combine with the local culture characteristic when they survey location. The managers pay more attention to other criteria such as public security, modes of transportation to reach scenic spots and to combine these with the local character when a hotel is being designed. Since these criteria provide relief, convenience and a good experience to the customers, an experiential marketing strategy can also be developed for the hotel. In real life, due to the uncertainty of information as well as the vagueness of human feeling and recognition, it is difficult to exactly evaluate and convey the feeling and recognition of objects. Hence, the author combine fuzzy sets theory with linguistic value concept in setting up a model that can help decision- makers deal with complex issues under the fuzzy environment. The model will further enhance organizational communication ability. Meanwhile, tourist hotel managers and investors should decide on the strength of each location in an effort to enhance their understanding of the new hotel s competitiveness. The work also demonstrates how comparisons could be made while selecting the model, which gives a clear direction for hotel managers and investors when devising operating strategies and activities. 69 Gunjan Gupta, Manish K. Srivastava and S. Kumar

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