Conceptual design evaluation considering the ambiguity semantic variables fusion with conflict beliefs: An integrated Dempster-Shafer evidence theory and intuitionistic fuzzy -VIKOR

https://doi.org/10.1016/j.aei.2021.101426Get rights and content

Highlights

  • Semantic variables fusion of IFSs in conceptual design based on DS evidence theory.

  • Conflicting beliefs of ambiguity semantics are considering in the concept evaluation.

  • IFS-VIKOR model based on information entropy is proposed to rank the schemes.

  • A case study of a new tree climbing and trimming machine is applied and constructed.

Abstract

Quantifying the uncertain linguistic evaluation from decision-makers (DMs) is one of the most challenging parts in the conceptual design decision. Although fuzzy decision models have been widely used to capture potential uncertainty by assigning a fuzzy term with the certain belief, the ambiguity subjective evaluation of semantic variables with conflict beliefs derived from DMs have not been well addressed. To solve this drawback, a concept decision model based on Dempster-Shafer (DS) evidence theory and intuitionistic fuzzy -Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) considering the ambiguity semantic variables fusion is proposed. Firstly, by incorporating semantic variables of intuitionistic fuzzy sets (IFSs), the diversified semantic judgments and its belief will be taken into account to form an ambiguity semantic initial decision matrix; secondly, the DS combination rule will be used to fuse the different semantic variables of multi-DMs in each scheme, update the belief of each semantic variable, and then the semantic fusion value matrix of the scheme will be constructed; finally, the weight of each evaluation objective will be calculated based on the value matrix and information entropy model, IFS-VIKOR model will be constructed to rank the concepts. A case study of the tree climbing and trimming machine will be employed to verify the proposed decision model. This decision model considering diversifying semantic variables and the conflict belief is proven to be effective compared with the IFS-SAW and ISF-TOPSIS.

Introduction

Conceptual design is the initial phase of the new product development (NPD) to obtain a conceptual scheme (CS) that meets design constraints and customer preferences. The quality of the conceptual scheme selection directly affects the product cost, safety, environment, and quality [1], [2]. Due to the incompleteness and innovation of the early design process, the decision of CSs is a complicated multi-objective evaluation problem [3], which mainly involves the acquisition of fuzzy evaluation information and the solution of multi-objective comprehensive value. However, most of the evaluation data come from DM's linguistic judgments and preferences [4], [5], which are inconsistent between different DMs, and may even be diverse [6]. Furthermore, unreliable decision data at this stage will cause almost irreparable design flaws [7]. Thus, how to consider the truth level of the evaluation information for the concept selection problems under uncertainty become necessary and need further investigation.

Appropriately, extensive studies have been conducted to investigate the conceptual design decision process. Five types of conceptual scheme decision methods are summarized by Ayağ [8], including analytic hierarchy process (AHP), utility method, graphical method, and quality function deployment (QFD), and fuzzy logic approach. Due to the complexity and uncertainty of the design environment, the CS evaluation process has been plagued by fuzzy and subjective evaluation information. To solve this inherent uncertainty [9], classical theories such as rough set theory, fuzzy set theory, and soft set have been proposed to capture uncertainty evaluation information. For fuzzy sets, due to its capability of dealing with vagueness and subjectivity, it is widely used in the early design decision process [10]. Fuzzy analysis does not require quantitative input from DMs, but can obtain initial evaluation information by the predetermined membership degree, and transform it into scheme evaluation data. Ma et al. [11] proposed a conceptual design decision model based on the fuzzy morphological matrix, and developed a fuzzy multi-objective optimization model to select the principle solution combination with maximum customer satisfaction. Jing et al. [12] developed a cooperative game model based on triangular fuzzy numbers to explore the equilibrium relationship between economic and technical objectives and ensure the overall design benefits. Previous theories involving fuzzy information modeling in decision includes IFS [13], 2-tuple linguistic [14], and trapezoidal fuzzy numbers [15]. For rough sets, rough numbers are a form of data representation based on the rough sets and use upper and lower limits to express the interval boundaries [16]. Compared with fuzzy sets, rough set technology can integrate the original evaluation data from various DMs [17] and does not require a predetermined membership function or auxiliary information. Song et al. [18] used the rough number-based AHP model to obtain the interval weight of the objective, and then a rough group technique for order of preference by similarity to ideal solution (TOPSIS) was proposed for scheme ranking. To customize the decision model that satisfies customer preferences, Qi et al. [16] proposed an integrated rough VIKOR model to obtain the rough preference of customers, so as to select the best concept to satisfy customer requirements. Shidpour et al. [19] used rough sets and fuzzy sets to simultaneously evaluate the scheme value with respect to qualitative and quantitative objectives to solve uncertain and fuzzy design data. However, as pointed out by Molodtsov [20], fuzzy sets and rough sets also show the inherent difficulties due to the intensive quantity and type of uncertainties. For this reason, soft set is proposed to estimate the reliable CS without finding precise numerical solution. For example, Feng et al. [21] combined intuitionistic fuzzy numbers and soft set to propose intuitionistic fuzzy soft sets to solve multi-objective decision problems. Hayat et al. [22] constructed a promising framework based on soft sets, Shannon entropy, and TOPSIS to obtain the CSs that meet different design preferences. To date, many studies hybridize the different multi-objective decision-making models (MODM) with the above classical theories in many applications (Jing et al., 2018). Please refer to [23], [24], [25], [26]. The above-mentioned classical theories can effectively quantify or transform uncertain information, such as transforming linguistic terms (e.g., high, medium, low), into crisp numbers through membership functions or interval numbers, but it does not involve the conflict of information belief caused by DMs’ preferences.

