[Paper Review] Fuzzy Relational Modeling of Cost and Affordability for Advanced Technology Manufacturing Environment

Ladislav Kohout, Eun‐jin Kim+1 more|ArXiv.org|Oct 11, 2003

Rough Sets and Fuzzy Logic30 references3 citations

TL;DR

This paper proposes a fuzzy relational modeling framework using BK-products to analyze cost and affordability in advanced manufacturing, integrating physical measurements and expert knowledge via repertory grids. It enables detection of relational properties like symmetry and transitivity, supporting decision-making under uncertainty with applications in technology ranking and cost driver analysis.

ABSTRACT

Relational representation of knowledge makes it possible to perform all the computations and decision making in a uniform relational way by means of special relational compositions called triangle and square products. In this paper some applications in manufacturing related to cost analysis are described. Testing fuzzy relational structures for various relational properties allows us to discover dependencies, hierarchies, similarities, and equivalences of the attributes characterizing technological processes and manufactured artifacts in their relationship to costs and performance. A brief overview of mathematical aspects of BK-relational products is given in Appendix 1 together with further references in the literature.

Motivation & Objective

• To develop a relational framework for modeling cost and affordability in advanced manufacturing under conditions of incomplete or uncertain data.
• To integrate both physical measurements and expert knowledge (via psychometric tools) into a unified relational structure for decision support.
• To detect relational properties such as reflexivity, symmetry, transitivity, and equivalence to uncover dependencies, hierarchies, and similarities in manufacturing attributes.
• To support early-stage design affordability assessment by enabling interval ranking of competing technologies using preorders.
• To identify unnecessary costs through value analysis using fuzzy relational computations on linguistic expert input.

Proposed method

• Employ fuzzy relational products (BK-products) — specifically triangle and square products — to compose and analyze relations derived from cost and performance data.
• Use repertory grids (RPG) as psychometric tools to elicit linguistic knowledge from engineers when physical data are unavailable.
• Apply fuzzy relational structures to represent and analyze dependencies, similarities, and equivalences among cost drivers and manufacturing processes.
• Utilize interval aggregation to combine cost estimates across different process parameters or materials.
• Construct preorders from relational data to enable interval ranking of competing technologies based on affordability.
• Perform value analysis using fuzzy relational computations to detect and eliminate unnecessary costs in design and manufacturing.

Experimental results

Research questions

• RQ1 How can fuzzy relational modeling be used to represent and analyze cost and affordability in advanced manufacturing when physical data are scarce?
• RQ2 What relational properties (e.g., symmetry, transitivity) can be extracted from expert-elicited linguistic data to reveal structural relationships among cost drivers?
• RQ3 How can BK-products be applied to integrate multiple expert perspectives and resolve inconsistencies in relational models?
• RQ4 In what way can interval aggregation and preorder-based ranking improve technology selection under uncertainty?
• RQ5 How can value analysis using fuzzy relations identify and eliminate unnecessary costs in manufacturing processes?

Key findings

• The use of repertory grids successfully elicited expert knowledge on cost drivers, enabling relational modeling even in the absence of physical measurements.
• Relational properties such as symmetry and transitivity were detected in expert-elicited data, revealing meaningful structural relationships among manufacturing attributes.
• BK-products enabled the integration of multiple expert perspectives and the resolution of conflicting interpretations into a coherent relational model.
• Interval aggregation of costs provided a robust method for combining uncertain or incomplete cost estimates across different process parameters.
• Preorder-based interval ranking allowed for the comparative evaluation of competing technologies, supporting decision-making under uncertainty.
• Value analysis using fuzzy relational computations successfully identified and highlighted unnecessary costs in the LPT cover plate case study.