Since the inconsistency judgment of scheme from DMs with different knowledge background, it is difficult for DMs to make accurate judgments on the scheme and give an accurate evaluation value [27]. Then, the problem arises while assigning a DM’s subjective judgment to the linguistic words with the uncertain or conflict beliefs (e.g., for CS1, the judgment of DM1 is {(high:0.6), (medium:0.4)}, and DM2 is {medium:1.0}) and its belief are ambiguity in the judgment process. To promote the truth degree of information, Aydoğan et al. [28] combined Z-number and axiom design to evaluate the information reliability, and considered the truth level of DMs to ensure the objectivity of decision results. Yang et al. [29] proposed an iterative stochastic multi-objective acceptability analysis method to improve the accuracy of the decision process. However, to the best of our knowledge, these related studies on the CS decision did not consider the conflict beliefs of the ambiguity semantic variables in the scheme evaluation, which partially motivates this research.

During the CS decision process, the fusion of ambiguity semantic variables with conflict beliefs among DMs need to be considered to improve the reliability of the decision result. In this study, IFS is used to quantify the vague evaluation of DMs on the scheme, and then the weighted average combination rule in DS evidence theory [30] will be used to fuse the multi-semantic variables to eliminate the semantics with low belief. The DS evidence theory was proposed by Shafer [31], which used a trust function to perform uncertain reasoning on different evidences (semantic variables), and updated the belief degree after the evidence is fused. Thus, when the semantic variables of the CS are inconsistent and conflict, the DS evidence theory can effectively deal with this problem [32], [33]. As a powerful decision approach under uncertainty, the VIKOR model based on IFS is constructed to effectively sort the schemes to obtain the comprehensive optimal scheme.

To summarize, the contributions of our work are listed follows: (1) an ambiguity semantic fusion model based on DS evidence theory is constructed to update the conflicting beliefs of the semantic variables and fuse diversifying semantic assessment information; (2) a case study of tree climbing and trimming (TCT) machine is introduced to illustrate the application, sort the schemes through the IFS-VIKOR model, and sensitivity analysis of DM's risk attitudes on the decision results is involved; (3) compared with IFS-TOPSIS and IFS-simple additive weighting (SAW) method, it is verified that the decision process after semantic variable fusion has good reliability, and the decision result has obvious discrimination. The breakdown of this paper is organized as follows: Section 2 reviews the relevant literature for the conceptual design decision and fuzzy model. Section 3 integrates DS evidence theory and the IFS-VIKOR model to realize the fusion of diversify semantic variables and obtain the optimal scheme. Section 4 uses the TCT machine as a case to verify the proposed approach and compare it with the other MODM methods. The conclusions and future work is drawn in Section 5.

Section snippets

Related literatures

In this section, we will summarize the related research of deterministic and uncertain methods in conceptual design decision process, the applications of multi-objective decision approach and intuitionistic fuzzy number.

Methodology

The proposed ambiguity semantic fusion IFS-VIKOR decision model incorporating DS evidence theory and IFS-VIKOR model, which is divided into three parts, as described in Fig. 2. Step A1, named Part Ⅰ, the DMs make ambiguity subjective judgments on the CSs and construct an ambiguity semantic initial evaluation matrix (ASIEM). Steps A1-A4, named Part Ⅱ, the evidence distance function is used to obtain the weight distribution of the DMs under each scheme, and the beliefs (i.e., the basic

Case study

In order to satisfy the market’s growing demand for wood, it is necessary to develop a TCT machine to prune the fast-growing forest efficiently. In the market, the problems such as single application scenario, low pruning efficiency, and poor operability, make it difficult to achieve the goal of flexible tree cutting. For this reason, this paper takes the conceptual design of the TCT machine as a case study, five conceptual schemes are selected for evaluation by setting qualitative evaluation

Conclusions and future work

The aim of this paper is to propose an integrated conceptual design decision approach by considering the DM's subjective judgment as well as the ambiguity and belief of semantic variables. The research framework focuses on the integration of the DS evidence theory and VIKOR model, and using the IFS as semantic variables to quantify DMs' vague evaluation for the schemes. Firstly, considering the ambiguity semantic variables evaluation of DMs under the uncertain environment, the evidence trust

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors, Liting Jing, Shun He, Shaofei Jiang was supported by the National Natural Science Foundation of China [under grant number 52105282], the Zhejiang Provincial Natural Science Foundation of China [under grant number LY20E050020], the Key R & D Program of Zhejiang Province [No.: 2021C01086], and the 111 Project (No.: D16004). And thanks to the support of National International Joint Research Center of Special Purpose Equipment and Advanced Processing Technology of Zhejiang University

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